In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

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 .

In this paper we establish some generalizations of Opial’s inequal- ities for Riemann-Stieltjes integral and for two functions. Applications related to trapezoid and Grüss’ ’type inequalities are also given.

In this paper, we introduce a general family of Lagrange-based Apostol-type Hermite polynomials thereby unifying the Lagrange-based Apostol Hermite-Bernoulli and the Lagrange-based Apostol Hermite-Genocchi polynomials. We also define Lagrange-based Apostol Hermite-Euler polynomials via the generating function. In terms of these generalizations, we find new and useful relations between the unified family and the Apostol Hermite-Euler polynomials. We also derive their explicit representations and list some basic properties of each of them. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.

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.

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.

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.

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.

Soft set theory is a mathematical tool for dealing with uncertainty. This paper investigates limits of interval type of soft sets (for short, it-soft sets). The concept of it-soft sets is first introduced. Then, limits of it-soft sets are proposed and their properties are obtained. Next, point-wise continuity of it-soft sets and continuous it-soft sets are discussed. Finally, an application for rough sets is given.

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.

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 .

The rapid penetration of social media has been redefining every facet of the old marketing and customer engagement tactics, not only for the low-end and mass products but also for luxury brands. In this context, brands are dealing with the challenge of keeping the balance between using mass marketing strategies concurrent with accentuating the exclusivity of their offerings. Social media can be considered a boon if brands employ them to reach the right audience and use the right platform by incorporating the right content. In this work, we propose a sector-specific, integrated, and holistic investigation of the social media strategies of luxury brands, together with the impact they generate in terms of the engagement level of the users as an indicator of their success. We provide empirical validation of the method in the sector of luxury fashion brands in the Italian market, providing qualitative and quantitative analysis of the content shared on social media, considering the type, timing, and modality of the sharing. We evaluate consumer-brand engagement in different contexts, including important live events in the field.

The prim objective of commenced article is to determine q-sumudu transforms of a product of unified family of q-polynomials with basic (or q-) analogue of fox’s H-function and q-analog of I-functions. Specialized cases of the leading outcome are further evaluated as q-sumudu transform of general class of q-polynomials and q-sumudu transforms of the basic analogues of Fox’s H-function and I-functions.

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.

This paper is concerned with representing sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials. Indeed, by explicit computations each of them is expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer and Jacobi polynomials which involve the hypergeometric functions ${}_1 F_1$ and ${}_2 F_1$.

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.

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.

In this paper, we consider the zero distributions of q-shift monomi-als and difference polynomials of meromorphic functions with zero order, that extends the classical Hayman results on the zeros of differential poly-nomials to q-shift difference polynomials. We also investigate problem of q-shift difference polynomials that share a common value.

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 paper, we introduce and study the notion of rough I₂-lacunary statistical convergence of double sequences in normed linear spaces. We also introduce the notion of rough I₂-lacunary statistical limit set of a double sequence and discuss about some properties of this set.

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: $R_0=4.91(33)$.

In this paper, we introduced many new notions and new contraction named as S-weakly contraction after that we obtained the p-common best proximity point theorems for different types of contractions in the setting of complete metric spaces by using weak P_p-property and proved the uniqueness of these points. Also we presented some examples to prove the validity of our results.

We analyze the modular geometry of the variable exponent Lebesgue space L^p(.). We show that L^p(.) possesses a modular uniform convexity property. Part of the novelty is that the property holds even in the case supp(x) = ∞ . We present specific applications to fixed point theory. xÆΩ

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.

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 work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci-Mann iteration process defined by $$x_{n+1} = t_n T^{\phi(n)}(x_n) + (1-t_n)x_n,$$ for $n \in \mathbb{N}$, when $T$ is a monotone asymptotically nonexpansive self-mapping.

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

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.

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.

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.

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.

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 provide amongst others some simple error bounds in approximating the weighted Riemann-Stieltjes integral $\int_{a}^{b}f\left(t\right) g\left(t\right) dv\left(t\right) $ by the use of three points formula \begin{equation*} f\left(b\right) \int_{c}^{b}g\left(s\right) dv\left(s\right) +f\left(a\right) \int_{a}^{d}g\left( s\right) dv\left( s\right) -f\left(x\right) \int_{c}^{d}g\left(t\right) dv\left(t\right) \end{equation*} where $x,$ $c,$ $d\in \left[a,b\right],$ $g,$ $v:\left[a,b\right] \rightarrow \mathbb{C}$ under bounded variation and Lipschitzian assumptions for the function $f$ and such that the involved Riemann-Stieltjes integrals exist.

We construct families of ground state representations of the U(1)-current net and of the Virasoro nets Vir_c with central charge c ≥ 1. We show that these representations are not covariant with respect to the original dilations, and those on the U(1)-current net are not solitonic. Furthermore, by going to the dual net of with respect to the ground state representations of Vir_c, one obtains possibly new family of Möbius covariant nets on S¹.

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 we provide some bounds for the error in approximating the Riemann-Stieltjes integral $\int_{a}^{b}f (t) du (t)$ by the generalized trapezoidal rule \begin{equation*} \left[ u\left( b\right) -u\left( x\right) \right] f\left( b\right) +\left[ u\left( x\right) -u\left( a\right) \right] f\left( a\right) \end{equation*} under various assumptions for the integrand $f$ and the integrator $u$ for which the above integral exists. Applications for continuous functions of selfadjoint operators and unitary operators in Hilbert spaces are provided as well.

We recently formulated Modular Dvoretzky, Type-Cotype, Khinchin-Kahane and Grothendieck Inequality problems in the Appendix of \textit{[arXiv:2302.03718v1]}. For the sake of wide accessibility we give a separate treatment of them.

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.

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.

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.

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.

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.

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.

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.

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.

Using a theorem of Ulam and Hyers, we will prove the Hyers-Ulam stability of two-dimensional Lagrange's mean value points $(\eta, \xi)$ which satisfy the equation, $f(u, v) - f(p, q) = (u-p) f_x(\eta, \xi) + (v-q) f_y(\eta, \xi)$, where $(p, q)$ and $(u, v)$ are distinct points in the plane. Moreover, we introduce an efficient algorithm for applying our main result in practical use.

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.

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.

The Medi-test system we developed was motivated by the large number of resources available for the medical domain, as well as the number of tests needed in this field (during and after the medical school) for evaluation, promotion, certification, etc. Generating questions to support learning and user interactivity has been an interesting and dynamic topic in NLP since the availability of e-book curricula and e-learning platforms. Current e-learning platforms offer increased support for student evaluation, with an emphasis in exploiting automation in both test generation and evaluation. In this context, our system is able to evaluate a student’s academic performance for the medical domain. Using as input medical reference texts and supported by a specially designed medical ontology, Medi-test generates different types of questionnaires for Romanian language. The evaluation includes 4 types of questions (multiple-choice, fill in the blanks, true/false and match), can have customizable length and difficulty and can be automatically graded. A recent extension of our system also allows for the generation of tests which include images. We evaluated our system with a local testing team, but also with a set of medicine students, and user satisfaction questionnaires showed that the system can be used to enhance learning.

This paper treats the connection problem of expressing sums of finite products of Chebyshev polynomials of the third and fourth kinds in terms of five classical orthogonal polynomials. In fact, by carrying out explicit computations each of them are expressed as linear combinations of Hermite, generalized Laguerre, Legendre, Gegenbauer, and Jacobi polynomials which involve some terminating hypergeometric functions ${}_2 F_0, {}_2 F_1$, and ${}_3 F_2$.

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.

In this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.

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 $\mathbb N$.}

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

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 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.

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.

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.

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.

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 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.

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 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.

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

We prove general stability theorems for $n$-dimensional quartic-cubic-quadratic-additive type functional equations of the form \begin{eqnarray*} \sum_{i=1}^\ell c_i f \big( a_{i1}x_1 + a_{i2}x_2 + \cdots + a_{in}x_n \big) = 0 \end{eqnarray*} by applying the direct method. These stability theorems can save us much trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

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

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

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.

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 [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.

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.

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.

COVID-19 is the most severe health crisis of the 21st century. COVID-19 presents a threat to almost all countries world-wide. The restriction of human mobility is one of the strategies used to control the transmission of COVID-19. However, it has yet to be determined how effective this restriction is in controlling the rise in COVID-19 cases, particularly in major capital cities such as Jakarta, Indonesia. Using Facebook's mobility data, our study explores the impact of restricting human mobility on COVID-19 case control in Jakarta. Our main contribution is showing how the restriction of human mobility data can give important information about how COVID-19 spreads in different places. We proposed modifying a global regression model into a local regression model by accounting for the spatial and temporal interdependence of COVID-19 transmission across space and time. We applied Bayesian hierarchical Poisson spatiotemporal models with spatially varying regression coefficients. We estimated the regression parameters using an Integrated Nested Laplace Approximation. We found that the local regression model with spatially varying regression coefficients outperforms the global regression model based on DIC, WAIC, MPL, and R2 criteria for model selection. In Jakarta's 44 districts, the impact of human mobility varies significantly. The impacts of human mobility on the log relative risk of COVID-19 range from –4.445 to 2.353. The prevention strategy involving the restriction of human mobility may be beneficial in some districts but ineffective in others. Therefore, a cost-effective strategy had to be adopted.

We prove the non-Archimedean (resp. p-adic) Banach space version of non-Archimedean (resp. p-adic) Welch bounds recently obtained by M. Krishna. More precisely, we prove following results. \begin{enumerate}[\upshape(i)] \item Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying $\left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2$ for all $ \lambda_j \in \mathbb{K}, 1\leq j \leq n$, for all $n \in \mathbb{N}.$ Let $\mathcal{X}$ be a $d$-dimensional non-Archimedean Banach space over $\mathbb{K}$. If $\{\tau_j\}_{j=1}^n$ is any collection in $\mathcal{X}$ and $\{f_j\}_{j=1}^n$ is any collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) satisfying $f_j(\tau_j) =1$ for all $1\leq j \leq n$ and the operator $S_{f, \tau} : \text{Sym}^m(\mathcal{X})\ni x \mapsto \sum_{j=1}^nf_j^{\otimes m}(x)\tau_j^{\otimes m} \in \text{Sym}^m(\mathcal{X})$, is diagonalizable, then \begin{align}\label{NONFUNCTIONALWELCH} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{NONFUNCTIONALWELCH}) as non-Archimedean functional Welch bounds. \item For a prime $p$, let $\mathbb{Q}_p$ be the p-adic number field. Let $\mathcal{X}$ be a $d$-dimensional p-adic Banach space over $\mathbb{Q}_p$. If $\{\tau_j\}_{j=1}^n$ is any collection in $\mathcal{X}$ and $\{f_j\}_{j=1}^n$ is any collection in $\mathcal{X}^*$ (dual of $\mathcal{X}$) satisfying $f_j(\tau_j) =1$ for all $1\leq j \leq n$ and there exists $b \in \mathbb{Q}_p$ such that $ \sum_{j=1}^{n}f_j^{\otimes m}(x) \tau_j^{\otimes m} =bx$ for all $ x \in \text{Sym}^m(\mathcal{X}),$ then \begin{align}\label{PADICFUNCTIONALWELCH} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |f_j(\tau_k)f_k(\tau_j)|^{m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{PADICFUNCTIONALWELCH}) as p-adic functional Welch bounds. \end{enumerate} We formulate non-Archimedean functional and p-adic functional Zauner conjectures.

In this work the close relation between vorticity and micro-rotation in micropolar flows in Rn (n = 2 or 3) is identified and used to explain the faster decay by t^(-1/2) of the angular velocity of the micro-rotation of fluid particles, as well as establishing its optimality. For this purpose important upper and lower bounds for Leray solutions in homogeneous Sobolev spaces are derived, using the monotonicity approach recently introduced by the authors for dissipative systems in general. Several related results of interest are also given along the discussion.

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.

Chinese divination of I Ching has a history of thousands of years. The six lines changes in 64 hexagrams have exceeded one billion scenarios, and the inherent laws among them have not been well revealed to this day. By using big data's technology and coin toss method, this paper simulates the change of 64 hexagrams, and explores the probability and proportion of each hexagram during the change from the perspective of quantification, as well as the maximum and minimum conversion rate of hexagram change. This paper summarizes the basic characteristics and the basic law of hexagram change, and accordingly constructs the spatial form of hexagram change, and reveals the hidden secrets of the ancient Book of changes (I Ching). To achieve this goal, we randomly toss three coins 600 million times to generate 100 million hexagrams. According to the basic rules of hexagram divination, we calculate the hexagram changes. The results showed that: (1) Changes of things are mostly simple changes. The probability of 1 billion randomly generated hexagrams from one to three dynamic lines is close to 80%. (2) About 17% of the 64 hexagrams have no dynamic lines, which means that a significant proportion of the 64 hexagrams are invariant. (3) Small probability changing hexagram certainty and large probability changing hexagram uncertainty. (4) After generating one billion hexagrams at random, the topographic map with the probability of changing hexagrams has axial symmetry and fractal geometric characteristics, and the fractal characteristics are mainly manifested in that the changes on both sides of the symmetry are presented based on the triangle background. These results reflect the obvious characteristics and internal regularity of the changes in the 64 hexagrams of the I Ching. This article provides new ideas for scientific exploration of the internal laws of the 64 hexagrams in the I Ching.

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 the literature, frames generated by unitary representations of groups (known as group-frames) are studied only for Hilbert spaces. We make first study of frames for Banach spaces generated by isometric invertible representations of discrete groups on Banach spaces. These frames are characterized using left regular, right regular, Gram-matrices and group-matrices on classical sequence spaces. A sufficiently large collection of functional-vector pairs using the double commutant of the representation is identified which generate group-frames for Banach spaces. Subsequently, we study Schauder frames generated by time-frequency shift operators on finite dimensional Banach spaces. We derive Moyal formula, fundamental identity of Gabor analysis, Wexler-Raz criterion and Ron-Shen duality in functional form.

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.

In the present paper we introduce three new classes of bi-univalent functions connected with Gregory coefficients. For functions in each of these three bi-univalent function classes we have derived the estimates of the Taylor--Maclaurin coefficients $\left|a_{2}\right|$ and $\left|a_{3}\right|$ and Fekete-Szeg\H{o} functional problems for functions belonging to these new subclasses. We defined three subclasses of the class of the bi-univalent functions $\Sigma$, namely $\mathfrak{HG}_{\Sigma}$, $\mathfrak{GM}_{\Sigma}(\mu)$ and $\mathfrak{G}_{\Sigma}(\lambda)$ by using the subordinations with the function whose coefficients are Gregory's numbers. First, we proved that these classes are not empty, i.e. contains other functions than the identity one. Using the well-known Carath\'eodory Lemma for the functions with real positive parts in the open unit disk, together with an estimation due to P. Zaprawa (see https://doi.org/10.1155/2014/357480) and another one of Libera and Zlotkiewicz, we gave upper bounds for the above mentioned initial coefficients and for the Fekete-Szeg\H{o} functionals. The main results are followed by some particular cases, and the novelty of the definitions and the proofs could involve further studies for such type of similarly defined subclasses.

With the advent of Neural Machine Translation, the more the achievement of human-machine parity is claimed at WMT, the more we come to ask ourselves if their evaluation environment can be trusted. In this paper, we argue that the low quality of the source test set of the news track at WMT may lead to an overrated human parity claim. First of all, we report nine types of so-called technical contaminants in the data set, originated from an absence of meticulous inspection after web-crawling. Our empirical findings show that when they are corrected, about 5% of the segments that have previously achieved a human parity claim turn out to be statistically invalid. Such a tendency gets evident when the contaminated sentences are solely concerned. To the best of our knowledge, it is the first attempt to question the “source” side of the test set as a potential cause of the overclaim of human parity. We cast evidence for such phenomenon that according to sentence-level TER scores, those trivial errors change a good part of system translations. We conclude that to overlook it would be a mistake, especially when it comes to an NMT evaluation.

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.

In this work, new refinements of some numerical radius inequalities are proved. Namely, new improvements and refinements purify the recent inequalities of some famous inequalities concerning the numerical radius of Hilbert space operators. The proven inequalities in this work are not only an improvement over old inequalities, but rather they are stronger than them. Several examples that support the validity of our results are established as well.

This review paper provides a comprehensive overview of machine vision pose measurement algorithms. The paper focuses on the state-of-the-art algorithms and their applications. The paper is structured as follows: The introduction in Section 1 provides a brief overview of the field of machine vision pose measurement. Section 2 describes the commonly used algorithms for machine vision pose measurement. Section 3 discusses the factors that affect the accuracy and reliability of machine vision pose measurement algorithms. Section 4 presents the applications of machine vision pose measurement in various fields. The paper provides specific examples of how machine vision pose measurement is used in each of these fields. Finally, Section 5 summarizes the paper and provides future research directions. The paper highlights the need for more robust and accurate algorithms that can handle varying lighting conditions and occlusion. It also suggests that the integration of machine learning techniques may improve the performance of machine vision pose measurement algorithms. Overall, this review paper provides a comprehensive overview of machine vision pose measurement algorithms, their applications, and the factors that affect their accuracy and reliability. It provides a valuable resource for researchers and practitioners working in the field of computer vision.

We prove the continuous non-Archimedean (resp. p-adic) Banach space and Hilbert space versions of non-Archimedean (resp. p-adic) Welch bounds proved by M. Krishna. We formulate continuous non-Archimedean and p-adic functional Zauner conjectures.

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.

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.

In this paper, the 1st level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and then specify a set of the kernels that satisfy this condition and posses an integrable singularity of power law type at the origin. The 1st level general fractional derivatives of arbitrary order are integro-differential operators of convolution type with the kernels from this set. They contain both the general fractional derivatives of arbitrary order of the Riemann-Liouville type and the regularized general fractional derivatives of arbitrary order considered in the literature so far. For the 1st level general fractional derivatives of arbitrary order, some important properties including the 1st and the 2nd fundamental theorems of Fractional Calculus are formulated and proved.

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.

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.

In the present paper we introduce the concept of orthogonal frames in Krein spaces, prove the independence of the choice of the fundamental symmetry, and from this we obtain a number of interesting properties that they satisfy. We show that there is no distinction between orthogonal frames in a Krein space and orthogonal frames in its associated Hilbert. Furthermore, we characterize frames dual to a given frame, which is a useful tool for constructing examples.

The divination function of China's Yijing has led to its circulation for thousands of years. In our exploration of Yijing's characteristics using big data, we have discovered variations in results between the coin toss method and the ancient yarrow-stalk method of divination, known as "the number for the great expansion method of divination(大衍之数)". The yarrow-stalk method serves as the fundamental method of divination in Yijing and continues to hold significance in studying the essential characteristics of Yijing. Despite the complexity of yarrow calculations, advancements in computer technology and big data have simplified its application. By employing the yarrow-stalk method, we simulated changes in the 64 hexagrams, calculated probabilities and proportions of hexagram alterations, and derived fundamental characteristics and patterns of hexagrams. Additionally, we constructed the spatial representation of lines and hexagrams. Through a binary system rearrangement, we created a 64x64 matrix illustrating hexagram transformations. Subsequently, we generated 100 million random hexagrams and analyzed line and hexagram changes accordingly. Our findings indicate the following:(1) Big data analysis reveals evident asymmetry in the hexagrams obtained through the yarrow-stalk method, with a triangular fractal characteristic forming the background.(2) Each of the 64 hexagrams exhibits a distinct probability distribution when transforming into other hexagrams, which can be categorized into five types.(3)The occurrence probabilities of Laoyang, Laoyin, Shaoyang, and Shaoyin are 18.61%, 6.387%, 31.38%, and 43.62% respectively. The probabilities of Yin and Yang occurrences are nearly equal, each close to 50%. However, the probability of Laoyang is approximately three times higher than that of Laoyin.(4) Visualized and analyzed the characteristics of hexagram changes greater than 100000 times using 3D statistical maps and Sankey diagram.These results demonstrate that the yarrow-stalk method effectively unveils the characteristics and underlying patterns of the 64 hexagrams. This study provides a novel approach for scientifically exploring the internal laws governing the 64 hexagrams in Yijing.

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.

Botnet Attacks are one of the many types of ways to attack users in their day to day browsing, often of different trends and techniques to take your information without your control. Most firewalls can amply protect you against these trends and techniques, but scarily enough, recent articles and research have shown that they are starting to bypass said firewalls through layers of attacks, confusing your best line of defense. In this Report, we will be looking into exactly what are Botnets and the different subsets, what we can do to combat Botnet Attacks, where do they come from, their origin, the analysis of their kit and what we can put together from information collected. Through this we will be able to reach a conclusion of what we can use to possibly mitigate the effect they have on the internet and stop them from enacting their purpose.

In this study, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings in [17]. Firstly we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of a class of hyper-modules, then we give some relevant properties of the hypermodule in this topological hyperspace.

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.

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.

Deep Learning is an extremely important research topic in Earth Observation. Current use-cases range from semantic image segmentation, object detection to more common problems found in computer vision such as object identification. Earth Observation is an excellent source for different types of problems and data for Machine Learning in general and Deep Learning in particular. It can be argued that both Earth Observation and Deep Learning as fields of research will benefit greatly from this recent trend of research. In this paper we take several state of the art Deep Learning network topologies and provide a detailed analysis of their performance for semantic image segmentation for building footprint detection. The dataset used is comprised of high resolution images depicting urban scenes. We focused on single model performance on simple RGB images. In most situations several methods have been applied to increase the accuracy of prediction when using deep learning such as ensembling, alternating between optimisers during training and using pretrained weights to bootstrap new models. These methods although effective, are not indicative of single model performance. Instead, in this paper, we present different topology variations of these state of the art topologies and study how these variations effect both training convergence and out of sample, single model, performance.

The COVID-19 pandemic resulted in government restrictions that altered the lifestyle of people worldwide. Studying the impact of these restrictions on exercise behaviors will improve our understanding of environmental factors that influence individuals’ PA. We conducted a retrospective analysis using an index of government pandemic stringency developed by Oxford and a wearable device for runners to compare strictness of lockdowns and exercise habits, using digitally-logged PA data from more than 7,000 runners on a global scale. Additionally, time-of-day of PA globally and levels of PA in 14 countries are compared between the pre-pandemic year of 2019 and the first pandemic year of 2020. We found that during the pandemic the time-of-day that people exercised experienced a major shift, with significantly more activities logged during standard working hours on workdays (p<0.001) and fewer during the same time frame on weekends (p<0.001). Of the countries examined, Italy and Spain had among the most strict lockdowns and suffered the largest decreases in activity counts, whereas France experienced a minimal decrease in activity counts despite enacting a similarly strict lockdown. This study suggests that there are several factors affecting PA, including government policy, workplace policy, and cultural norms.