In the paper it is demonstrated that a valid path to a contradiction in complex number theory exists. In the path use is made of Euler’s identity and simple trigonometry. Each step can be easily verified.

Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan super-coalgebras are given. We give examples of a non-locally finite differential coalgebra, Novikov coalgebra, Lie coalgebra, Jordan super-coalgebra, and right-alternative coalgebra. The dual algebra of each of these examples satisfies very strong additional identities. We also constructed examples of an infinite dimensional simple differential coalgebra, Novikov coalgebra, Lie coalgebra, and Jordan super-coalgebra over a field of characteristic zero.

Applying a procedure similar to that of E.S. Bring, by using a 4^th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2^nd, 4^th and 6^th terms which was transformed into a cubic (solvable) equation. By applying a 6^th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2^nd, 3^rd, 4^th and 5^th terms) form was obtained.

Applying a procedure similar to that of E.S. Bring, by using a 4^th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2^nd, 4^th and 6^th terms which was transformed into a cubic (solvable) equation. By applying a 6^th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2^nd, 3^rd, 4^th and 5^th terms) form was obtained.

Depression is considered by WHO as the main contributor to global disability and it poses dangerous threats to approximately all aspects of human life, in particular public and private health. This mental disorder is usually characterized by considerable changes in feelings, routines, or thoughts. With respect to the fact that early diagnosis of this illness would be of critical importance ineffective treatment, some development has occurred in the purpose of depression detection. EEG signals reflect the working status of the human brain by which are considered the most proper tools for a depression diagnosis. Deep learning algorithms have the capacity of pattern discovery and extracting features from the raw data which is fed into them. Owing to this significant characteristic of deep learning, recently, these methods have intensely utilized in the diverse field of researches, specifically medicine and healthcare. Thereby, in this article, we aimed to review all papers concentrated on using deep learning to detect or predict depressive subjects with the help of EEG signals as input data. Regarding the adopted search method, we finally evaluated 22 articles between 2016 and 2021. This article which is organized according to the systematic literature review (SLR) method, provides complete summaries of all exploited studies and compares the noticeable aspects of them. Moreover, some statistical analysis performs to gain a depth perception of the general ideas of the latest researches in this area. A pattern of a five-step procedure was also established by which almost all reviewed articles fulfilled the goal of depression detection. Finally, open issues and challenges in this way of depression diagnosis or prediction and suggested works as the future directions discussed.

Let $a, b$ and $n > 1$ be three positive integers such that $a$ and $\sum_{j=0}^{n-1} b^j$ are relatively prime. In this paper, we prove that the toric ideal $I$ associated to the submonoid of $\mathbb{N}$ generated by $\{\sum_{j=0}^{n-1} b^j\} \cup \{\sum_{j=0}^{n-1} b^j + a\, \sum_{j=0}^{i-2} b^j \mid i = 2, \ldots, n\}$ is determinantal. Moreover, we prove that for $n > 3$, the ideal $I$ has a unique minimal system of generators if and only if $a < b-1$.

Robin criterion states that the Riemann Hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma } \times n \times \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant. Let $q_{1} = 2, q_{2} = 3, \ldots, q_{m}$ denote the first $m$ consecutive primes, then an integer of the form $\prod_{i=1}^{m} q_{i}^{a_{i}}$ with $a_{1} \geq a_{2} \geq \cdots \geq a_{m} \geq 0$ is called an Hardy-Ramanujan integer. If the Riemann Hypothesis is false, then there are infinitely many Hardy-Ramanujan integers $n > 5040$ such that Robin inequality does not hold and $n < (4.48311)^{m} \times N_{m}$, where $N_{m} = \prod_{i = 1}^{m} q_{i}$ is the primorial number of order $m$.

Let's define $\delta(x) = (\sum_{{q\leq x}}{\frac{1}{q}}-\log \log x-B)$, where $B \approx 0.2614972128$ is the Meissel-Mertens constant. The Robin theorem states that $\delta(x)$ changes sign infinitely often. Let's also define $S(x) = \theta(x) - x$, where $\theta(x)$ is the Chebyshev function. It is known that $S(x)$ changes sign infinitely often. We define the another function $\varpi(x) = \left(\sum_{{q\leq x}}{\frac{1}{q}}-\log \log \theta(x)-B \right)$. We prove that when the inequality $\varpi(x) \leq 0$ is satisfied for some number $x \geq 3$, then the Riemann hypothesis should be false. The Riemann hypothesis is also false when the inequalities $\delta(x) \leq 0$ and $S(x)\geq 0$ are satisfied for some number $x \geq 3$ or when $\frac{3 \times \log x + 5}{8 \times \pi \times \sqrt{x} + 1.2 \times \log x + 2} + \frac{\log x}{\log \theta(x)} \leq 1$ is satisfied for some number $x \geq 13.1$.

In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The purpose of this paper is to introduce the concept of weakly S-primary ideals as a new generalization of weakly primary ideals. An ideal I of R disjoint with S is called a weakly S-primary ideal if there exists s∈S such that whenever 0≠ab∈I for a,b∈R, then sa∈√I or sb∈I. The relationships among S-prime, S-primary, weakly S-primary and S-n-ideals are investigated. For an element r in any general ZPI-ring, the (weakly) S_{r}-primary ideals are charctarized where S={1,r,r²,⋯}. Several properties, characterizations and examples concerning weakly S-primary ideals are presented. The stability of this new concept with respect to various ring-theoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal are studied. Furthermore, weakly S-decomposable ideals and S-weakly Laskerian rings which are generalizations of S-decomposable ideals and S-Laskerian rings are introduced.

In this note we generalize the regularity concept for semigroups in two ways simultaneously: to higher regularity and to higher arity. We show that the one-relational and multi-relational formulations of higher regularity do not coincide, and each element has several inverses. The higher idempotents are introduced, and their commutation leads to unique inverses in the multi-relational formulation, and then further to the higher inverse semigroups. For polyadic semigroups we introduce several types of higher regularity which satisfy the arity invariance principle as introduced: the expressions should not depend of the numerical arity values, which allows us to provide natural and correct binary limits. In the first definition no idempotents can be defined, analogously to the binary semigroups, and therefore the uniqueness of inverses can be governed by shifts. In the second definition called sandwich higher regularity, we are able to introduce the higher polyadic idempotents, but their commutation does not provide uniqueness of inverses, because of the middle terms in the higher polyadic regularity conditions.

Text summarization remains a challenging task in the Natural Language Processing field despite the plethora of applications in enterprises and daily life. One of the common use cases is the summarization of web pages which has the potential to provide an overview of web pages to devices with limited features. In fact, despite the increasing penetration rate of mobile devices in rural areas, the bulk of those devices offer limited features in addition to the fact that these areas are covered with limited connectivity such as the GSM network. Summarizing web pages into SMS becomes, therefore, an important task to provide information to limited devices. This work introduces WATS-SMS, a T5-based French Wikipedia Abstractive Text Summarizer for SMS. It is built through a transfer learning approach. The T5 English pre-trained model is used to generate a French text summarization model by retraining the model on 25,000 Wikipedia pages then compared with different approaches in the literature. The objective is twofold: (1) to check the assumption made in the literature that abstractive models provide better results compared to extractive ones; and (2) to evaluate the performance of our model compared to other existing abstractive models. A score based on ROUGE metrics gave us a value of 52% for articles with length up to 500 characters against 34.2% for transformer-ED and 12.7% for seq-2seq-attention; and a value of 77% for articles with larger size against 37% for transformers-DMCA. Moreover, an architecture including a software SMS-gateway has been developed to allow owners of mobile devices with limited features to send requests and to receive summaries through the GSM network.

Simple measures often couldn’t count a deep complexity. In the case of semantic complexity, conventional readability formulas share a common style, a common sort of achievements and a common borders of limitation: These formulas lack a semantics-aware approach and as a result, a precise measurement of semantic complexity couldn’t be done. In this paper, we introduce DASTEX, a novel semantics-aware complexity measure for semantic complexity of text. By DASTEX, a new layer of complexity analysis are opened for NLP, cognitive and computational tasks. This measure benefits from an intuitionistic underlying formal model which consider semantic as a lattice of intuitions. This yields to a well-defined definition for semantic of a text and its complexity. DASTEX is a practical analysis method upon this formal model. So a complete suite of idea, model and method are prepared to result in a simple but yet deep measure for semantic complexity of text. The evaluation of the proposed approach is done by 4 Experiments. The results show DASTEX is capable of measuring the semantic complexity of text in 6 application-tasks.

The Ramanujan primes are the least positive integers Rn having the property that if m ≥ Rn, then π_m − π_(m/2) ≥ n. This document develops several bounds related to the Ramanujan primes, sharpening the currently known results. The theory presented is by no means exhaustive, however it provides insights for future research work. Alternatively, we may say that it is a road map which may be followed to make further discoveries.

Elliptic scator algebra is possible in 1+n dimensions, n∈N. It is isomorphic to complex algebra in 1+1 dimensions, when the real part and any one hypercomplex component are considered. It is endowed with two representations: an additive one, where the scator components are represented as a sum; and a polar representation, where the scator components are represented as products of exponentials. Within the scator framework, De Moivre’s formula is generalized to 1+n dimensions in the so called victoria equation. This novel formula is then used to obtain compact expressions for the integer powers of scator elements. A scator in S1+n can be factored into a product of n scators that are geometrically represented as its projections onto n two dimensional planes. A geometric interpretation of scator multiplication in terms of rotations with respect to the scalar axis is expounded. The powers of scators, when the ratio of their director components is a rational number, lie on closed curves. For 1+2 dimensional scators, twisted curves in a three dimensional space are obtained. Collecting previous results, it is possible to evaluate the exponential of a scator element in 1+2 dimensions.

Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that P\bigcap S=\emptyset In this article, we introduce several results concerning graded S-prime ideals. Then we introduce the concept of graded weakly S-prime ideals which is a generalization of graded weakly prime ideals. We say that P is a graded weakly S-prime ideal of R if there exists s\in S such that for all x, y\in h(R), if 0\neq xy\in P, then sx\in P or sy\in P. We show that graded weakly S-prime ideals have many acquaintance properties to these of graded weakly prime ideals.

The Mobius function is commonly used to define Euler's totient function and the Mangoldt function. Similarly, the summatory Mobius function (the Mertens function) can be used to define the summatory totient function and the summatory Mangoldt function (the second Chebyshev function).

While Europe was beginning to deal with the resurgence of COVID-19 due to the Delta variant, the European football championship took place, June 11 - July 11, 2021. We studied the inversion in the decrease/increase rate of new SARS-COV-2 infections in the countries of the tournament, investigating the hypothesis of an association. Using a Bayesian piecewise regression with a Poisson Generalized Linear Model, we looked for a changepoint in the timeseries of the new SARS-COV-2 cases of each country, expecting it to appear not later than two to three weeks after the date of their first match. The two slopes, before and after the changepoint, were used to discuss the reversal from a decreasing to an increasing rate of the infections. For 17 out of 22 countries (77%) the changepoint came on average 14.97 days after their first match [95% CI 12.29 to 17.47]. For all those 17 countries, the changepoint coincides with an inversion from a decreasing to an increasing rate of the infections. Before the changepoint, the new cases were decreasing, halving on average every 18.07 days [95% CI 11.81 to 29.42]. After the changepoint, the cases begin to increase, doubling every 29.10 days [95% CI 14.12 to 49.78]. This inversion in the SARS-COV-2 case rate, happened during the tournament, provides evidence in favor of a relationship

In this paper any superalgebra is generalized to a new form, namely ultra algebra. We study some algebraic structure results for ultra algebras and we have defined some maps on ultra algebras to know ultra derivation and Jordan ultra derivation. Moreover on certain assumptions we have proved that Jordan ultra derivation is an ultra derivation.

In this paper defines the consecutive sum of the digits of a natural number, so far as it becomes less than ten, as an arithmetic function called and then introduces some important properties of this function by proving a few theorems in a way that they can be used as a powerful tool in many cases. As an instance, by introducing a test called test, it has been shown that we are able to examine many algebraic equalities in the form of in which and are arithmetic functions and to easily study many of the algebraic and diophantine equations in the domain of whole numbers. The importance of test for algebraic equalities can be considered equivalent to dimensional equation in physics relations and formulas. Additionally, this arithmetic function can also be useful in factorizing the composite odd numbers.

This article describes an algorithm for estimation the variance of Gaussian noise. The data is smoothed using the Savitsky-Golay polynomial filter. Absolute differences between original and smoothed data are sorted in ascending order. The initial part of this sequence is selected for analysis. The result of calculation mean value of differences can be used to estimate the variance of the noise. By selecting points for analysis, the impact of cosmic ray noise and other artifacts can be reduced. The use of the proposed method for artificial and real spectra shows the ability to effectively estimate the noise variance. The algorithm contains no user-defined parameters.

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

Clustering, or otherwise known as cluster analysis, is a learning problem that takes place without any human supervision. This technique has often been utilized, much efficiently, in data analysis, and serves for observing and identifying interesting, useful, or desired patterns in the said data. The clustering technique functions by performing a structured division of the data involved, in similar objects based on the characteristics that it identifies. This process results in the formation of groups, and each group that is formed, is called a cluster. A single said cluster consists of objects from the data, that have similarities among other objects found in the same cluster, and resemble differences when compared to objects identified from the data that now exist in other clusters. The process of clustering is very significant in various aspects of data analysis, as it determines and presents the intrinsic grouping of objects present in the data, based on their attributes, in a batch of unlabeled raw data. A textbook or otherwise said, good criteria, does not exist in this method of cluster analysis. That is because this process is so different and so customizable for every user, that needs it in his/her various and different needs. There is no outright best clustering algorithm, as it massively depends on the user’s scenario and needs. This paper is intended to compare and study two different clustering algorithms. The algorithms under investigation are k-mean and mean shift. These algorithms are compared according to the following factors: time complexity, training, prediction performance and accuracy of the clustering algorithms.

This paper presents a complete derivation and design of a physics-informed neural network (PINN) applicable to solve initial- and boundary value problems described by linear ordinary differential equations. The objective not to develop a numerical solution procedure which is more accurate and efficient than standard finite element or finite difference based methods, but to give a fully explicit mathematical description of a PINN and to present an application example in the context of hydrodynamic lubrication. It is, however, worth noticing that the PINN developed herein, contrary to FEM and FDM, is a meshless method and that training does not require big data which is typical in machine learning.

This mathematical observation deals with the development of a completely new expression [(S/4D) × √ {(S₁²-D²)(D²-D₁²)}] to calculate the area of a trapezoid system. Because of the difficulties of the previous methods to find out the area of a trapezoid (AOT), the proposed formula has thus indicated the best way to determine the AOT more precisely and easily beyond limitation, successfully. It is obvious that the derived formula is helpful to determine AOT more easily and precisely rather than existing method. And this developed theorem for the trapezoid system is observed for the first time.

Optical motion capture is a mature contemporary technique for the acquisition of motion data, alas it is non-error-free. Due to technical limitations and occlusions of markers, gaps might occur in such recordings. The article reviews various neural network architectures applied for gap filling problem in motion capture sequences within FBM framework providing the representation for body kinematic structure. The results are compared with interpolation and matrix completion methods. We found out, that for longer sequences simple linear feedforward neural networks can outperform the other, sophisticated architectures. We were also able to identify, that acceleration and monotonicity of input sequence are the parameters that have a notable impact on the obtained results.

This paper presents the evaluation of a fungal disease forecast model in vineyards for qualitative parameter analysis using the data from off the shelf sensors, i.e. temperature and air relative humidity, rain precipitation, and leaf wetness. The rules for the fungal disease models are digitalized as a decision support tool that serve as an indicator to farmers for the need of spraying of the chemical substances to ensure the best growing condition and suppress the level of parasites. The temperature and humidity contexts are used interchangeably in practice to detect the risk of the disease occurrence. By taking into account a number of influences on these parameters collected from the shelf sensors, new topics for research in the multidimensional field of precision agriculture emerge. In this study, the impact of the humidity is evaluated by assessing how different humidity parameters correlate with the accuracy of the Botrytis cinerea fungi forecast. Each humidity parameter has it’s own threshold that triggers the second step of the disease modeling - risk index based on the temperature. The research showed that for humidity a low-cost relative humidity sensor can detect in average 14.61% risk values, a leaf wetness sensor an additional 3.99% risk cases, and finally, a precipitation sensor will detect only an additional 0.59% risk cases.

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

In this paper, the notion of θ∗-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan [Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

Haemodynamic indices are widely used in clinical practice for deciding on a particular type of treatment. Low quality of the CT data and tachycardia complicate interpretation of the measured or simulated values. In this work, we present a novel approach for evaluating resistances in terminal coronary arteries. Using 14 measurements from 10 patients, we show that this algorithm retains the accuracy of 1D haemodynamic simulations in less detailed (truncated) geometric models of coronary networks. We also apply the variable systole fraction model to study the effect of elevated heart rate on the values of FFR, CFR and iFR. We conclude that tachycardia may produce both overestimation or underestimation of coronary stenosis significance.

In the early 1980s it was well established that Leray solutions of the unforced Navier-Stokes equations in Rn decay in energy norm for large time. With the works of T. Miyakawa, M. Schonbek and others it is now known that the energy decay rate cannot in general be any faster than t^-(n+2)/4 and is typically much slower. In contrast, we show in this note that, given an arbitrary Leray solution u(.,t), the difference of any two Stokes approximations to the Navier-Stokes flow u(.,t) will always decay at least as fast as t^-(n+2)/4, no matter how slow the decay of || u(.,t) ||_L2 might happen to be.

Neural decoding from spiking activity is an essential tool for understanding the information encoded in population neurons, especially in applications like brain-computer interface (BCI). Various quantitative methods have been proposed and have shown superiorities under different scenarios respectively. From the machine learning perspective, the decoding task is to map the high-dimensional spatial &amp; temporal neuronal activity to the low-dimensional physical quantities (e.g., velocity, position). Because of the complex interactions and the abundant dynamics among neural circuits, good decoding algorithms usually have the capability of capturing flexible spatiotemporal structures embedded in the input feature space. Recently, the Transformer-based models are widely used in processing natural languages and images due to its superior performances in handling long-range and global dependencies. Hence, in this work we examine the potential applications of Transformers in neural decoding and introduce two Transformer-based models. Besides adapting the Transformer to neuronal data, we also propose a data augmentation method for overcoming the data shortage issue. We test our models on three experimental datasets and their performances are comparable to the previous state-of-the-art (SOTA) RNN-based methods. In addition, Transformer-based models show increased decoding performances when the input sequences are longer, while LSTM-based models deteriorate quickly. Our research suggests that Transformer-based models are important additions to the existing neural decoding solutions, especially for large datasets with long temporal dependencies.

Background: There is little clarity in the application of content related to improper integrals in university students, due to the absence of meaning, which prevents them from making a connection with everyday problem situations. Methods: we designed a mathematical modelling proposal where a specific situation involving the instrumentation, use and application of this type of integrals is experimented and solved with a population of engineering students, who learn to use them. Results: The importance of using mathematical modelling as a didactic-dynamic resource is highlighted because it helps students to reach an understanding of real situations involving improper integrals in different contexts. Conclusions: Despite the numerous errors detected in the students, this strategy made it possible to demonstrate the development of advanced mathematical thinking skills in young people.

The colossal depths of the deep neural network sometimes suffer from ineffective backpropagation of the gradients through all its depths. Whereas, The strong performance of shallower multilayer neural structures prove their ability to increase the gradient signals in the early stages of training which easily gets backpropagated for global loss corrections. Shallow neural structures are always a good starting point for encouraging the sturdy feature characteristics of the input. In this research, a shallow, deep neural structure called PrimeNet is proposed. PrimeNet is aimed to dynamically identify and encourage the quality visual indicators from the input to be used by the subsequent deep network layers and increase the gradient signals in the lower stages of the training pipeline. In addition to this, the layerwise training is performed with the help of locally generated errors which means the gradient is not backpropagated to previous layers, and the hidden layer weights are updated during the forward pass, making this structure a backpropagation free variant. PrimeNet has obtained state-of-the-art results on various image datasets, attaining the dual objective of (1) compact dynamic deep neural structure, which (2) eliminates the problem of backwards-locking. The PrimeNet unit is proposed as an alternative to traditional convolution and dense blocks for faster and memory-efficient training, outperforming previously reported results aimed at adaptive methods for parallel and multilayer deep neural systems.

Background: Zebrafish (Danio rerio) is a model organism emerged for the study of human cancer. Compared with the murine model, the zebrafish model has several properties ideal for personalized therapies. The transparency of the zebrafish embryos and the development of the pigment-deficient “casper” zebrafish line give the capacity to directly observe cancer formation and progression in the living animal. Automatic quantification of cellular proliferation in vivo is critical to the development of personalized medicine. Methods: A new methodology was defined to automatically quantify the cancer cellular evolution. ZFTool was developed to establish a base threshold that eliminates the embryo auto-fluorescence and automatically measures the area and intensity of GFP (green-fluorescent protein) marked cells and define a proliferation index. Results: Proliferation index automatically computed on different targets demonstrates the efficiency of ZFTool to provide a good automatic quantification of cancer cell evolution and dissemination. Conclusion: Our results demonstrate that ZFTool is a reliable tool for the automatic quantification of the proliferation index, being a measure of cancer mass evolution in zebrafish eliminating the influence of its autofluorescence.

Semantic segmentation is a very popular topic in modern computer vision and it has applications to many fields. Researchers proposed a variety of architectures over time, but the most common ones exploit an encoder-decoder structure that aims to capture the semantics of the image and it low level features. The encoder uses convolutional layers, in general with a stride larger than one, to extract the features, while the decoder recreates the image by upsampling an using skip connections with the first layers. In this work, we use DeepLab as architecture to test the effectiveness of creating an ensemble of networks by randomly changing the activation functions inside the network multiple times. We also use different backbone networks in our DeepLab to validate our findings. We manage to reach a dice coefficient of 0.888, and a mean Intersection over Union (mIoU) of 0.825, in the competitive Kvasir-SEG dataset. Results in skin detection also confirm the performance of the proposed ensemble, which is ranked first with respect to other state-of-the-art approaches (including HardNet) in a large set of testing datasets. The developed code will be available at https://github.com/LorisNanni.

Sleep deficiency impacts the quality of life and may have serious health consequences in the long run. Questionnaire-based subjective assessment of sleep deficiency has many limitations. On the other hand, objective assessment of sleep deficiency is challenging. In this study, we propose a polysomnography-based mathematical model for computing baseline sleep deficiency severity score and then investigated the estimation of sleep deficiency severity using features available only from wearable sensor data including heart rate variability and single-channel electroen-cephalography for a dataset of 500 subjects. We used Monte-Carlo Feature Selection (MCFS) and inter-dependency discovery for selecting the best features and removing multi-collinearity. For developing the Regression model we investigated both the frequentist and the Bayesian ap-proaches. An Artificial Neural Network achieved the best performance of RMSE = 5.47 and an R-squared value of 0.67 for sleep deficiency severity estimation. The developed method is com-parable to conventional methods of Functional Outcome of Sleep Questionnaire and Epworth Sleepiness Scale for assessing the impact of sleep apnea on sleep deficiency. Moreover, the results pave the way for reliable and interpretable sleep deficiency severity estimation using a wearable device in Smart Health.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

Anonymous communications networks were born to protect the privacy of our communications, preventing censorship and traffic analysis. The most famous anonymous communication network is Tor. This anonymous communication network provides some interesting features, among them, we can mention user’s IP location or Tor Hidden Services (THS) as a mechanism to conceal the location of servers, mainly, web servers. THS is an important research field in Tor. However, there is a lack of reviews that sump up main findings and research challenges. In this article we present a systematic literature review that aims to offer a comprehensive view on the research made on Tor Hidden services presenting the state of the art and the different research challenges to be addressed. This review has been developed from a selection of 57 articles and present main findings and advances regarding Tor Hidden Services, limitations found, and future issues to be investigated.

The spread of the Coronavirus pandemic has been accompanied by an infodemic. The false information that is embedded in the infodemic affects people’s ability to have access to safety information and follow proper procedures to mitigate the risks. This research aims to target the falsehood part of the infodemic, which prominently proliferates in news articles and false medical publications. Here, we present NeoNet, a novel supervised machine learning text mining algorithm that analyzes the content of a document (news article, a medical publication) and assigns a label to it. The algorithm is trained by TFIDF bigram features which contribute a network training model. The algorithm is tested on two different real-world datasets from the CBC news network and Covid-19 publications. In five different fold comparisons, the algorithm predicted a label of an article with a precision of 97-99 %. When compared with prominent algorithms such as Neural Networks, SVM, and Random Forests NeoNet surpassed them. The analysis highlighted the promise of NeoNet in detecting disputed online contents which may contribute negatively to the COVID-19 pandemic.

Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of nonlocality and spatial heterogeneity of complex materials and systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such operators to complex-order counterparts. In this work, we introduce new definitions for the complex-order fractional Laplacian, fully consistent with the theory of averaging of smooth functions over fractal sets, and present tailored spectral methods for their numerical treatment. The proposed complex-order operators exhibit a dual particle-wave behaviour, with solutions manifesting wave-like features depending on the magnitude of the imaginary part of the fractional order. Reaction-diffusion systems driven by the complex-order fractional Laplacian exhibit unique spatio-temporal dynamics, such as equilibrium of diffusion in random materials by interference of scattered waves, conduction block and highly fractionated propagation, or the generation of completely novel Turing patterns. Taken together, our results support that the proposed complex-order operators hold unparalleled capabilities to advance the description of multiscale transport phenomena in physical and biological processes highly influenced by the heterogeneity of complex media.

The Unmanned Aerial Vehicles (UAVs), used in civilian applications such as emergency medical deliveries, precision agriculture, wireless communication provisioning, etc., face the challenge of limited flight time due to their reliance on the on-board battery. Therefore, developing efficient mechanisms for in-situ power transfer to recharge UAV batteries hold potential in extending their mission time. In this paper, we study the use of far-field wireless power transfer (WPT) technique from specialized, transmitter UAVs (tUAVs) carrying Multiple Input Multiple Output (MIMO) antennas for transferring wireless power to receiver UAVs (rUAVs) in a mission. The tUAVs can fly and adjust their distance to the rUAVs to maximize energy transfer. The use of MIMO antennas further boost the energy reception by narrowing the energy beam toward the rUAVs. The complexity of their dynamic operating environment increases with the growing number of tUAVs, and rUAVs with varying levels of energy consumption and residual power. We propose an intelligent trajectory selection algorithm for the tUAVs based on a deep reinforcement learning model called Proximal Policy Optimization (PPO) to optimize the energy transfer gain. Simulation results demonstrate that with the use of PPO, the system achieves a tenfold flight time extension compared to no wireless recharging. Further, PPO outperforms the benchmark movement strategies of ’Traveling Salesman Problem’ and ’Low Battery First’ when used by the tUAVs.

In this paper, the problem of observer-based adaptive sliding mode control is discussed for nonlinear systems with sensor and actuator faults. The time-varying actuator degradation factor and external disturbance are considered in the system simultaneously. In this study, the original system is described as a new normal system by combining the state vector, sensor faults and external disturbance into a new state vector. For the augmented system, a new sliding mode observer is designed, where a discontinuous term is introduced such that the effects of sensor and actuator faults and external disturbance will be eliminated. In addition, based on a tricky design of the observer, the time-varying actuator degradation factor term is developed in the error system. On the basis of the state estimation, an integral-type adaptive fuzzy sliding mode controller is constructed to ensure the stability of the closed-loop system. Finally, the effectiveness of the proposed control methods can be illustrated with a numerical example.

We study factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let $D=\prod_{i\in I}D_i$ be a product of paratopological groups, $S$ be a dense subgroup of $D$, and $\chi$ a continuous character of $S$. Then one can find a finite set $E\subset I$ and continuous characters $\chi_i$ of $D_i$, for $i\in E$, such that $\chi=\big(\prod_{i\in E} \chi_i\circ p_i\big)\hs1\res\hs1 S$, where $p_i\colon D\to D_i$ is the projection.

Alcoholism is attributed to regular or excessive drinking of alcohol and leads to the disturbance of the neuronal system in the human brain. This results in certain malfunctioning of neurons that can be detected by an electroencephalogram (EEG) using several electrodes on a human skull at appropriate positions. It is of great interest to be able to classify an EEG activity as that of a normal person or an alcoholic person using data from the minimum possible electrodes (or channels). Due to the complex nature of EEG signals, accurate classification of alcoholism using only a small data is a challenging task. Artificial neural networks, specifically convolutional neural networks (CNN), provide efficient and accurate results in various pattern-based classification problems. In this work, we apply CNN on raw EEG data, and demonstrate how we achieved 98% average accuracy by optimizing a baseline CNN model and outperforming its results in a range of performance evaluation metrics on the UCI-KDD EGG dataset. This article explains the step-wise improvement of the baseline model using the dropout, batch normalization, and kernel regularization techniques, and provides a comparison of the two models that can be beneficial for aspiring practitioners who aim to develop similar classification models in CNN. A performance comparison is also provided with other approaches using the same dataset.

Continuous and emerging advances in Information and Communication Technology (ICT) have enabled IoT-to-Cloud applications to be induced by data pipelines coupled with Edge Intelligence-based architectures. Advanced vehicular networks greatly benefit from these architectures due to the implicit functionalities that are focused on realizing the Internet-of-Vehicle (IoV) vision. However, IoV is susceptible to attacks, where adversaries can easily exploit existing vulnerabilities. Several attacks may succeed due to inadequate or weaker authentication techniques. Hence, there is a timely need for hardening the authentication process through cutting-edge access control mechanisms. This paper proposes a Blockchain-based Multi-Factor authentication model that uses an embedded Digital Signature (MFBC_eDS) for vehicular clouds and Cloud-enabled IoV. Our proposed MFBC_eDS model consists of a scheme that integrates the Security Assertion Mark-up Language (SAML) to the Single Sign-On (SSO) capabilities for a connected Edge-to Cloud ecosystem. MFBC_eDS draws an essential comparison with the baseline authentication scheme suggested by Karla and Sood. Based on the foundations of Karla and Sood’s scheme, an embedded Probabilistic Polynomial-Time Algorithm (ePPTA) and an additional Hash function for the Pi generated during Karla and Sood’s authentication are proposed and discussed. The preliminary analysis of the proposition shows that the approach is more suitable to counter major adversarial attacks in an IoV-centered environment based on Dolev-Yao adversarial model while satisfying aspects of the CIA triad.

The aim of this article is to introduce the new notion on a given graph. The notions of valued set, valued function, valued graph and valued quotient are introduced. The attributes of these new notions are studied. Valued set is about the set of vertices which have the maximum number of neighbors. The kind of partition of the vertex set to the vertices of the valued set is introduced and its attributes are studied. The behaviors of classes of graphs under these new notions are studied and the algebraic operations on these sets in the different situations get new result to understand the classes of graphs, these notions and the general graphs better and more.

In this note we study the binomial model applied to European, American and Bermudan type of derivatives. Our aim is to give the necessary and sufficient conditions under which we can define a fair value via replicating portfolios for any derivative using simple mathematical arguments and without using no arbitrage techniques. Giving suitable definitions we are able to define rigorously the fair value of any derivative without using concepts from probability theory or stochastic analysis therefore is suitable for students or young researchers. It will be clear in our analysis that if $e^{r \delta} \notin [d,u]$ then we can not define a fair value by any means for any derivative while if $d \leq e^{r \delta} \leq u$ we can. Therefore the definition of the fair value of a derivative is not so closely related with the absence of arbitrage. In the usual probabilistic point of view we assume that $d < e^{r \delta} < u$ in order to define the fair value but it is not clear what we can (or we can not) do in the cases where $e^{r \delta} \leq d$ or $e^{r \delta} \geq u$.

Visual Question Generation (VQG) from images is a rising research topic in both fields of natural language processing and computer vision. Although there are some recent efforts towards generating questions from images in the open domain, the VQG task in the medical domain has not been well-studied so far due to the lack of labeled data. In this paper, we introduce a goal-driven VQG approach for radiology images called VQGRaD that generates questions targeting specific image aspects such as modality and abnormality. In particular, we study generating natural language questions based on the visual content of the image and on additional information such as the image caption and the question category. VQGRaD encodes the dense vectors of different inputs into two latent spaces, which allows generating, for a specific question category, relevant questions about the images, with or without their captions. We also explore the impact of domain knowledge incorporation (e.g., medical entities and semantic types) and data augmentation techniques on visual question generation in the medical domain. Experiments performed on the VQA-RAD dataset of clinical visual questions showed that VQGRaD achieves 61.86% BLEU score and outperforms strong baselines. We also performed a blinded human evaluation of the grammaticality, fluency, and relevance of the generated questions. The human evaluation demonstrated the better quality of VQGRaD outputs and showed that incorporating medical entities improves the quality of the generated questions. Using the test data and evaluation process of the ImageCLEF 2020 VQA-Med challenge, we found that relying on the proposed data augmentation technique to generate new training samples by applying different kinds of transformations, can mitigate the lack of data, avoid overfitting, and bring a substantial improvement in medical VQG.

The purpose of this paper is to find the time optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is construct a fundamental solution for corresponding linear systems and establish variations of constant formula of solutions for given stochastic equations. The existence result of time optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

Metaheuristic algorithms have been frequently using to tackle optimization problems, however such algorithms in the analysis of health-related data is not commonly used as developing metaheuristic algorithms that work well on health-related data is a difficult task due to complexity of the health data in particular genomics and epigenetics data. One of the important tasks in genomics is to predict genomic elements that are incorporating together to regulate a disease-related genes. Predicting such elements are important as they can be used to develop a personalized cure. In this study, we present for the first time, a multi-object simulated annealing algorithm to identify enhancer-promoter like interactions from Hi-C (chromosome conformation capture) data. These regulatory elements can potentially play vital roles as promoters and/or enhancers in appearance and exacerbation of the regulation of gene.s To evaluate the efficiency of the proposed method, we applied our proposed method and traditional methods on the Hi-C data from mice and compared together. Our results show that the interacting elements identified by our new method are more likely to be functional. The source code of the method is publicly available.

Deep Learning is developing interesting tools which are of great interest for inverse imaging applications. In this work, we consider a medical imaging reconstruction task from subsampled measurements, which is an active research field where Convolutional Neural Networks have already revealed their great potential. However, the commonly used architectures are very deep and, hence, prone to overfitting and unfeasible for clinical usages. Inspired by the ideas of the green-AI literature, we here propose a shallow neural network to perform an efficient Learned Post-Processing on images roughly reconstructed by the filtered backprojection algorithm. The results obtained on images from the training set and on unseen images, using both the non-expensive network and the widely used very deep ResUNet show that the proposed network computes images of comparable or higher quality in about one fourth of time.

Port state control inspections implemented under the Paris Memorandum of Understanding (MoU) have become known as one of the best instruments for maritime administrations in European Union (EU) Member States to ensure that the ships docked in their ports comply with all maritime safety requirements. This paper focuses on the analysis of all inspections made between 2013 and 2018 in the top ten EU ports incorporated in the Paris MoU (17,880 inspections). The methodology consists of a multivariate statistical information system (STATIS) analysis using the inspected ship’s characteristics as explanatory variables. The variables used describe both the inspected ships (classification society, flag, age and gross tonnage) and the inspection (type of inspection and number of deficiencies), yielding a dataset with more than 600,000 elements in the data matrix. The most important results are that the classifications obtained match the performance lists published annually by the Paris MoU and the classification societies. Therefore, the approach is a potentially valid classification method and would then be useful to maritime authorities as an additional indicator of a ship’s risk profile to decide inspection priorities and as a tool to measure the evolution in the risk profile of flag over time.

A new kind of quantum gates, higher braiding gates, as matrix solutions of the polyadic braid equations (different from the generalized Yang-Baxter equations) is introduced. Such gates lead to another special multiqubit entanglement which can speed up key distribution and accelerate algorithms. Ternary braiding gates acting on three qubit states are studied in details. We also consider exotic noninvertible gates which can be related with qubit loss, and define partial identities (which can be orthogonal), partial unitarity, and partially bounded operators (which can be noninvertible). We define two classes of matrices, star and circle ones, such that the magic matrices (connected with the Cartan decomposition) belong to the star class. The general algebraic structure of the introduced classes is described in terms of semigroups, ternary and $5$-ary groups and modules. The higher braid group and its representation by the higher braid operators are given. Finally, we show, that for each multiqubit state there exist higher braiding gates which are not entangling, and the concrete conditions to be non-entangling are given for the obtained binary and ternary gates.

Decentralized Finance (DeFi) takes the promise of blockchain a step further and aims to transform traditional financial products into trustless and transparent protocols that run without involving intermediaries. Similar to how 2017 was the year of ICOs, 2020 was the year of DeFI with more than $15 billion of total investments. The decentralized platforms utilize oracles to retrieve asset data from the external world, but their choice and management criteria are often unknown to the end-users. If oracles are poorly selected or managed, the funds of a rising number of investors are inevitably in danger. The issue known as “the oracle problem,” which makes real-world applications controversial and debated due to the loss of decentralization, had recently drawn attention to DeFi given the crescent number of related hacks that caused the loss of millions of dollars held in DeFi projects. With a multivocal approach, this paper aims to shed light on the pattern that identifies the oracle problem in DeFi and outline the most promising ways to overcome the related weaknesses. This research supports the view that the oracle problem in decentralized finance bears specific characteristics which require standardization and appropriate economic incentives to be addressed.

In this research paper, we implement the theory of the primorial function, to develop the Supremum and Infimum bounds for the sum of (log(p))². There are, however, considerable computational difficulties related to these bounds. Therefore, from a pragmatic point of view, a set of Upper and Lower bounds had been developed to bypass this issue. Despite the increased estimation error, the Upper and Lower bounds are still considered sufficiently accurate, while facilitating an easy and fast computation of the estimate of the sum.

In this paper we establish a topological framework of τ-structures to quantify the evolutionary transitions between two RNA sequence-structure pairs. τ-structures developed here consist of a pair of RNA secondary structures together with a non-crossing partial matching between the two backbones. The loop complex of a τ-structure captures the intersections of loops in both secondary structures. We compute the loop homology of τ-structures. We show that only the zeroth, first and second homology groups are free. In particular, we prove that the rank of the second homology group equals the number γ of certain arc-components in a τ-structure, and the rank of the first homology is given by γ−χ+1, where χ is the Euler characteristic of the loop complex.

Virtual Reality(VR) is an emerging technology with a broad range of application in training, entertainment, and business. To maximize the potentials of virtual reality as a medium, the unwelcome feeling of simulation sickness needs to be minimized. Even with advancements in VR, the usability concerns are barriers for a wide-spread acceptance. Several factors (hardware, software, human) play a part towards a pleasant VR experience. The reviewed scientific articles are mostly part of documents indexed in digital libraries. In this paper, we review the potential factors which cause simulation sickness and minimize the usability of virtual reality systems. We review the best practices from a developer’s perspective and some of the safety measures a user must follow while using the VR systems from existing research. Even after following some of the guidelines and best practices VR environments do not guarantee a pleasant experience for users. Limited research in VR environments towards requirement specification, design, and development for maximum usability and adaptability was the main motive for this work.

This paper presents a novel architecture for detecting mathematical formulas in document images, which is an important step for reliable information extraction in several domains. Recently, Cascade Mask R-CNN networks have been introduced to solve object detection in computer vision. In this paper, we suggest a couple of modifications to the existing Cascade Mask R-CNN architecture: First, the proposed network uses deformable convolutions instead of conventional convolutions in the backbone network to spot areas of interest better. Second, it uses a dual backbone of ResNeXt-101, having composite connections at the parallel stages. Finally, our proposed network is end-to-end trainable. We evaluate the proposed approach on the ICDAR-2017 POD and Marmot datasets. The proposed approach demonstrates state-of-the-art performance on ICDAR-2017 POD at a higher IoU threshold with an f1-score of 0.917, reducing the relative error by 7.8%. Moreover, we accomplished correct detection accuracy of 81.3% on embedded formulas on the Marmot dataset, which results in a relative error reduction of 30%.

Ransomware is continually evolving. The most recent tactic is to combine crypto-ransomware with data exfiltration, mandate fraud, and other such schemes to steal from victims and attempt to blackmail them. This paper examines the new trend, its underlying motives, and proposes practical recommendations to help organizations defend against this menace

Our aim is to implement and test some less known numerical methods that might be used to solve an advection equation. The description is restricted to information necessary to implement and test the presented methods and it is given only for one-dimensional case.

Human Activity Recognition (HAR) is a process to automatically detect human activities based on stream data generated from various sensors, including inertial sensors, physiological sensors, location sensors, cameras, time, and many others. In this paper, we propose a robust SimCLR model for human activity recognition with a temperature variance study. In this work, SimCLR, a contrasting learning technique is optimized via regulating the temperature for visual representations, is incorporated for improving the HAR performance in healthcare.

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

Today’s purchasing companies demand an advanced buyer equal of enactment from their supplier while the two parties maintain a respectful connection. Although the supplier selection (SC) product life cycle cost (SCPLCC) is an important consideration among corporations, SCPLCC problem has become associated with deciding how one supplier should be selected from possible alternatives. In this study, we applied two types of goal programming, multiobjective linear programming and revised multichoice goal programming to develop a PLCC-based concept to solve the SCPLCC problem and construct a decision-making tool for application to a case of supply chain management in a Taiwanese light-emitting diode company in the high-tech industry. Our study main contribution Company managers can easily use the two approaches of the SCPLCC model with different parameters to solve SCPLCC model problems. Finally, we comparing five models found RMCGP with weighted linear goal programming had an adequate effect for application to the PLCC concept for high-technology comapny; this cloud make company decision–makers focus on low PLCC and select better supplier.

We define degree of dependence of two events A and B in a probability space by using Boltzmann-Shannon entropy function of an appropriate probability distribution produced by these events and depending on one parameter (the probability of intersection of A and B) varying within a closed interval I. The entropy function attains its global maximum when the events A and B are independent. The important particular case of discrete uniform probability space motivates this definition in the following way. The entropy function has a minimum at the left endpoint of I exactly when one of the events and the complement of the other are connected with the relation of inclusion (maximal negative dependence). It has a minimum at the right endpoint of I exactly when one of these events is included in the other (maximal positive dependence). Moreover, the deviation of the entropy from its maximum is equal to average information that carries one of the binary trials defined by A and B with respect to the other. As a consequence, the degree of dependence of A and B can be expressed in terms of information theory and is invariant with respect to the choice of unit of information. Using this formalism, we describe completely the screening tests and their reliability, measure efficacy of a vaccination, the impact of some events from the financial markets to other events, etc. A link is available for downloading an Excel program which calculates the degree of dependence of two events in a sample space with equally likely outcomes.

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

Legacy IPv4 networks are strenuous to manage and operate. Network operators are in need to minimize the capital and operational expenditure of running network infrastructure. The implementation of Software-defined networking (SDN) addresses those issues by minimizing the expenditures in the long run. Legacy networks need to integrate with the SDN networks for the smooth migration towards the fully functional SDN environment. In this paper, we compare the network performance of the legacy network with the SDN network for IP routing in order to determine the feasibility of the SDN deployment in the Internet Service provider (ISP) network. The simulation of the network is performed in the Mininet test-bed and the network traffic is generated using distributed Internet traffic generator. Open network operating system is used as a controller for the SDN network in which SDN-IP application is used for IP routing. Round trip time, bandwidth, and packet transmission rate from both SDN and legacy networks are first collected and then the comparison is done. We found that SDN-IP performs better in terms of bandwidth and latency as compared to legacy routing. The experimental analysis of interoperability between SDN and legacy networks shows that SDN implementation in production level carrier-grade ISP network is viable and progressive.

The use of Information Communication Technologies (ICT) in education brings up new possibilities of promoting the learning and health experiences. In this sense, education contexts of 21st century must consider these two areas of knowledge, especially their integration. This article presents learning practices developed with mobile devices and games, in order to improve learning and well-being in children and adolescents undergoing cancer treatment in non-formal educational setting. The methodology is based on qualitative case studies with content-based data analysis, involving informal interviews and observation methods. The study considers data from 5 patients who participated in the research between 2015 and 2019. The results demonstrate a positive influence of the practices with mobile technologies and games in terms of learning and in the well-being feeling of patients during the treatment.

The Covid-19 pandemic has resulted in the closure of schools at every level, globally, forcing education to move online. Meeting the needs of students online for Science Lab classes, in particular, is a challenge since the physical labs are not available to the teachers or students. OLabs is a virtual Science Lab providing a complete learning environment of theory, experimental procedures, videos, animations, simulations, and assessments that capture real lab experiences with the relevant pedagogy. This study looks at the acquisition and behaviors of users, on the OLabs platform, during pre and Covid-19 times. Using Google Analytics, we observe that, during the pandemic time, users increasingly adopted OLabs as a new learning pedagogy for performing experiments as indicated by parameters like the number of users; the number of unique pages viewed per session; time spent on viewing content; bounce rate; and preference for content types such as theory, simulations, videos, and animations.

Recommender systems have been applied in a wide range of domains such as e-commerce, media, banking, and utilities. This kind of system provides personalized suggestions based on large amounts of data in order to increase user satisfaction. These suggestions help client select products, while organizations can increase the consumption of a product. In the case of social data, sentiment analysis can help gain better understanding of a user’s attitudes, opinions and emotions, which is beneficial to integrate in recommender systems for achieving higher recommendation reliability. On the one hand, this information can be used to complement explicit ratings given to products by users. On the other hand, sentiment analysis of items that can be derived from online news services, blogs, social media or even from the recommender systems themselves is seen as capable of providing better recommendations to users. In this study, we present and evaluate a recommendation approach that integrates sentiment analysis into collaborative filtering methods. The recommender system proposal is based on an adaptive architecture, which includes improved techniques for feature extraction and deep learning models based on sentiment analysis. The results of the empirical study performed with two popular datasets show that sentiment–based deep learning models and collaborative filtering methods can significantly improve the recommender system’s performance.

This work is driven by a practical question, corrections of Artificial Intelligence (AI) errors. Systematic re-training of a large AI system is hardly possible. To solve this problem, special external devices, correctors, are developed. They should provide quick and non-iterative system fix without modification of a legacy AI system. A common universal part of the AI corrector is a classifier that should separate undesired and erroneous behavior from normal operation. Training of such classifiers is a grand challenge at the heart of the one- and few-shot learning methods. Effectiveness of one- and few-short methods is based on either significant dimensionality reductions or the blessing of dimensionality effects. Stochastic separability is a blessing of dimensionality phenomenon that allows one-and few-shot error correction: in high-dimensional datasets under broad assumptions each point can be separated from the rest of the set by simple and robust linear discriminant. The hierarchical structure of data universe is introduced where each data cluster has a granular internal structure, etc. New stochastic separation theorems for the data distributions with fine-grained structure are formulated and proved. Separation theorems in infinite-dimensional limits are proven under assumptions of compact embedding of patterns into data space. New multi-correctors of AI systems are presented and illustrated with examples of predicting errors and learning new classes of objects by a deep convolutional neural network.

In this paper, we present the definition, some properties, and solve a problem on special primes. These properties help in providing us with a better understanding of the problem posed related to special primes on the open problem garden website. The problem involves finding all the primes q, given a prime p such that q≡1(mod p) and 2^((q−1)/p)≡1(mod q). We prove that a prime number q is a special prime of p if and only if the order of 2 in U(q) divides q−1p. Also, we prove that a prime number q is not a special prime for any prime number if 2 is a generator of the group U(q) and that there exist infinitely many special primes for any given prime number.

Outcomes of repeated decision--making processes may be affected by adversarial actors, without being noticed. Adversaries may try to gain knowledge about a particular decision--making process, identify its decision--makers, and guess which underlying decision support model is used. Then they can simulate the process, and craft different scenarios to affect its decision outcomes. Therefore, designers of decision support systems need to incorporate this in the decision modeling phase. The purpose of this study is to demonstrate this for the repeated decision--making in a patent application process. In this process, two sequential decision outcomes can be affected by adversarial actors: a company's decision to which type of patent office to send a patent request to, and the decision of a specialized patent officer to grant an application, or not. It is motivated that the company's decision--maker is \emph{bounded} rational. A theory for information--theoretic bounded rational decision--making under uncertainty proposed by Ortega et al.\ is adopted to model this type of decision--maker. A framework is provided to simulate a number of scenarios that adversaries may deploy to affect decision outcomes of a repeated patent application decision--making process. The framework is also utilized for statistically testing the presence of the scenarios, and to demonstrate how to discourage adversaries from deploying them.

Capability assessment plays a crucial role in the demonstration and construction of equipment. To improve the accuracy and stability of capability assessment, we study the neural network learning algorithms in the field of capability assessment and index sensitivity. Aiming at the problem of over-fitting and parameter optimization in neural network learning, the paper proposes an improved machine learning algorithm—the Ensemble Learning Based on Policy Optimization Neural Networks (ELPONN) algorithm with the policy optimization and ensemble learning. This algorithm presents optimized neural network learning algorithm through different strategies evolution, and builds an ensemble learning model of multi-intelligent algorithms to assessment the capability and analyze the sensitivity of the indexes. Through the assessment of capabilities, the algorithm effectively avoids parameter optimization from entering the minimum point in performance to improve the accuracy of equipment capability assessment, which is significantly better than previous neural network assessment methods. The experimental results show that the mean relative error is 4.10%, which is better than BP, GABP, and early stopping. The ELPONN algorithm has better accuracy and stability performance, and meets the requirements of capability assessment.

A way of systematizing different geometries by geometrical transformations is presented by using Klein’s perspective. Symmetry is considered the basic precedent, and different groups of transformations are introduced by using Erlangen program ideas. So, to focus on the importance of geometric transformations, two purposes are shown: first, the classification of geometries is based on the invariants of geometric transformations; and second, the construction of geometry unlike the theory of deduction can be done by means of geometric transformations.

It is introduced and studied para-Ricci-like solitons with potential Reeb vector field on almost paracontact almost paracomplex Riemannian manifolds. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field have been considered. It is proved a necessary and sufficient condition the manifold to admit a para-Ricci-like soliton which is the structure to be para-Einstein-like. Explicit examples are provided in support of the proven statements.

The issues concerning the development of the smart systems for the management of freight transport are related to many factors which are influencing by properties of such a complex processes and ICT development. We are concerned with the recognition of a wide spectrum of services and provision specifics under conditions of wireless communication networks. Also, we are investigated for the adequate provision of context data with problematic of a definition of such context data and with possibilities to apply formalized artificial intelligence methods for recognition of this context information needs for transportation. In this stage of application of the smart system, we are solving the problem of priority of provision of possible providing services, ensuring of quite optimal quality of data supply channels and restriction of flooding of wireless communication channels. The proposed methodology is based on methods of indication of con-text-aware situations and integration of such data into the situation recognition algorithms. The constructions of smart service provision system are developed for more safety management of transportation. The experimental results are demonstrated on analysis of heterogeneity of smart services, construction of schemas for service provision priorities, and extension of potential of intelligent transport with intellectual recognition possibilities of context-aware information in the transportation process.

Intelligent systems are transforming the world, as well as our healthcare system. We propose a deep learning-based cough sound classification model that can distinguish between children with healthy versus pathological coughs such as asthma, upper respiratory tract infection (URTI), and lower respiratory tract infection (LRTI). In order to train a deep neural network model, we collected a new dataset of cough sounds, labelled with clinician's diagnosis. The chosen model is a bidirectional long-short term memory network (BiLSTM) based on Mel Frequency Cepstral Coefficients (MFCCs) features. The resulting trained model when trained for classifying two classes of coughs -- healthy or pathology (in general or belonging to a specific respiratory pathology), reaches accuracy exceeding 84\% when classifying cough to the label provided by the physicians' diagnosis. In order to classify subject's respiratory pathology condition, results of multiple cough epochs per subject were combined. The resulting prediction accuracy exceeds 91\% for all three respiratory pathologies. However, when the model is trained to classify and discriminate among the four classes of coughs, overall accuracy dropped: one class of pathological coughs are often misclassified as other. However, if one consider the healthy cough classified as healthy and pathological cough classified to have some kind of pathologies, then the overall accuracy of four class model is above 84\%. A longitudinal study of MFCC feature space when comparing pathologicial and recovered coughs collected from the same subjects revealed the fact that pathological cough irrespective of the underlying conditions occupy the same feature space making it harder to differentiate only using MFCC features.

Given any sequence a = (an)n1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn)n1 such that y=a = (yn=an)n1 2 E. In this paper, we use the spaces w1, w0 and w of strongly bounded, summable to zero and summable sequences, that are the sets of all sequences y such that ? n?1Pn k=1 jykj
n is bounded, tends to zero and such that y ? le 2 w0, for some scalar l, respectively, (cf. [24, 22]). These sets where used in the statistical convergence, (cf. [17, Chapter 4]). Then we deal with the solvability of each of the (SSIE) F
 E + F0x where E is a linear space of sequences, F = c0, c, `1, w0, w, or w1 and F0 = c0, c, or `1. For instance, the solvability of the (SSIE) w
 w0+s(c) x consists in determining the set of all sequences x = (xn)n1 2 U+ that satisfy the following statement. For every sequence y that satisfy the condition limn!1 n?1Pn k=1 jyk ? yk?1 ? lj = 0, there are two sequences u and v, with y = u+v such that limn!1 n?1Pn k=1 jukj = 0 and limn!1 (vn=xn) = L for some scalars l and L. These results extend those stated in [11, 12, 10].

An evolutionary game is introduced which considers game-theoretic strategies in the context of non-linear population matrix models. This game considers the states and actions of the organisms of the evolving population, and a notion of dynamic equilibrium between strategies is described. The game’s formalism is expounded and a proof about equilibrium is given; specifically that any stable equilibrium can be described by proportions of pure strategies; particularly when population matrices are not defective.

Recent progress in deep learning has led to accurate and efficient generic object detection networks. Training of highly reliable models depends on large datasets with highly textured and rich images. However, in real-world scenarios, the performance of the generic object detection system decreases when (i) occlusions hide the objects, (ii) objects are present in low-light images, or (iii) they are merged with background information. In this paper, we refer to all these situations as challenging environments. With the recent rapid development in generic object detection algorithms, notable progress has been observed in the field of object detection in challenging environments. However, there is no consolidated reference to cover state-of-the-art in this domain. To the best of our knowledge, this paper presents the first comprehensive overview, covering recent approaches that have tackled the problem of object detection in challenging environments. Furthermore, we present the quantitative and qualitative performance analysis of these approaches and discuss the currently available challenging datasets. Moreover, this paper investigates the performance of current state-of-the-art generic object detection algorithms by benchmarking results on the three well-known challenging datasets. Finally, we highlight several current shortcomings and outline future directions.

In fisheries monitoring, catch is assumed to be a product of fishing intensity, catchability, and availability, where availability is defined as the number or biomass of fish present and catchability refers to the relationship between catch rate and the true population. Ecological monitoring programs use catch per unit of effort (CPUE) to standardize catch and monitor changes in fish populations; however, CPUE is proportional to the portion of the population that is vulnerable to the type of gear that is used in sampling, which is not necessarily the entire population. Programs often deal with this problem by assuming that catchability is constant, but if catchability is not constant, it is not possible to separate the effects of catchability and population size using monitoring data alone. This study uses individual-based simulation to separate the effects of changing environmental conditions on catchability and availability in environmental monitoring data. The simulation combines a module for sampling conditions with a module for individual fish behavior to estimate the proportion of available fish that would escape from the sample. The method is applied to the case study of the well-monitored fish species Delta Smelt (Hypomesus transpacificus) in the San Francisco Estuary, where it has been hypothesized that changing water clarity may affect catchability for long-term monitoring studies. Results of this study indicate that given constraints on Delta Smelt swimming ability, it is unlikely that the apparent declines in Delta Smelt abundance are due to an effect of changing water clarity on catchability.

India is ranked 5th in world in terms of Covid-19 publications accounting for 6.7% of the total. About 60% of the Covid-19 publications in the year 2020 are from United States, China, UK, Italy, and India. We present a bibliometrics analysis of the publi-cation trends and citation structure along with identification of major research clusters. By performing network analysis of authors, citations, institutions, key-words, and countries, we explore semantic associations by applying visualization techniques. Our study shows lead taken by United States, China, UK, Italy, India in Covid-19 research may be attributed to the high prevalence of Covid-19 cases in those countries witnessing the first outbreak and also due to access to Covid-19 data, access to labs for experimental trials, immediate funding, and overall support from the govt. agencies. Large number of publications and citations from India are due to co-authored publications with countries like United States, UK, China, and Saudi Arabia. Findings show health sciences with highest the number of publications and citations, while physical sciences and social sciences and humanities counts were low. A large proportion of publications fall into the open access category. With India as focus, by comparing three major pandemics SARS, MERS, Covid-19 from biblio-metrics perspective, we observe much broader involvement of authors from multiple countries for Covid-19 studies as compared to SARS and MERS. Finally, by applying bibliometric indicators, we see an increasing number of sustainable develop-ment-related studies from the Covid-19 domain, particularly concerning the topic of good health and well-being. This study allows for a deeper understanding on how the scholarly community from a populous country like India pursued research in the midst of a major pandemic which resulted in closure of scientific institutions.

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

Due to the unanticipated, forced migration of classroom activities to a fully remote format because of the coronavirus pandemic, there is a critical need for progress in the online education system. Not only that, but online education is the way of the future, and its infrastructure must be enhanced for teaching and learning to be effective. Engaging the students and enhancing their focus is one of the major concerns in the current video calling-based system. In this research, we propose a VR and AR-based virtual classroom environment system called "Edu VR" which encourages students to learn with a high level of involvement and attentiveness. We have divided the system into 2 distinct categories. one amongst which incorporates the virtual reality classroom, wherever the students can have a similar feel of actual school with peer-to-peer-based interactions and student-to-teacher interactions with Unity3D. We are able to conjointly deploy AR models with Vuforia, which permits the teachers to take classes more efficiently with student’s engagement. The other category involves the AI-based classroom assessment system, which enables teachers to produce assessments, which in turn are proctored by Artificial Intelligence. The results are automatically sent to the student within a short period, with the assistance of text similarity analysis for evaluating the answer scripts with Machine learning. This approach solves the drawbacks of video call-based systems with enhanced focus and engagement.

There are given algebraic and integral identities for a pair or a triple of plane solenoidal fields. As applications, we obtain sufficient potentiality conditions for a plane vector field. The integral identities are also important for exact a priori estimates.

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. In this case, the mutation parameter is dynamically moved during the evolution process by using a shadowed and general type-2 fuzzy systems. The main idea of this work is to make a performance comparison between using shadowed and general type 2 fuzzy systems as controllers of the mutation parameter in differential evolution. The performance is compared with the problem of optimizing fuzzy controllers for a D.C. Motor. Simulation results show that general type-2 fuzzy systems are better when higher levels of noise are considered in the controller.

With the introduction of HTTP/3, whose transport is no longer the traditional TCP protocol but the novel QUIC protocol, research for solutions to the unfairness of Adaptive Streaming over HTTP (HAS) has become more challenging. That is, because of different transport layers, the HTTP/3 may not be available for some networks and the clients have to use HTTP/2 for their HAS applications instead. Therefore, the scenario that HAS over HTTP/3 (HAS/3) compete against HTTP/2 (HAS/2) must be considered seriously. However, there have been a shortage of investigations on the performance and the origin of the unfairness in such a cross-protocol scenario in order to produce proper solutions. Therefore, this paper provides a performance evaluation and root-cause analysis of the cross-protocol unfairness between HAS/3 and HAS/2. It is concluded that, due to differences in the congestion control mechanisms of QUIC and TCP, HAS/3 clients obtain larger congestion windows, thus requesting higher video bitrates than HAS/2. As the problem lies in the transport layer, existing client-side ABR-based solutions for the unfairness from the application layer may perform suboptimally for the cross-protocol case.

This paper presents a non-random weight initialization method in convolutional layers of neural networks examined with the Fast Gradient Sign Method (FSGM) attack. This paper's focus is convolutional layers, and are the layers that have been responsible for better than human performance in image categorization. The proposed method induces earlier learning through the use of striped forms, and as such has less unlearning of the existing random number speckled methods, consistent with the intuitions of Hubel and Wiesel. The proposed method provides a higher performing accuracy in a single epoch, with improvements of between 3-5% in a well known benchmark model, of which the first epoch is the most relevant as it is the epoch after initialization. The proposed method is also repeatable and deterministic, as a desirable quality for safety critical applications in image classification within sensors. That method is robust to Glorot/Xavier and He initialization limits as well. The proposed non-random initialization was examined under adversarial perturbation attack through the FGSM approach with transferred learning, as a technique to measure the affect in transferred learning with controlled distortions, and finds that the proposed method is less compromised to the original validation dataset, with higher distorted datasets.

Number is based in special edges, is introduced. The kind of natural extension from edges toward vertex and the set of vertices in the way that, the final notion is number, is studied. The result is obtained which is about the study on the classes of graphs in the matter of new notions. There is the extended notion about having edge amid two vertices toward having some edges in the word of neighbor and in another stage going into the atmosphere of having consecutive edges in the terminology of path and in the upper vision going on the notion about path with jargon and buzzword of distance as if the minimal vertices has concluded the new notions with the word, number.

In this paper, we propose a robust video understanding model for activity recognition by learning the actor’s pair-wise correlations and relational reasoning, exploiting spatial and temporal information. In order to measure the similarity between the pair appearances and construct an actor relations map, the Zero Mean Normalized Cross-Correlation (ZNCC) and the Zero Mean Sum of Absolute Differences(ZSAD) is proposed to allow the Graph Convolution Network (GCN) to learn how to distinguish group actions. We recommend that MNASNet be used as the backbone to retrieve features. Experiments show a 38.50% and 23.7% reduction in training time in the 2-stage training process along with a 1.52% improvement in accuracy against traditional methods.

The virus SARS-CoV-2 has resulted in numerous modelling approaches arising rapidly to understand the spread of the disease COVID-19 and to plan for future interventions. Herein, we present an SEIR model with a spatial spread component as well as four infectious compartments to account for the variety of symptom levels and transmission rate. The model takes into account the pattern of spatial vulnerability in South Africa through a vulnerability index that is based on socioeconomic and health susceptibility characteristics. Another spatially relevant factor in this context is level of mobility throughout. The thesis of this study is that without the contextual spatial spread modelling, the heterogeneity in COVID-19 prevalence in the South African setting would not be captured. The model is illustrated on South African COVID-19 case counts and hospitalisations.

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

Rice is the grain feeds more than half of the world population. It is an important staple food provides twenty percent of the calories consumed worldwide. Food safety affects the health of consumers. Establishing an effective traceability system is one of the primary measures to protect rice quality and food safety. Blockchain-based traceability system has the characteristics of data tamper-proofing, decentralization, and co-governance. This paper proposed a rice traceability scheme based on blockchain technology that selects the critical nodes in the rice industry chain to construct a blockchain network to achieve transparent data sharing. It is meaningful for both enterprises and consumers. It can let enterprises get the real quality information of rice and related raw materials. Consumers can get the true information of rice and rice products to buy safe and healthy food. The scheme is proved feasible by simulating the traceability of the rice supply chain.

The COVID-19 pandemic starting in the first half of 2020 has changed the lives of everyone across the world. Reduced mobility was essential due to it being the largest impact possible against the spread of the little understood SARS-CoV-2 virus. To understand the spread, a comprehension of human mobility patterns is needed. The use of mobility data in modelling is thus essential to capture the intrinsic spread through the population. It is necessary to determine to what extent mobility data convey the same message of mobility within a region. This paper compares different mobility data sources by constructing spatial weight matrices and further compares the results through hierarchical clustering. This provides insight for the user into which data provides what type of information and in what situations a particular source is most useful.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

Around the world, every year, about 17 million people death cause happen due to CardioVascular Diseases (CVD). As per clinical records, primarily sufferers exhibit myocardial infarctions and Heart Failures (HF). Creatinine is a Musculo - skeletal waste product. The kidneys filter creatinine from the blood and excrete it through the urine in a healthy body. High creatinine levels can suggest renal problems. Elevated Serum Creatinine (SC) has been well established in the HF. Patients’ electronic medical records can be used to quantify symptoms and other related clinical laboratory test values, which would then be utilized to direct biostatistics exploration to uncover patterns and associations that doctors would otherwise miss. The latest American Heart Association guidelines for 1500 mg/d sodium tend to be sufficiently relevant for patients with stage A and B with HF. In this article, we used a dataset of the year 2015 of heart patients records of 299 patients. The present paper used the data analytic and statistical tools to verify the significant differences between alive and dead patients’ SC and Serum Sodium (SS). It also demonstrates the impact of significant features on abnormal SC and SS on the Survival-Status levels. The Age-Group feature, which is derived from age attribute and, Ejection Fraction (EF), anemia, platelets, Creatinine Phosphokinase (CPK), Blood-Pressure (BP), gender, diabetes, and smoking-status were utilized to determine the potential contributing features to mortality with Cox regression model. The Kaplan Meier plot was used to investigate the overall pattern of survival concerning age-group. During pre-processing of the dataset, Age and SS were removed due to multicollinear features during performing machine learning algorithms experiments. This paper also predicted patients’ survival, age group, and gender using supervised machine learning classifiers. Detection of significant features would help in making informed decisions to balance the lifestyle of heart patients. The author revealed that the patient’s follow-up months, as well as SC, EF, CPK, and platelets, are sufficient key features to predict heart patient survival using Random Forest (RF) stratified 10-fold CV method with accuracy (96%) with 5% Standard Deviation (SD) from medical records dataset. We identified the age-group and gender of the patient, and the RF model outperformed others with the best accuracy 96% and 94% in both cases having 11% SD. Also, prominent features such as CPK, SC, follow-up month, platelets, and ejection were found to be significant factors in predicting the patient’s age-group. Smoking habits, CPK, platelets, follow-up month, and SC of each patient were discovered to be significant predictors of patient gender. The hypothetical study proved that SC and SS making substantial differences in the survival of patients (p &lt; 0.05) and failed to reject that anemia, diabetes, and BP making a significant impact on the creatinine and sodium of each patient (p &gt; 0.05). With χ2(1) = 8.565, the Kaplan Meier plot revealed that mortality was high in the extremely elder age-group. The finding has possible effects on clinical practice and becomes a new medical support system when predicting whether a patient can survive a heart attack or not. The doctor should primarily concentrate on follow-up month, SC and EF, CPK, and platelet count since the aim is to understand whether a patient survives after HF.

We consider a discrete-time random walk (xt) which at random times is reset to the starting position and performs a deterministic motion between them. We show that the quantity Prxt+1=n+1|xt=n,n→∞ determines if the system is averse, neutral or inclined towards resetting. It also classifies the stationary distribution. Double barrier probabilities, first passage times and the distribution of the escape time from intervals are determined.

In this article, there's an effort to make sense about the new versions of matroid. I believe that there's new idea on the background of. matroid. Two styles of matroid is defined in the background of fixed graphs and after that the attributes of these new notion on the graph and its parameters have been studied. The focus of this article is on the version of matroid which has the basis on the cycles as if there's gentle discussion on the results which are based on the set of independent vertices as matroid-x. The relation amid fundamental parameters and specific set like independent set and minimal set in the terminology of graph theory have been considered. Matroid is the word to use in the study on the parameters of graph theory as if set theory and its terminology are also recorded. The terms of word in various terminology have been relatively used. There are open ways to use hypergraphs or some serious relations amid these two types.

In this paper, the author derives an explicit form of Heaviside Step Function, which evidently constitutes a fundamental concept of Operational Calculus and is also involved in many other fields of applied and engineering mathematics.In particular, this special function is exhibited in a very simple manner as a summation of four inverse tangent functions. The novelty of this work is that the proposed exact formulae are not performed in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc and also are neither the limit of a function, nor the limit of a sequence of functions with point – wise or uniform convergence.Hence, this formula may be much more appropriate and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.