In this work we introduce a novel approach to generate lower and upper L2 estimates for solution derivatives of arbitrary order to a general class of dissipative systems in the case that such estimates are available for the solutions themselves. Our method also works in reverse order: from the L2 estimates of solution derivatives of some (arbitrary) order we can derive lower and upper L2 estimates for the solutions and then to their derivatives of any order. This procedure is based on very simple monotonicity properties combined with standard energy estimates in physical space, following previous ideas of Kreiss, Hagstrom, Lorenz and Zingano. For simplicity, it is applied here in the context of algebraic rates, but the method can be used in other contexts as well (exponential, logarithm, and so forth).

Visually impaired people encounter many impediments and challenges in their lives such as related to their mobility, education, communication, use of technology, and others. This paper reports the results of an online survey to understand the requirements and challenges blind and visually impaired people face in their daily lives regarding the availability and use of digital devices. The survey was conducted among the blind and visually impaired in Saudi Arabia using digital forms. A total of 164 people responded to the survey most of them using the VoiceOver function. People were asked about the use of smart devices, special devices, operating systems, object recognition apps, indoor and outdoor navigation apps, virtual digital assistive apps, the purpose (navigation, education, etc.) of and difficulty in using these apps, the type of assistance needed, the reliance on others in using the assistive technologies, and the level of satisfaction from the existing assistive technologies. The majority of the participants were 18 – 65 years old with 13% under 18 and 3% above 65. Sixty-five percent of the participants were graduates or postgraduates and the rest only had secondary education. White Cane, mobile phones, Apple iOS, Envision, Seeing AI, VoiceOver, and Google Maps were the most used devices, technologies, and apps used by the participants. Navigation at 39.6% was the most reported purpose of the special devices followed by education (34.1%) and office jobs (12.8%). The information from this survey along with a detailed literature review of academic and commercial technologies for the visually impaired was used to establish the research gap, design requirements, and a comprehensive understanding of the relevant landscape, which in turn was used to design smart glasses called LidSonic for visually impaired.

In this article, rst we are going to review the concept of ordinary frames , in more general case in measure spaces, namely, gc-frames. We try to develop the use of measure space in describing frames. Then by means of the gc-frames, we shall introduce gn-operators, which we shall show that each trace class operator has a vector-valued integral representation and vice-versa.

In this paper, the concept of fuzzy locally convex spaces generated by a family of fuzzy seminorms is introduced. We prove that a Minkowski functional of zero neighborhoods generates a seminorm and finally deduce that the topology generated by the family of seminorms coincides with that of the Minkowski functional.

The emergence of blockchain know-how currently presents the opportunity for the health sector to adopt such technologies in electronic health records. Blockchain assists in maintaining and sharing the relevant medical records of the patient with the relevant group of healthcare providers and the hospital. Numerous specific applications include traceability of drug and patient monitoring or Electronic Health Records (EHR). While Blockchain assists in maintaining and sharing the relevant medical records of the patient with the relevant group of healthcare providers and the hospital, it is important to note that the moral consciousness of the healthcare professionals is the main guide of the moral consciousness is ethics. This paper presents an overview of the application of blockchain in the healthcare and medical sector, highlighting the specific challenges and concerns. The study adopted a systematic review of secondary literature in answering the research question.

It is known that the class of p-normed spaces (0 < p ≤ 1) is an important generalization of usual normed spaces with rich topological and geometrical structure, but the most of tools and general principles in nature with nonlinearity have not been developed yet, thus the main goal of this paper is to develop tools for nonlinear analysis under the framework of p-vector spaces. In particular, we first develop the general fixed point theorems which provide solutions to answer Schauder conjecture since 1930’s in the affirmative for p-vector spaces when p = 1 (which is just general topological vector spaces); then the one best approximation result for upper semi-continuous mappings is given, which is used as a powerful tool to establish fixed points for non-self set-valued mappings with either inward or outward set conditions; and finally we establish comprehensive existence results of solutions for Birkhoff-Kellogg Problems, and the general principle of nonlinear alternative by including Leray-Schauder alternative and related results. The results given in this paper not only include the corresponding results in the existing literature as special cases, but also expected to be useful tools for the study of nonlinear problems arising from theory to practice.

The sudden onset of the Covid-19 pandemic disrupted the modern multi-national interconnected society and led the countries and societies to enforce unprecedented restrictions on movement. Among myriad containment measures, the policy of trace and quarantine found universal adoption among countries; the swift adoption of the policy was soon met with widespread criticism and opposition activists who questioned the utility and the risk associated with such a large scale collection of data and infringement on the movement of individuals. Consequently, one often tends to be either pro- or anti-trace and quarantine; the ensuing polarizing and politicized left little room for nuance. In this work, we undertake a methodology study to understand the nuances of the impact of different implementations of trace and quarantine. To this end, we design a user-friendly and intuitive tool that can be employed by experts to model the disease dynamics and societal structure. We focus on the study of the cost of policy with respect to quarantine degree, which captures the distance between the person required to quarantine after a person is detected to be infected. Our study results in a surprising conclusion: the cost is not necessarily monotone with respect to the degree of quarantine. Our analysis indicates that governments must curb the urge to adopt simplistic policy and the optimal policy of trace and quarantine for a country strongly depends on its societal structure and disease dynamics.

Plagiarism means taking another person’s work and not giving any credit to them for it. Plagiarism is one of the most serious problems in academia and among researchers. Even though there are multiple tools available to detect plagiarism in a document but most of them are domain-specific and designed to work in English texts, but plagiarism is not limited to a single language only. Bengali is the most widely spoken language of Bangladesh and the second most spoken language in India with 300 million native speakers and 37 million second-language speakers. Plagiarism detection requires a large corpus for comparison. Bengali Literature has a history of 1300 years. Hence most Bengali Literature books are not yet digitalized properly. As there was no such corpus present for our purpose so we have collected Bengali Literature books from the National Digital Library of India and with a comprehensive methodology extracted texts from it and constructed our corpus. Our experimental results find out average accuracy between 72.10 % - 79.89 % in text extraction using OCR. Levenshtein Distance algorithm is used for determining Plagiarism. We have built a web application for end-user and successfully tested it for Plagiarism detection in Bengali texts. In future, we aim to construct a corpus with more books for more accurate detection.

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.

For disciplines like biological science, security, and the medical field, link prediction is a popular research area. To demonstrate the link prediction many methods have been proposed. Some of them that have been demonstrated through this review paper are TransE, Complex, DistMult, and DensE models. Each model defines link prediction with different perceptions. We argue that the practical performance potential of these methods, having similar parameter values, using the fine-tuning technique to evaluate their reliability and reproducibility of results. We describe those methods and experiments; provide theoretical proofs and experimental examples, demonstrating how current link prediction methods work in such settings. We use the standard evaluation metrics for testing the model's ability.

The giant challenge breeding flood-irrigated rice is to identify superior genotypes that present high-yielding with specific grain qualities, resistance to abiotic and biotic stresses, excellent adaptation to the target environment. Thus, the objectives of this study were to propose a bayesian multi-trait model, estimate genetic parameters, and select flood-irrigated rice genotypes with better genetic potentials in different evaluation environments. For this, twenty-five rice genotypes belonging to the flood-irrigated rice improvement program were evaluated. The grain yields, grain length, width and thickness, grain length, and grain width and weight of 100 grains in the agricultural year 2016/2017. The experimental design used in all experiments was a randomized block design with three replications. The Monte Carlo Markov Chain algorithm estimated genetic parameters and genetic values. The grain thickness trait was considered highly heritable, with a credibility interval ranging from: h^2: 0.9480; 0.9440; 0.8610, in environments 1, 2, and 3, respectively. The grain yields showed a low correlation estimate between grain thickness and 100-grain weight, in all environments, with a credibility interval ranging from (ρ= 0.5477; 0.5762; 0.5618 and 0.5973; 0.5247; 0.5632, grain thickness and 100-grain weight, in environments 1, 2, and 3, respectively). The Bayesian multi-trait model proved to be an adequate strategy for the genetic improvement of flood-irrigated. Genotypes 2 and 15 had similar potential in the three environments, they should be selected as high-performance multi-trait genotypes for the genetic breeding of flood-irrigated rice in the program.

The concept of distributed generation has made photovoltaic an integral source of energy in smart grid systems, especially in peer-to-peer energy trading frameworks that exploit excess power to fulfill the energy requirements of consumers in cost-efficient and eco-friendly manner. It is believed that P2P energy trading will dominate a significant portion of research in forthcoming power generation systems due to the excessive rise of energy demands across the globe. Despite a plethora of studies on energy optimization solutions in P2P trading, minimizing nanogrid energy trading cost and efficient energy sharing between consumers and prosumers are deemed among the challenging problems. This study overcomes essential issues overlooked by the contemporary P2P energy trading models by introducing a predictive optimization-oriented nanogrid energy trading model. The proposed study encompasses two stages: (1) predictive optimization model which harnesses BD-LSTM-based forecasted energy parameters (energy load, energy consumption, and PV generation) that are later incorporated in PSO-enabled objective function to reduce nanogrid trading cost, (2) optimal energy sharing plan is devised to decide the role of nanogrids as prosumers or consumers by emphasizing the use of PV-produced energy. The proposed model is validated on the case study containing nanogrid houses data. The simulation provides detailed experiments by comparing the energy demand and response using the proposed energy sharing model. The outcomes yield that the energy sharing plan holds a significant potential to fulfill maximum energy requirements of nanogrid house in P2P cluster and significantly reduces the energy cost compared to grid.

This paper deals with the analysis of trends in road accidents on major highways in Brazil. Using updated time series techniques, our results indicate that a low degree of long memory was detected in the series with shocks having transitory effects over time. We further find that the number of accidents taking place in Brazil has been reducing over time, though in the presence of negative shocks, the recovery is not going to be immediate due to the long memory nature of the data. Despite the absence of relevant investment relating to infrastructure expansion, it is worth mentioning the consolidation of a nationwide tolled road system in Brazil involving concessions to private administrators, alongside more severe traffic laws that can impose limitations on driving licences.

As an implementation of inverse Radon transform, the Second-order Divided-difference Back Projection (SDBP) technique has been proposed in this paper, by which the accurate CT reconstruction can be theoretically realized. A computational model for CT reconstruction filter expressions has been derived on the basis of SDBP technique. The method reveals the correlation between the convolution kernel for data restoration and the filter expression. By substituting kernel functions into the computational model, the amplitude sequences of a variety of filters can be calculated. On the proposed filter construction method, the decomposition form of filters has been discovered, where a series of basic filters have been acquired. The properties of any filter depend on the decomposed basic filters. Basic filters can be used to compose filters in actual needs.

We define the notions of strong and strict recurrency for actions of countable ordered groups on $\sigma$-finite non atomic measure spaces with quasi-invariant measures. We show that strong recurrency is equivalent to non existence of weakly wandering sets of positive measure. We also show that for certain p.m.p ergodic actions the system is not strictly recurrent, which shows that strong and strict recurrency are not equivalent.

We studies the initial value problem for the fractional Navier-Stokes-Coriolis equations, which obtained by replacing the Laplacian operator in the Navier-Stokes-Coriolis equation by the more general operator $(-\Delta)^\alpha$ with $\alpha>0$. We introduce function spaces of the Besove type characterized by the time evolution semigroup associated with the general linear Stokes-Coriolis operator. Next, we establish the unique existence of global in time mild solutions for small initial data belonging to our function spaces characterized by semigroups in both the scaling subcritical and critical settings.

In this paper we study solutions and drift homogenization for a class of viscous lake equations by using the method of semigroups of bounded operators. Suppose that the initial value i.e.,for some Hölder continuous function onwith smooth function value satisfying and Then the initial value problem (2) for viscous lake equations has a unique smooth local strong solution. Using this result we study the drift homogenization for three-dimensional stationary Stokes equation in the usual sense

The rapid infiltration of fake news is a flaw to the otherwise valuable internet, a virtually global network that allows for the simultaneous exchange of information. While a common, and normally effective, approach to such classification tasks is designing a deep learning-based model, the subjectivity behind the writing and production of misleading news invalidates this technique. Deep learning models are unexplainable in nature, making the contextualization of results impossible because it lacks explicit features used in traditional machine learning. This paper emphasizes the need for feature engineering to effectively address this problem: containing the spread of fake news at the source, not after it has become globally prevalent. Insights from extracted features were used to manipulate the text, which was then tested on deep learning models. The original unknown yet substantial impact that the original features had on deep learning models was successfully depicted in this study.

Background: The new media provides a convenient digital platform to access, use and exchange health information. As a special group of health care, maternal is still of international concern due to their high mortality rate. Improving maternal health as a Millennium Development Goal of the United Nations is an important quest for the health care system. Scientific research provides advice on how to improve maternal health through stringent reasoning and accurate data. However, the dramatic increase of publications, the diversity of themes, and the dispersion of researchers may reduce efficiency. Objective: This study aims to analyze the research progress on maternal health under the global new media environment, exploring the current research hotspots and research frontiers. Methods: A scientometric analysis was carried out by CiteSpace5.7.R1, searching in the core database of Web of Science for articles published in English from 1998 to 2021, and combined topic words such as new media, maternal, and health. In total, 3312 articles have been retrieved, of which 2270 studies have been included for further analysis. Top countries and institutions, potentially high-impact literature, research frontiers, and hotspots were analyzed in this study. Results: The number of publications grew rapidly after 2008, from 29 publications sharply increasing to 472 publications by 2020. Research centers concentrated in Latin America, such as the University of Toronto, the University of California. The work of Larsson M, Lagan BM, Tiedje L, and Helle C had a high potential impact. Most of the research subjects were maternal and newborn babies, and the research frontiers focused on health education and maternal psychological problems. Maternal mental health, maternal and infant nutrition, weight, production technology, and equipment were hotspots. Conclusion: The development of new media has brought a new era for maternal health, characterized by psychological qualities, healthy and reasonable physical conditions, and advanced technology.

Ukraine is an associate member of the European Union and in the coming years it is expected that all the data and services already used by European Union countries will become available for Ukraine. An important program, which is the basis for building European monitoring services for Smart Cities, is the Copernicus program. The two most important services of this program are Copernicus Land Monitoring Service (CLMS) and Copernicus Atmosphere Monitoring Service (CAMS). CLMS provides important information on Land Use in Europe. In the context of Smart Cities, the most valuable one is the Urban Atlas service, which is related to local CLMS services and provides a detailed digital city plan in vector form, which is segmented into small functional areas classified by the CORIN nomenclature. The Urban Atlas is a geospatial layer with high-resolution, which is built for all European cities with a population of more than 100,000 that combines high-resolution sat-ellite data, city segmentation by blocks and functional areas, important city infrastructure, etc. This product is used as a basis for city planning and obtaining analytics on the most important indicators of city development including air quality monitoring. For Ukraine, such geospatial products are not provided under the Copernicus program. It is important to start work on its development and implementation as early as possible, so that when the first city atlas appears, Ukraine will be ready to work with it together with the European community. This requires preparing the basis for na-tional research and training national stakeholders and users to use this product. To make this happen it’s necessary to have national geospatial product, which can be used as an analogue of the city atlas. In this article authors analyzed the existing methods of air quality assessment and assessment of the SDG indicator 11.6.2 achieving for European cities, based on which the indicator 11.6.2 for Ukraine for 5 years was evaluated for the first time. The obtained results are analyzed and the values of indicator 11.6.2 for Ukraine are compared with European countries.

The newly discovered coronavirus (COVID-19) has disrupted traditional methods of conducting research, particularly qualitative research. However, there remains a number of methods by which qualitative data can still be collected. These include the use of digital voice, video, and text-based tools, online surveys, and content analysis. Text-based sources can help to overcome the limitations of time and space, and also can be cost-effective. This chapter draws from data collected from 12 participants across Zimbabwe and demonstrates how these tools can be used to generate data or to sample data that is already available to satisfy research questions and meet research objectives. It recommends researchers to experiment with new ways of collecting qualitative data while also observing safety protocols and ethical considerations.

In this article, the concept of fuzzy $(\sigma,\mathcal{Z})$-contractive mapping has been introduced in fuzzy metric spaces which is an improvement over the corresponding concept recently introduced by Shukla et al. [Fuzzy Sets and system. 350 (2018) 85--94]. Thereafter, we utilized our newly introduced concept to prove some existence and uniqueness theorems in $\mathcal{M}$-complete fuzzy metric spaces. Our results extend and generalize the corresponding results of Shukla et al.. Moreover, an example is adopted to exhibit the utility of newly obtained results.

The strategy of any organization is based on the growth of its customer base, and one of 6 its principles is that selling a product to an existing customer is much more profitable than acquiring 7 a new customer. However, this approach has several opportunities for improvement, since it usu- 8 ally has a totally reactive approach, which does not give opportunity to the areas specialized in 9 customer experience and recovery, to give an effective response for that moment, since the customer 10 is gone at the time of the intervention. This happens because usually a diagnostic analysis of cus- 11 tomers who have stopped buying products or services in a defined period, commonly three (3) pe- 12 riods or months, is performed. This paper challenges the way to face this problem, and proposes 13 the development of a complete solution, which does not focus exclusively on the prediction of 14 churn, as is usually done in the state of the art research, but to intervene in different interactions 15 that can be carried out with customers. The above focused not only to prevent customer churn, but 16 to generate an added value of continuous improvement in sales processes, increase customer pene- 17 tration, leading to an improvement in customer experience and consequently, an increase in cus- 18 tomer loyalty.

A global event such as the COVID-19 crisis presents new, often unexpected responses that are fascinating to investigate from both, scientific and social standpoints. Despite several documented similarities, the Coronavirus pandemic is clearly distinct from the 1918 flu pandemic in terms of our exponentially increased, almost instantaneous ability to access/share information, offering an unprecedented opportunity to visualise rippling effects of global events across space and time. Personal devices provide “big data” on people’s movement, the environment and economic trends, while access to the unprecedented flurry in scientific publications and media posts provides a measure of the response of the educated world to the crisis. Most bibliometric (co-authorship, co-citation, or bibliographic coupling) analyses ignore the time dimension, but COVID-19 has made it possible to perform a detailed temporal investigation into the pandemic. Here, we report a comprehensive network analysis based on more than 20000 published documents on viral epidemics, authored by over 75,000 individuals from 140 nations in the past one year of the crisis. In contrast to the 1918 flu pandemic, access to published data over the past two decades enabled a comparison of publishing trends between the ongoing COVID-19 pandemic and those of the 2003 SARS epidemic, to study changes in thematic foci and societal pressures dictating research over the course of a crisis.

The eruption of COVID-19 patients in 215 countries worldwide has urged for robust predictive methods that can detect as early as possible the size and duration of the contagious disease and also providing precision predictions. In much recent literature reported on COVID-19, one or more essential parts of such investigation were missed. One of the crucial elements for any predictive method is that such methods should fit simultaneously as much data as possible; these data could be total infected cases, daily hospitalized cases, cumulative recovered cases, and deceased cases, and so on. Other crucial elements include sensitivity and precision of such predictive methods on the amount of data as the contagious disease evolved day by day. To show the importance of these aspects, we have evaluated the standard SIRD model and a newly introduced Gaussian-SIRD model on the development of COVID-19 in Kuwait. It is observed that the SIRD model quickly picks up the main trends of COVID-19 development, but the Gaussian-SIRD model provides precise prediction a longer period of time.

In this paper we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators. We constructed some examples of polynomial automorphisms which show that a natural analogue of the Jacobian Conjecture for infinite dimensional spaces is not true. Also, we prove that any separable Fréchet space supports a transitive analytic operator which is not a polynomial. We found some connections of analytic automorphisms and algebraic bases of symmetric polynomials and applications to hypercyclisity of composition operators.

This paper is a slightly modified, abridged version of a previous work "Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference "Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

YH-DIE must have continuity . Given the basic algebraic clusters of homogeneous configurations,we can get the basic three equations: \begin{array}{l} {\mathop{\int}\nolimits_{0}\nolimits^{{x}_{i}}{\frac{{G}\left({{x}_{i}\mathrm{,}s}\right)}{{\left({{x}_{i}\mathrm{{-}}{s}}\right)}^{\mathit{\alpha}}}\mathrm{\varphi}\left({s}\right){ds}}\mathrm{{=}}{f}\left({{x}_{i}}\right)}\ ;\ {\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{i}}\left({\frac{{\mathrm{\partial}}_{{x}_{i}}G}{\sqrt{{1}\mathrm{{+}}{\left|{\mathrm{\nabla}{G}}\right|}^{2}}}}\right)\mathrm{{=}}{0}}\ ;\ {{i}\mathrm{{=}}\mathop{\sum}\limits_{{x}_{i}\mathrm{{=}}{1}}\limits^{\mathrm{\infty}}{\arccos\hspace{0.33em}\mathrm{\varphi}\left({{x}_{i}}\right)}\mathrm{{=}}{f}\left({\fbox{${Yuh}$}}\right)} \end{array} YH-DIE has become a fusion point and access point in the fields of algebraic geometry and partial differential equations, and its mapping on multidimensional algebraic clusters or manifolds is very special. The minimal surface equation is a special case.

We search for limit cycles in the dynamical model of two-species chemical reactions that contain seven reaction rate coefficients as parameters and at least one third-order reaction step, that is, the induced kinetic differential equation of the reaction is a planar cubic differential system. Symbolic calculations were carried out using the Mathematica (or, Wolfram language) mathematical program package, and it was also used for the numerical verifications to show the following facts: the kinetic differential equations of these reactions each has two limit cycles surrounding the stationary point of focus type in the positive quadrant. In the case of Model 1, the outer limit cycle is stable and the inner one is unstable that appears in a supercritical Hopf bifurcation. Moreover, the oscillations in a neighborhood of the outer limit cycle are slow-fast oscillations. In the case of Model 2, the outer limit cycle is unstable and the inner one is stable. With another set of parameters, the outer limit cycle can be made stable and the inner one unstable.

COVID-19 has created anxiety not only in individuals but also in health organizations, and countries worldwide. Not a single industry is left un-influenced and loss is being estimated in billions of dollars. The widespread of this pandemic disease has challenged researchers all over the world. Some of the researchers are working to invent its cure while, others are applying computing technologies to stop its spread, by analyzing and identifying patterns for prediction and forecasting. This is by no doubt the hottest area of research for the last 100 years. This survey has targeted the research published in computing sub-domains to combat the pandemic. The survey has clustered the scientific efforts into logical groups: surveillance, metrological effects, social media analytics, image processing and business and economy, analysis and modeling. It will serve as a leading source for the followings: researchers who want to identify what has been achieved in different computing sub-domains, those who need fresh authenticated datasets openly accessible for different research contexts and what are future directions in this area of research. The findings of analysis and modeling can be also useful for government agencies who want to set priorities and formulate policies.

While there are many models of epidemic evolution perhaps the basis for such models finds itself in the lumped behavior expressed through the so-called SIR model (Susceptible, Infectious, Recovered) from which spring many related models. This paper discusses multiple analytic solutions to that equation including those that are available in closed analytic form and those for which at least one final integral has to be done numerically, so-called quasi-analytic solutions. The solutions are intrinsically time-dependent of course. The hope is that such an investigation will lead to a better understanding of when and how models can be of use in studying the dynamical evolution of diseases including, perhaps, the great influenza pandemic of 1918 together with later pandemics and epidemics not excluding the Covid-19 pandemic of the present day.

COVID-19 emerged in Wuhan and is later declared as a pandemic by World Health Organization. Different-aged people have varying gender-wise immunity control properties that necessitates understanding COVID-19 impact on age and gender which does not exist, currently. In this paper, COVID-19 surveillance variables are extensively studied along with hospitalization, tests-performed, and recovery data. Dataset is curated from three sources; however, age and gender data belong to Belgium, particularly. Visualizations, frequencies, Pearson’s and polyserial correlation, student’s t-test, and Cramer’s V are used for enhanced analysis. Results show higher mortality rate in males and need of more ventilators to combat severe symptoms.

The use of smartphones, coupled with different sensors, makes it an attractive solution for measuring different physical and physiological features, allowing for the monitoring of various parameters and even identifying some diseases. The BITalino device allows the use of different sensors, including Electroencephalography (EEG) and Electrocardiography (ECG) sensors, to study different health parameters. With these devices, the acquisition of signals is straightforward, and it is possible to connect them using a Bluetooth connection. With the acquired data, it is possible to measure parameters such as calculating the QRS complex and its variation with ECG data to control the individual's heartbeat. Similarly, by using the EEG sensor one could analyze the individual's brain activity and frequency. The purpose of this paper is to present a method for recognition of the diseases related to ECG and EEG data, with sensors available in off-the-shelf mobile devices and sensors connected to a BITalino device. The data were collected during the elderly's experiences, performing the Timed-Up and Go test, and the different diseases found in the sample in the study. The data were analyzed, and the following features were extracted from the ECG, including heart rate, heart rate variability, the average QRS interval, the average R-R interval, and the average R-S interval, and the EEG, including frequency and variability. Finally, the diseases are correlated with different parameters, proving that there are relations between the individuals and the different health conditions.

A family of linear singularly perturbed Cauchy problems is studied. The equations defining the problem combine partial differential operators together with the action of linear fractional transforms. The exotic geometry of the problem in the Borel plane, involving both sectorial regions and strip-like sets, gives rise to asymptotic results relating the analytic solution and the formal one through Gevrey asymptotic expansions. The main results lean on the appearance of domains in the complex plane which remain intimately related to Lambert W function, which turns out to be crucial in the construction of the analytic solutions.

Kim-Kim [19] studied the type 2 degenerate poly-Bernoulli numbers and polynomials by using modified degenerate polylogarithm function. In this paper, we construct the type 2 degenerate poly-Cauchy polynomials and numbers of the second kind, called degenerate poly-Cauchy polynomials and numbers of the second kind by using degenerate polylogarithm function and derive several properties on the degenerate poly-Cauchy polynomials and numbers of the second kind. Furthermore, we consider the degenerate unipoly-Cauchy polynomials of the second kind and discuss some properties of them.

In [18], Kim et al. introduced the degenerate poly-Bernoulli polynomials by using polyexponential function. In this paper, we study the degenerate poly-Frobenius-Genocchi polynomials, which are called the type 2 degenerate poly-Frobenius-Genocchi polynomials, by means of polyexponential function. Then, we derive some useful relations and properties. We derive type 2 degenerate poly-Frobenius-Genocchi polynomials equal a linear combination of the degenerate Frobenius-Genocchi polynomials and Stirling numbers of the first kind. Furthermore, we introduce type 2 degenerate unipoly-Frobenius-Genocchi polynomials by means of unipoly function and derive explicit multifarious properties.

The COVID-19 infections in Pakistan are spreading at an exponential rate and a point may soon be reached where rigorous prevention measures would need to be adopted. Mathematical models can help define the scale of an epidemic and the rate at which an infection can spread in a community. I used ARIMA Model, Diffusion Model, SIRD Model and Prophet Model to forecast the magnitude of the COVID-19 pandemic in Pakistan and compared the numbers with the reported cases on the national database. Results depicts that Pakistan could hit peak number of infectious cases between June 2020 and July, 2020.

The work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work by the first two authors. The result leans on the application of a fixed point argument and the classical Ramis-Sibuya theorem.

A compartmental epidemiological model with seven groups is introduced herein, to account for the dissemination of diseases similar to the Coronavirus disease 2019 (COVID-19). In its simplified version, the model contains ten parameters, four of which relate to characteristics of the virus, whereas another four are transition probabilities between the groups; the last two parameters enable the empirical modelling of the effective transmissibility, associated in this study with the cumulative number of fatalities due to the disease within each country. The application of the model to the fatality data (the main input herein) of five countries (to be specific, of those which had suffered most fatalities by April 30, 2020) enabled the extraction of an estimate for the basic reproduction number $R_0$ for the COVID-19 disease: $R_0=4.91(33)$.

The world is facing new challenges every day; however, with the spread of the pandemic around the world, this new challenge is different. The pandemic is increasing and concentrating various challenges simultaneously. Although different sectors are facing consequences, the most important sectors, that is, health and economy are the most affected. When the pandemic began, it was not known how long it would last, which complicated health and economic planning. Therefore, it is important for decision makers and the public to know the predictions and expectations of the future of these challenges. In this work, the current situation is analyzed. Then, an expectation model is developed based on the statistics of the pandemic using a growth rate model based on an exponential and logarithmic rate of increase. Based on the available open data about the pandemic spread, the model can successfully predict future expectations, including the duration and maximum number of cases of the pandemic. The model uses the equilibrium point as the day the cases decrease. The model can be used for planning and the development of strategies to overcome these challenges.

This paper presents a new interactive visualization system to represent and compare rate of spread of COVID 19 pandemic across different countries over time. We surveyed existing visualization techniques used in various websites and media outlets and introduced use of a knee detection algorithm that divides the exponential spread in multiple linear components. A set of use cases demonstrates the utility of the system in comparing the spread across different countries for both analysis and prediction.

Increasingly, genomics is being used for the prediction of specific traits and diseases (phenotypes) among humans. Wider availability of genomics data through multiple research projects (such as International HapMap Project1 and 1000 Genomes2) has been a catalyst in that direction. With the recent advances in machine learning and big data analysis, data computation resources and data models needed for genomics data analysis are readily available. However, the prediction of traits and diseases has its own challenges in terms of computational requirements and computational analysis, statistical analysis (example: confounding variables), and limited quality of data collection. Linear Mixed Models (LMM, a type of linear regression) is a common approach for Genome-wide Association Studies (GWAS) for the prediction of common traits among humans using genomics. This paper researches the existing LMM-based approaches for Genome-wide Association Studies (GWAS), describes the experiment performed on FaST-LMM approach from Microsoft Research, and then proposes an enhanced approach (called LMM-22) on how to address computational and statistical issues. LMM-22 focuses on the parallelization of LMM computations and execution of LMM-22 on General Purpose Graphics Processing Units (GPU) as against CPUs to accelerate the LMM approach for GWAS studies.

We know that the classical Mittag-Leffler function play an important role as solution of fractional order differential and integral equations. We introduce the j-generalized p - k Mittag-Leffler function. We evaluate the second order differential recurrence relation and four different integral representations and introduce a homogeneous linear differential equation whose one of the solution is the j-generalized p-k Mittag-Leffler function. Also we evaluate the certain relations that exist between j-generalized p - k Mittag-Leffler function and Riemann-Liouville fractional integrals and derivatives. We evaluate Mellin-Barnes integral representation of j-generalized p-k Mittag-Le er Function. The relationship of j-generalized p-k Mittag-Leffler Function with Fox H-Function and Wright hypergeometric function is also establish. we obtained its Euler transform, Laplace Transform and Mellin transform. Finally we derive some particular cases.

A nonlinear singularly perturbed Cauchy problem with confluent fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value problem with logarithmic reliance in time has been investigated by the author in a recent work, for which sets of holomorphic inner and outer solutions were built up and expressed as a Laplace transform with logarithmic kernel. Here, a family of holomorphic inner solutions are constructed by means of exponential transseries expansions containing infinitely many Laplace transforms with special kernel. Furthermore, asymptotic expansions of Gevrey type for these solutions relatively to the perturbation parameter are established.

The necessary and sufficient conditions of existence of the nonlinear operator equations' branches of solutions in the neighbourhood of branching points are derived. The approach is based on reduction of the nonlinear operator equations to finite-dimensional problems. Methods of nonlinear functional analysis, integral equations, spectral theory based on index of Kronecker-Poincare, Morse-Conley index, power geometry and other methods are employed. Proposed methodology enables justification of the theorems on existence of bifurcation points and bifurcation sets in the nonstandard models. Formulated theorems are constructive. For a certain smoothness of the nonlinear operator, the asymptotic behaviour of the solutions is analysed in the neighbourhood of the branch points and uniformly converging iterative schemes with a choice of the uniformization parameter enables the comprehensive analysis of the problems details. General theorems are illustrated on the nonlinear integral equations.

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on Jan 30, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April 2020. Taking this into account, in the present work, we are studying a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual social response and control measures by the government. The real data available about infectious cases from $14^{th}$ March to $26^{th}$ March 2020 is analysed and accordingly various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Numerical computations are done utilizing the iterative Laplace transform method. In the end, we illustrate the obtained results graphically. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

In this manuscript we report new effects of resonance detuning on various dynamical parameters of a generic 3-wave system. Namely, for suitably chosen values of detuning the variation range of amplitudes can be significantly wider than for exact resonance. Moreover, the range of energy variation is not symmetric with respect to the sign of the detuning. Finally, the period of the energy oscillation exhibits non-monotonic dependency on the magnitude of detuning. These results have important theoretical implications where nonlinear resonance analysis is involved, such as geophysics, plasma physics, fluid dynamics. Numerous practical applications are envisageable e.g. in energy harvesting systems.

In this article, we introduce a relatively new concept of multi-valued (θ;R)-contractions and utilize the same to prove some xed point results for a new class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type.

This work investigates centered polygonal lacunary functions restricted from the unit disk onto symmetry angle space which is defined by the symmetry angles of a given centered polygonal lacunary function. This restriction allows for one to consider only the p-sequences of the centered polygonal lacunary functions which are bounded, but not convergent, at the natural boundary. The periodicity of the $p$-sequences naturally gives rise to a convergent subsequence, which can be used as a grounds for decomposition of the restricted centered polygonal lacunary functions. A mapping of the unit disk to the sphere allows for the study of the line integrals of restricted centered polygonal that includes analytic progress towards closed form representations. Obvious closures of the domain obtained from the spherical map lead to four distinct topological spaces of the "broom topology'' type.

Industry 4.0 is having a great impact in all smart efforts. This is not a single product, but is composed of several technologies, being one of them Industrial Internet of Things (IIoT). Currently, there are very varied implementation options offered by several companies, and this imposes a new challenge to companies that want to implement IoT in their processes. This challenge suggests to use multi-criteria analysis to make a repeatable and justified decision, requiring a set of alternatives and criteria. This paper proposes a new methodology and comprehensive criteria to help organizations to take an educated decision by applying multi-criteria analysis. Here, we suggest a new original use of PROMETHEE-II with full example from weight calculation up to IoT platform selection, showing this methodology as an effective study for other organizations interested to select an IoT platform. The criteria proposed outstands from previous work by including not only technical aspects, but economic and social criteria, providing a full view of the problem analyzed. A case of study was used to prove this proposed methodology.

Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results. This involves the expression for the Laurent coefficients including the residue, the Kronecker limit formulas and higher order coefficients as well as the difference formed to cancel the inaccessible part, typically the Clausen functions. We also state Abelian results which yield asymptotic formulas for weighted summatory function from that for the original summatory function

In the present work we study the existence of solutions for hybrid nonlinear fractional integrodifferential equations. We developed an algorithm by using the operator theoretical techniques in order to obtain the approximate solutions. The main results depend on the Dhage iteration method that were incorporated with the modern hybrid fixed point theorems. The approximate solutions were obtained by using Lipschitz conditions and weaker form of mixed partial continuity. Further, we provide some examples to explain the hypotheses and the related results.

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

This note first summarizes the history of the manuscript "On a Continuum Model for Avalanche Flow and Its Simplified Variants" by Grigorian and Ostroumov―published in the Special Issue on snow avalanche dynamics of Geosciences―since the early 1990s and explains the guiding principles in editing it for publication. The changes are then detailed and some explanatory notes given for the benefit of readers who are not familiar with the early Russian work on snow avalanche dynamics. Finally, the editor's personal views as to why he still considers this paper of relevance for avalanche dynamics research today are presented in brief essays on key aspects of the paper, namely the role of simple and complex models in avalanche research and mitigation work, the status and possible applications of Grigorian's stress-limited friction law, and non-monotonicity of the dynamics of the Grigorian–Ostroumov model in the friction coefficient. A comparison of the erosion model proposed by those authors with two other models suggests to enhance it with an additional equation for the balance of tangential momentum across the shock front. A preliminary analysis indicates that continuous scouring entrainment is possible only in a restricted parameter range and that there is a second erosion regime with delayed entrainment.

In this article, we establish sharp trigonometric-polynomial bounds for unnormalized sinc function.

In this paper, we consider the generalized sextic functional equation \begin{align*} \sum_{i=0}^{7}{}_7 C_{i} (-1)^{7-i}f(x+iy) = 0. \end{align*} And by applying the fixed point theory in the sense of L. C\u adariu and V. Radu, we will discuss the stability of the solutions for this functional equation.

Risk modelling along with multi-objective optimization problems have been at theepicenter of attention for supply chain managers. In this paper, we introduce a datasetfor risk modelling in sophisticated supply chain networks based on formal mathematical models. We have discussed the methodology and simulation tools used to synthesize the dataset. Additionally, the underlying mathematical models are discussed in granular details along with providing directions to conducting statistical analyses or neural machine learning models. The simulation is performed using MATLAB ™Simulink and the models are illustrated as well.

We show that if $f$ is a non-negative superquadratic function, then $A\mapsto\mathrm{Tr}f(A)$ is a superquadratic function on the matrix algebra. In particular, \begin{align*} \tr f\left( {\frac{{A + B}}{2}} \right) +\tr f\left(\left| {\frac{{A - B}}{2}}\right|\right) \leq \frac{{\tr {f\left( A \right)} + \tr {f\left( B \right)} }}{2} \end{align*} holds for all positive matrices $A,B$. In addition, we present a Klein's inequality for superquadratic functions as $$ \mathrm{Tr}[f(A)-f(B)-(A-B)f'(B)]\geq \mathrm{Tr}[f(|A-B|)] $$ for all positive matrices $A,B$. It gives in particular improvement of Klein's inequality for non-negative convex function. As a consequence, some variants of the Jensen trace inequality for superquadratic functions have been presented.

This paper deals with the study of the existence and non existence of solutions of a three parameter's family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the $\alpha$-Riemann-Liouville fractional derivative, with $\alpha \in (1,2]$. In order to deduce the existence and non existence results, we first study the linear equation, by deducing the main properties of the related Green's functions. We obtain the optimal set of parameters where the Green's function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results.

In this article, we show the existence of fixed point for the derivative of interval-valued functions. Meanwhile, the fixed point inquiry will utilize the common fixed point methods under the condition of compatibility of the hybrid composite mappings in the sense of the Hausdorff metric. Some examples are given to support the usability of the result of this research .

There are many criterion to generalize the concept of numerical radius; one of the most recent interesting generalization is what so called the generalized Euclidean operator radius. Simply, it is the numerical radius of multivariable operators. In this work, several new inequalities, refinements and generalizations are established for this kind of numerical radius.

We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. Equivalent statements of a non-commutative version of Jensen's inequality for operator superquadratic function are established. A generalization of the main result to any positive unital linear map is also provided.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2}% ,\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

In this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta's inequality are obtained. Some particular cases are also provided.

Statistical inferences is regarded as the general criteria for statistical conclusion and drawing generalizations. However, most of the inferential statistical tools are based on strong assumptions which create a strict limitations on their use and application. Analysis of variance (ANOVA) is one of such statistics. In this article, eight (8) new ANOVA-like methodologies were proposed, in alternative to one-way ANOVA, based on the assumptions of statistical mirroring. Methods validation in comparison with one-way ANOVA was designed to assess the suitability and statistical power of the new proposals as an alternative methods, using different sets of logically generated multivariate datasets with different problems and statistical complications. The results of comparisons validate that the eight (8) proposed ANOVA-like methodologies were suitable alternatives to ANOVA, in the sense that they require no normality assumption to be meet, used different ways to compare the data with different statistical elements rather than depending on only variance, efficient with negative values, and results interpretation is easier.

Assume that $f:C\rightarrow \mathbb{R}$ is subadditive (superadditive) and hemi-Lebesgue integrable on $C,$ a cone in the linear space $X$ with $0\in C. $ Then for all $x,$ $y\in C$ and a symmetric Lebesgue integrable and nonnegative function $p:\left[ 0,1\right] \rightarrow \lbrack 0,\infty ),$ \begin{align*} \frac{1}{2}f\left( x+y\right) \int_{0}^{1}p\left( t\right) dt& \leq \left( \geq \right) \int_{0}^{1}p\left( t\right) f\left( \left( 1-t\right) x+ty\right) dt \\ & \leq \left( \geq \right) \int_{0}^{1}p\left( t\right) f\left( tx\right) dt+\int_{0}^{1}p\left( t\right) f\left( ty\right) dt. \end{align*} In particular, for $p\equiv 1,$ we have \begin{equation*} \frac{1}{2}f\left( x+y\right) \leq \left( \geq \right) \int_{0}^{1}f\left( \left( 1-t\right) x+ty\right) dt\leq \left( \geq \right) \int_{0}^{1}f\left( tx\right) dt+\int_{0}^{1}f\left( ty\right) dt. \end{equation*} Some particular inequalities related to Jensen's dicrete inequality for convex functions are also given.

This paper aims to investigate the criteria of behaviour of certain type of third order neutral generalized difference equations with distributed delay. With the technique of generalized Riccati transformation and Philos-type method, some oscillation criteria are obtained to ensure convergence and oscillatory solution of suitable example is listed to illustrate the main result.

In this study, we define new classes of convexity called of h-Godunova-Levin and h-Godunova-Levin preinvexity, through which some new inequalities of Hermite-Hadamard type were established. These new classes are the generalisation of several known convexity including the s-convex, P-function, Godunova-Levin. Further, the properties of h-Godunova-Levin function were also discussed. Meanwhile, the applications of h-Godunova-Levin Preinvex function are given

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

In this article, the new Hermite–Hadamard type inequalities are studied via generalized s-convexity on fractal sets. These inequalities derived on fractal sets are shown to be the generalized s-convexity on fractal sets. We proved that the absolute values of the first and second derivatives for the new inequalities are the generalization of s-convexity on fractal sets.

Some refinements and reverses of the Fejer's inequality for convex functions are given.

In this article, we establish the existence of and then compare smallest eigenvalues for nabla fractional boundary value problems involving a fractional difference boundary condition, using the theory of u0-positive operators with respect to a cone in a Banach space.

We present a discussion and analysis regarding the benefits and limitations of open and non-anonymized peer review based on literature results and responses to a survey on the reviewing process of alt.chi, a more or less open-review track within the CHI conference, the predominant conference in the field of human-computer interaction (HCI). This track currently is the only implementation of an open-peer-review process in the field of HCI while, with the recent increase in interest in open science practices, open review is now being considered and used in other fields. We collected 30 responses from alt.chi authors and reviewers and found that, while the benefits are quite clear and the system is generally well liked by alt.chi participants, they are reluctant to see it used in other venues. This concurs with a number of recent studies that suggest a divergence between support for a more open review process and its practical implementation. The data and scripts are available on https://osf.io/vuw7h/, and the figures and follow-up work on http://tiny.cc/OpenReviews.

Let ${\mathcal{SR}}^*$ be the class of starlike functions with real coefficients, i.e., the class of analytic functions $f$ which satisfy the condition $f(0)=0=f'(0)-1$, Re{z f'(z) / f (z)} > 0, for $z\in\mathbb{D}:=\{z\in\mathbb{C}:|z|<1 \}$ and $a_n:=f^{(n)}(0)/n!$ is real for all $n\in\mathbb{N}$. In the present paper, the sharp estimates of the third Hankel determinant $H_{3,1}$ over the class ${\mathcal{SR}}^*$ are computed.

Comorbidities can have a cumulative effect on hospital outcomes of care, such as the length of stay (LOS), and hospital mortality. This study examines patients hospitalized with Congestive Heart Failure (CHF), a life-threatening condition, which, when it coexists with a burdened disease profile, the risk for negative hospital outcomes increases. Since coexisting conditions co-interact, with a variable effect on outcomes, clinicians should be able to recognize these joint effects. In order to study CHF comorbidities, we used medical claims data from CMS. After extracting the most frequent cluster of CHF comorbidities, we: (i) Calculated, step-by-step, the conditional probabilities for each disease combination inside this cluster (ii) Estimated the cumulative effect of each comorbidity combination on the LOS and hospital mortality (iii) Constructed (a) Bayesian, scenario-based graphs and (b) Bayes-networks to visualize results. Results show that, for CHF patients, different comorbidity constructs have variable effect on the LOS and hospital mortality. Therefore, dynamic comorbidity risk assessment methods should be implemented for informed clinical decision making in any ongoing effort for quality of care improvements.

The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

Frames are more stable as compared to bases under the action of a bounded linear operator. Sums of different frames under the action of a bounded linear operator are studied with the help of analysis, synthesis and frame operators. A simple construction of frames from the existing ones under the action of such an operator is presented here. It is shown that a frame can be added to its alternate dual frames, yielding a new frame. It is also shown that the sum of a pair of orthogonal frames is a frame. This provides an easy construction of a frame where the frame bounds can be computed easily. Moreover, for a pair of orthogonal frames, the necessary and sufficient condition is presented for their alternate dual frames to be orthogonal. This allows for an easy construction of a large number of new frames.

The complete-lattice approach to optimization problems with a vector- or even set-valued objective already produced a variety of new concepts and results and was successfully applied in finance, statistics and game theory. For example, the duality issue for multi-criteria and vector optimization problems could be solved using the complete-lattice approach, compare [11]. So far, it has been applied to set-valued dynamic risk measures (in the stochastic case), as discussed in Feinstein, Rudloff etc. (see [11], for example), but it has not been applied to deterministic calculus of variations and optimal control problems. In this paper, the following problem of set-valued optimization is considered: minimize the functional $$ \overline J_t[y]=\int_0^t \overline L(s,y(s),\dot y(s))\ ds + U_0(y(0)) $$ over all admissible arcs $y$, where $\overline L$ is the associated multifunction to a vector-valued Lagrangian $L$, the integral is in the Aumann sense and $U_0$ is the initial cost. A new concept of \emph{value function}, for which a Bellman's optimality principle holds, is introduced. Also the classical result of the Hopf-Lax formula holds for the generalized value function. Finally, a derivative with respect to the time $t$ and a directional derivative with respect to $x$ of the value function are defined, based on ideas close to the concepts in [12]. The value function is proved to be solution of a suitable Hamilton-Jacobi equation.

This paper is devoted to the study of reproducing kernels on 2-inner product Hilbert spaces. We focus on a new structure to produce reproducing kernel Hilbert and Banach spaces. According to multi-variable computing, this structures can be useful in electrocardiographs, machine learning and economy

Partial sums of analytic univalent functions and partial sums of starlike have been investigated extensively by several researchers. In this paper, we investigate a partial sums of convex harmonic functions that are univalent and sense preserving in the open unit disk.

In this paper, it is proved that s-iteration with error and Picard-Mann iteration with error iterative processes converge strongly to the unique fixed point of Lipschitzian strongly pseudo-contractive map. This convergence is almost -stable and -stable. Applications of these results to the operator equations, where is a strongly accretive and accretive mappings of into itself.

In this paper, I investigate Hyers-Ulam-Rassias stabilities of the general quintic functional equation and the general sextic functional equation.

Optinalysis, as a method of symmetry detection, is a new advanced computational algorithm that intrametrically (within elements) or intermetrically (between elements) computes and compares two or more multivariate sequences in an unclustered or clustered manner as a mirror-like reflection of each other (optics-like manner), hence the name is driven. Optinalysis is based by the principles of reflection and moment about a symmetrical line which detects symmetry that reflects a similarity measurement. Optinalysis is suitable for quantitative and qualitative data types, with or without replications, provided it conform the algorithmic requirements there provided. Optinalysis can be organized for geometrical, geostatistical and statistical analysis in one-way, two-way, or three-way approach. A simulation comparisons shows that Optinalysis is a simple alternative approach of multivariate analysis of sociometric, demographic, socio-demographic, psychometric, ecological, experimental, genomic, nanoparticle and shape morphometric data. Optinalysis of these data matrix shows very similar results or conclusions with some multivariate analysis such as skewness measure, one-way ANOVA, paired t-test, one sample t-test, Tukey’s multiple comparisons, BLAST sequence algorithmic analysis (percentages of identity, similarity, gabs, and positives, and the Needleman-Wunsch score), and Riemannian distance.

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

In the present paper, we introduced and study a new class of harmonic univalent functions on unit disc U. also we obtain coefficient conditions, extreme points, convolution condition for the above class of harmonic univalent functions.

In the neuroscience research field, specific for medical imaging analysis, how to mining more latent medical information from big medical data is significant for us to find the solution of diseases. In this review, we focus on neuroimaging data that is functional Magnetic Resonance Imaging (fMRI) which non-invasive techniques, it already becomes popular tools in the clinical neuroscience and functional cognitive science research. After we get fMRI data, we actually have various software and computer programming that including open source and commercial, it's very hard to choose the best software to analyze data. What's worse, it would cause final result imbalance and unstable when we combine more than software together, so that's why we want to make a pipeline to analyze data. On the other hand, with the growing of machine learning, Python has already become one of very hot and popular computer programming. In addition, it is an open source and dynamic computer programming, the communities, libraries and contributors fast increase in the recent year. Through this review, we hope that can make neuroimaging data analysis more easy, stable and uniform base the one platform system.

In this paper, we study the weighted reproducing kernels. We introduce a generalization of weighted reproducing property and extend it to relative reproducing property on Banach spaces. This generalization will develop the parallel computing and it can be used as a base of parallel learning for machines especially in the case that there are non-homogenous weighted hypothesis. This methods formulate learning and estimation problems in a relative reproducing kernel Banach space (RRKBS) of functions defined on the data domain, expanded in terms of a kernel.

We present smooth approximations to $ \vert{x} \vert $ using sigmoid functions. In particular $ x\,erf(x/\mu) $ is proved to be better smooth approximation for $ \vert{x} \vert $ than $ x\,tanh(x/\mu) $ and $ \sqrt{x^2 + \mu} $ with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for error function.

In this paper, we study the convergence of new implicit iterations dealing with n-tupled fixed point results for nonlinear contractive-like mappings on W-hyperbolic metric spaces. Herein, we demonstrate that our newly implicit iteration schemes have faster rate of convergence than implicit S-iteration process, implicit Ishikawa and Mann type iteration processes. Furthermore, a numerical simulation to improve our theoretical results is obtained.

In this review paper, we present a pellucid proof of how x tanh(x/µ) approximates |x|and is better than √x² +µ  when we are concernedwith accuracy.

E-commerce businesses employ recommender models to assist in identifying a personalized set of products for each visitor. To accurately assess the recommendations’ influence on customer clicks and buys, three target areas—customer behavior, data collection, user-interface —will be explored for possible sources of erroneous data. Varied customer behavior misrepresents the recommendations’ true influence on a customer due to the presence of B2B interactions and outlier customers. Non-parametric statistical procedures for outlier removal are delineated and other strategies are investigated to account for the effect of a large percentage of new customers or high bounce rates. Subsequently, in data collection we identify probable misleading interactions in the raw data, propose a robust method of tracking unique visitors, and accurately attributing the buy influence for combo products. Lastly, user-interface issues discuss the possible problems caused due to the recommendation widget’s positioning on the e-commerce website and the stringent conditions that should be imposed when utilizing data from the product listing page. This collective methodology results in an exact and valid estimation of the customer’s interactions influenced by the recommendation model in the context of standard industry metrics such as Click-through rates, Buy-through rates, and Conversion revenue.

In this paper we define a continuous wavelet transform of a Schwartz tempered distribution $f \in S^{'}(\mathbb R^n)$ with wavelet kernel $\psi \in S(\mathbb R^n)$ and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of $S^{'}(\mathbb R^n)$. It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.

We present the real number system as a natural generalization of the natural numbers. First, we prove the co-finite topology, $Cof(\mathbb N)$, is isomorphic to the natural numbers. Then, we generalize these results to describe the continuum $[0,1]$. Then we prove the power set $2^{\mathbb Z}$ contains a subset isomorphic to the non-negative real numbers, with all its defining structure of operations and order. Finally, we provide two different constructions of the entire real number line. We see that the power set $2^{\mathbb N}$ can be given the defining structure of $\mathbb R$. The constructions here provided give simple rules for calculating addition, multiplication, subtraction, division, powers and rational powers of real numbers, and logarithms. The supremum and infimum are explicitly constructed by means of a well defined algorithm that ends in denumerable steps. In section 5 we give evidence our construction of $\mathbb N$ and $\mathbb R$ are canonical; these constructions are as natural as possible. In the same section, we propose a new axiomatic basis for analysis. In the last section we provide a series of graphic representations and physical models that can be used to represent the real number system. We conclude that the system of real numbers is completely defined by the order structure of $\mathbb N$.}

The authors intend to establish new oscillation criteria for a class of generalized third order functional difference equation of the form \begin{equation}{\label{eq01}} \Delta_{\ell}\left(a_2(n)\left[\Delta_{\ell}\left(a_1(n)\left[\Delta_{\ell}z(n)\right]^{\beta_1}\right)\right]^{\beta_2}\right)+q(n)f(x(g(n)))=0, ~~n\geq n_0, \end{equation} where $z(n)=x(n)+p(n)x(\tau(n))$. We also present sufficient conditions for the solutions to converges to zero. Suitable examples are presented to validate our main results.

The aim of this article is to extend the local as well as the semi-local convergence analysis of multi-point iterative methods using center Lipschitz conditions in combination with our idea, of the restricted convergence region. It turns out that this way a finer convergence analysis for these methods is obtained than in earlier works and without additional hypotheses. Numerical examples favoring our technique over earlier ones completes this article.

In this paper, we study sums of finite products of Chebyshev polynomials of the first kind and Lucas polynomials and represent each of them in terms of Chebyshev polynomials of all kinds. Here the coefficients involve terminating hypergeometric functions ₂F₁ and these representations are obtained by explicit computations.

Consider a uniquely ergodic $C^*$-dynamical system ba\-sed on a unital $*$-endomorphism $\Phi$ of a $C^*$-algebra. We prove the uniform convergence of Cesaro averages $\frac1{n}\sum_{k=0}^{n-1}\lambda^{-n}\Phi(a)$ for all values $\lambda$ in the unit circle which are not eigenvalues corresponding to "measurable non continuous" eigenfunctions. This result generalises the analogous one in commutative ergodic theory presented in [19], which turns out to be a combination of the Wiener-Wintner Theorem (cf. [22]) and the uniformly convergent ergodic theorem of Krylov and Bogolioubov (cf. [15]).