Frequency, amplitude and phase information of the grid voltage are of great importance in constructing a robust controller structure for grid connected inverter systems. This paper presents a simple and robust approach for the instantaneous estimation of positive and negative sequence voltage components under distorted voltage conditions. A second order generalized integrator (SOGI) is used to filter the distorted voltage and to generate orthogonal voltage components for each of the three phases. These filtered and orthogonal components are used for instantaneous calculation of symmetrical components. The implemented method is frequency adaptive; the method is demonstrated and compared to a conventional phase locked loop (PLL) technique with both MATLAB/Simulink simulations and experiments utilizing the dSPACE ds1103 digital controller.

Maximum likelihood estimation (MLE) is a popular method for parameter estimation in both applied probability and statistics but MLE cannot solve the problem of incomplete data or hidden data because it is impossible to maximize likelihood function from hidden data. Expectation maximum (EM) algorithm is a powerful mathematical tool for solving this problem if there is a relationship between hidden data and observed data. Such hinting relationship is specified by a mapping from hidden data to observed data or by a joint probability between hidden data and observed data. In other words, the relationship helps us know hidden data by surveying observed data. The essential ideology of EM is to maximize the expectation of likelihood function over observed data based on the hinting relationship instead of maximizing directly the likelihood function of hidden data. Pioneers in EM algorithm proved its convergence. As a result, EM algorithm produces parameter estimators as well as MLE does. This tutorial aims to provide explanations of EM algorithm in order to help researchers comprehend it. Moreover some improvements of EM algorithm are also proposed in the tutorial such as combination of EM and third-order convergence Newton-Raphson process, combination of EM and gradient descent method, and combination of EM and particle swarm optimization (PSO) algorithm.

Combining modern thermodynamics theory branches, including finite time thermodynamics or entropy generation minimization, constructal theory and entransy theory, with metallurgical process engineering, this paper provides a new exploration on generalized thermodynamic optimization theory for iron and steel production processes. The theoretical core is to thermodynamically optimize performances of elemental packages, working procedure modules, functional subsystems, and whole process of iron and steel production processes with real finite-resource and/or finite-size constraints with various irreversibilities toward saving energy, decreasing consumption, reducing emission and increasing yield, and to achieve the comprehensive coordination among the material flow, energy flow and environment of the hierarchical process systems. A series of application cases of the theory are reviewed. It can provide a new angle of view for the iron and steel production processes from thermodynamics, and can also provide some guidelines for other process industries.

Although Eulerian approaches are standard in computational acoustics, they are less effective for certain classes of problems like bubble acoustics and combustion noise. A different approach for solving acoustic problems is to compute with individual particles following particle motion. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically, using three meshfree methods to solve the Lagrangian acoustic perturbation equations (LAPE) in the time domain. The LAPE split the fluid dynamic equations into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, three meshfree methods, the smoothed particle hydrodynamics (SPH) method, the corrective smoothed particle (CSP) method, and the generalized finite difference (GFD) method, are introduced to solve the LAPE and the linearized LAPE (LLAPE). The SPH and CSP methods are widely used meshfree methods, while the GFD method based on the Taylor series expansion can be easily extended to higher orders. Applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. A comparison of the LAPE and the LLAPE using the three meshfree methods is also presented. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP and GFD method exhibit convergence in cases with different background flow. The GFD method is more accurate, while the CSP method can handle higher Courant numbers.

In this paper we consider type II bivariate generalized power series Poisson distribution as a compound Poisson distribution with bivariate generalized power series compounding distribution. We obtain some properties, p.m.f. and conditional distributions. In addition we also give a brief discussion about the multivariate extension of this case. Then we introduce type II bivariate generalized power series Poisson process and consider a bivariate risk model with type II bivariate generalized power series Poisson model as the counting process. For this model we derive distribution of the time to ruin and bounds for the probability of ruin. We obtain partial integro-differential equation for the ruin probabilities and express its bivariate transform through two univariate boundary transforms,where one of the initial capitals is fixed at zero.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.

Land Surface Temperature (LST) is routinely retrieved from remote sensing instruments using semi-empirical relationships between top of atmosphere (TOA) radiances and LST, using ancillary data such as total column water vapor or emissivity. These algorithms are calibrated using a set of forward radiative transfer simulations that return the TOA radiances given the LST and the thermodynamic profiles. The simulations are done in order to cover a wide range of surface and atmospheric conditions and viewing geometries. This work analyses calibration strategies, considering some of the most critical factors that need to be taken into account when building a calibration dataset, covering the full dynamic range of relevant variables. A sensitivity analysis of split-windows and single channel algorithms revealed that selecting a set of atmospheric profiles that spans the full range of surface temperatures and total column water vapor combinations that are physically possible seems beneficial for the quality of the regression model. However, the calibration is extremely sensitive to the low-level structure of the atmosphere indicating that the presence of atmospheric boundary layer features such as temperature inversions or strong vertical gradients of thermodynamic properties may affect LST retrievals in a non-trivial way. This article describes the criteria established in the EUMETSAT Land Surface Analysis – Satellite Application Facility to calibrate its LST algorithms applied both for current and forthcoming sensors.

Crash prediction of the sharp horizontal curve segment (SHCS) of a freeway is an important tool in analyzing safety of SHCSs and in building a crash prediction model (CPM). The design and crash report data of 88 SHCSs from different institutions were surveyed and three negative binomial (NB) regression models and three generalized negative binomial (GNB) regression models were built to prove that the interactive influence of explanatory variables plays an important role in fitting goodness. The study demonstrates the effective use of the GNB model in analyzing the interactive influence of explanatory variables and in predicting freeway basic segments. Traffic volume, highway horizontal radius, and curve length have been formulated as explanatory variables. Subsequently, we performed statistical analysis to determine the model parameters and conducted sensitivity analysis. Among the six models, the result of model 6, which considered interactive influence, is much better than those of the other models by fitting rules. We also compared the actual results from crashes of 88 SHCSs with those predicted by models 1, 3, and 6. Results demonstrate that model 6 is much more reasonable than models 1 and 3.

Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E. T. Copson in 1958. This study extends that work. Firstly, three solution methods were overlooked in Copson’s original paper. Secondly, several new approaches for finding Riemann functions have been developed since 1958. Those techniques are included here and placed in the context of Copson’s original study. There are also numerous equivalences between Riemann functions that have not previously been identified in the literature. Those links are clarified here by showing that many known Riemann functions are often equivalent due to the governing equation admitting a symmetry algebra isomorphic to $SL(2,R)$. Alternatively, the equation admits a Lie-Bäcklund symmetry algebra. Combining the results from several methods, a new class of Riemann functions is then derived which admits no symmetries whatsoever.

In this article, a generalization of the geometry of Grassmannian chain complex of free abelian groups generated by the projective configuration of points and Cathelineau's infinitesimal complex of polylogarithmic groups is proposed. Firstly, homomorphisms for weight n =2 up to weight n=6 will be introduced to connect sub-complexes of Grassmannian and Cathelineau. Lately, generalization of these morphisms will be shown for weight n=N. The associated diagrams will also be proven to be commutative and bi-complex.

The aim of this research work was to provide model for predicting stock volatility in Nigeria Stock market. To achieve this, monthly data for Nigerian stock exchange, Exchange rate, Share index and inflation rate was collected for a period of January 1990 to December 2016.The descriptive statistics revealed these variables to exhibit volatility as a characteristics of financial time –varying series. DCC Model was fitted, were the coefficients for all the parameters and that of the correlation-Targeting (rho_21) are both negative and positive and tend very close to 1 and -1, indicating that high persistence in the conditional variances. The Model DCC, satisfied the properties of a good model of conditional mean and variance of the confidential Interval (C.I) of 1 and -1, that is, the conditional variances are finites and their series are strictly stationary. This therefore implies that the Nigerian Stock Exchange, Exchange rate, share index and Inflation rate will experience a non-steady shock in the Stock market. However Each of these variables have different length of recovery (volatility half- life) ranging from 1.5month, 6.5months, 6months to 2,4months for stock exchange, exchange rate, share index and inflation rate respectively. By implication, the volatility of these variables had a long memory, persistence and mean-reverting.

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters which fit the shape of peakedness in bimodality on real line. The special values of peakedness parameters of the distribution are combination of half Laplace and half normal distributions on real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data.

In previous studies we found that generalized functions can be smooth, discrete, periodic or discrete periodic and they can either be local or global and they are regular or generalized functions. We also saw that these properties were related to Poisson’s summation formula on one hand and to Heisenberg’s uncertainty principle on the other. In this paper, we interlink these studies and show that scalars (real or complex numbers) considered as trivial functions are discrete and periodic, local and global as well as regular and generalized, simultaneously. However, this is also a paradox because it means that Dirac’s δ and 1 (its Fourier transform) coincide. They both are unity. We show that δ and 1 coincide in the sense of scalars (real or complex numbers) but they differ in the sense of (generalized) functions. This result can moreover be related to Max Born’s principle of reciprocity. It also answers an open question in present-day quantum mechanics because it means that the Dirac delta squared is simply delta.

This paper is motivated by spatio-temporal pattern in the occurrence of Leishmaniasis in Afghanistan and the relatively high number of zero counts. We hold the view that correlations that arise from spatial and temporal sources are inherently distinct. Our method decouples these two sources of correlations, there are at least two advantages in taking this approach. First, it circumvents the need to inverting a large correlation matrix, which is a commonly encountered problem in spatio-temporal analyses. Second, it simplifies the modelling of complex relationships such as anisotropy, which would have been extremely difficult or impossible if spatio-temporal correlations were simultaneously considered. We identify three challenges in the modelling of a spatio-temporal process: (1) accommodation of covariances that arise from spatial and temporal sources; (2) choosing the correct covariance structure and (3) extending to situations where a covariance is not the natural measure of association. Moreover, because the data covers a period that overlaps with the US invasion of Afghanistan, the high number of zero counts may be the result of no disease incidence or lapse of data collection. To resolve this issue, a model truncated at zero built on a foundation of the generalized estimating equations was proposed.

Dietary patterns established during adolescence might play a role in adulthood disease. We examined the stability of dietary patterns (DPs) from childhood through adolescence and into young adulthood (from age 8 to 34 years). Data from 130 participants (53 females) of Saskatchewan Pediatric Bone Mineral Accrual Study (aged 8-15 years, at baseline) were included. Multiple 24-hour recalls were collected annually from 1991 to 1997, 2002 to 2005 and 2010 and 2011. Using principal component analysis, “Vegetarian-style”, “Western-like”, “High-fat, high-protein”, “Mixed” and “Snack” DPs were derived at baseline. Applied DP scores for all annual measurements were calculated using factor loading of baseline DPs and energy-adjusted food group intakes. We analyzed data using generalized estimating equations. The tracking coefficient represents correlation between baseline dietary pattern scores and all other follow-up dietary pattern scores. We found a moderate tracking for the “Vegetarian-style” (ß=0.44, P<0.001) and “High-fat, high-protein” (ß=0.39, P<0.001) DPs in females and “Vegetarian-style” DP (ß=0.30, P<0.001) in males. Remaining DPs showed a poor-to-fair tracking in both sexes. No tracking for “Western-like” DP in females was observed. Assessing overall change in DP scores from childhood to young adulthood showed an increasing trend in adherence to “Vegetarian-style” DP and decreasing trend in adherence to “High-fat, high-protein” DP by age in both sexes (P<0.001). While “Western-like” and “Mixed” DP scores increased only in males (P<0.001). These findings suggest that healthy dietary habits established during childhood and adolescence moderately continue into adulthood.

The formula of the Generalized Ambiguity Function (GAF) of passive bistatic SAR system using the non-cooperative illuminators which transmit PSK modulating signals is derived to analyze the spatial resolution of the system. The average GAF is introduced to remove the effect of particular sequence of symbols on resolution because the particular sequence of symbols is usually unpredictable before being received. The influence of the waveform parameters of the PSK modulating signals, such as length of the symbol sequence and roll-off factor, on spatial resolution is investigated by numerical simulation. It is confirmed that the influence of the length of the symbol sequence and roll-off factor is very slight but still exists.

In the paper, the authors find two explicit formulas and recover a recursive formula for the generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.

Satellite scene classification is challenging because of the high variability inherent in satellite data. Although rapid progress in remote sensing techniques has been witnessed in recent years, the resolution of the available satellite images remains limited compared with the general images acquired using a common camera. On the other hand, a satellite image usually has a greater number of spectral bands than a general image, thereby permitting the multi-spectral analysis of different land materials and promoting low-resolution satellite scene recognition. This study advocates multi-spectral analysis and explores the middle-level statistics of spectral information for satellite scene representation instead of using spatial analysis. This approach is widely utilized in general image and natural scene classification and achieved promising recognition performance for different applications. The proposed multi-spectral analysis firstly learns the multi-spectral prototypes (codebook) for representing any pixel-wise spectral data, and then based on the learned codebook, a sparse coded spectral vector can be obtained with machine learning techniques. Furthermore, in order to combine the set of coded spectral vectors in a satellite scene image, we propose a hybrid aggregation (pooling) approach, instead of conventional averaging and max pooling, which includes the benefits of the two existing methods but avoids extremely noisy coded values. Experiments on three satellite datasets validated that the performance of our proposed approach is much more accurate than even the deep learning framework for spatial analysis.

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy.” Upper and lower error bars on the accuracy are provided by the arithmetic mean and the -2/3 mean. The arithmetic is called the “Decisiveness” due to its similarity with the cost of a decision and the -2/3 mean is called the “Robustness”, due to its sensitivity to outlier errors. Visualization of inference performance is facilitated by plotting the reported model probabilities versus the histogram calculated source probabilities. The visualization of the calibration between model and source is summarized on both axes by the arithmetic, geometric, and -2/3 means. From information theory, the performance of the inference is related to the cross-entropy between the model and source distribution. Just as cross-entropy is the sum of the entropy and the divergence; the accuracy of a model can be decomposed into a component due to the source uncertainty and the divergence between the source and model. Translated to the probability domain these quantities are plotted as the average model probability versus the average source probability. The divergence probability is the average model probability divided by the average source probability. When an inference is over/under-confident, the arithmetic mean of the model increases/decreases, while the -2/3 mean decreases/increases, respectively.

In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty principle. They both express Fourier dualities within the space of tempered distributions and these dualities are furthermore the inverses of one another. While Poisson’s summation formula expresses a duality between discretization and periodization, Heisenberg’s uncertainty principle expresses a duality between regularization and localization. We define regularization and localization on generalized functions and show that the Fourier transform of regular functions are local functions and, vice versa, the Fourier transform of local functions are regular functions.

This paper aims to quantify the effect of the deadly novel coronavirus (COVID-19) pandemic outbreak on Chinese stock market performance. Shanghai Stock Exchange Composite Index and its component sector indices are examined in this study. The pandemic is represented by a lockdown dummy, new COVID-19 cases and a dummy for 3 February 2020. First, descriptive analysis is performed on these indices to compare their performances before and during the lockdown period. Next, regression analysis with Exponential Generalized Autoregressive Conditional Heteroscedasticity specification is estimated to quantify the pandemic effect on the Chinese stock market. This paper finds that health care, information technology and telecommunication services sectors were relatively more pandemic-resistant, while other sectors were more severely hurt by the pandemic outbreak. The extent to which each sector was affected by pandemic and sentiments in other financial and commodity markets were reported in details in this paper. The findings of this paper are resourceful for investors to avoid huge loss amid pandemic outburst and the China Securities Regulatory Commission in handling future pandemic occurrence to cool down excessive market sentiments.

In this paper, a novel voltage control strategy of stand-alone operation brushless doubly fed induction generator for variable speed constant frequency wind energy conversion systems was presented and discussed particularly. Based on the model of the generator power system, the proposed direct flux control strategy employs a nonlinear reduced-order generalized integrator based resonant sliding-mode control scheme to directly calculate and regulated the output value of converter which control winding stator required so as to eliminate the instantaneous errors of power winding stator flux, and no involving any synchronous rotating coordinate transformations. The stability, robustness and convergence capability of the proposed control strategy were described and analyzed. Owing to no extra current control loops involved, therefore simplifying the system configuration design and enhancing the transient performance. Constant converter switching frequency was achieved by using space vector pulse width modulation, which reduce the harmonic of generator terminal voltage. In addition, experimental results prove the feasibility and validity of the proposed scheme, and excellent steady and dynamic state performance is achieved.

The remaining capacity can only be measured with offline method. This brings great challenge for the online prediction of Li-ion battery’s RUL. A novel online prediction method for Li-ion battery’s RUL was proposed, which is based on multiple health indicators (HIs) and can be derived from the batteries’ historical operation data. Firstly, four indirect HIs were built according to the battery’s operation current, voltage and temperature data respectively. On that basis, a generalized regression neural network (GRNN) was developed to estimate the battery’s remaining capacity, and the non-linear autoregressive approach (NAR) was utilized to predict the battery’s RUL based on the estimated capacity value. Furthermore, to reduce the interference, twice wavelet denoising were performed with different thresholds. A case study is conducted with a NASA battery dataset to demonstrate the effectiveness of the method. The result shows that the proposed method can obtain Li-ion batteries’ RUL effectively.

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

Let g be a strictly increasing function on $\left(a,b\right),$ having a continuous derivative g′ on $\left(a,b\right).$ For the Lebesgue integrable function $f:\left(a,b\right)\to \mathbb{C}$ , we define the k-g-left-sided fractional integral of f by $S_{k,g,a+}f\left(x\right)={\int }_a^{x}k\left(g\left(x\right)-g\left(t\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in \left(a,b\right]$ and the k-g-right-sided fractional integral of f by $S_{k,g,b-}f\left(x\right)={\int }_x^{b}k\left(g\left(t\right)-g\left(x\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in [a,b),$ where the kernel k is defined either on $\left(0,\infty \right)$ or on $\left[0,\infty \right)$ with complex values and integrable on any finite subinterval. In this paper we establish some Ostrowski and trapezoid type inequalities for the k-g-fractional integrals of functions of bounded variation. Applications for mid-point and trapezoid inequalities are provided as well. Some examples for a general exponential fractional integral are also given.

The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. As a crucial part, alternative approach for generalized quaternion matrix with elliptic number entries are developed.

For evaluating probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based upon the Gauss-Laplace law. The latter will be considered here as an element of the newly introduced family of (p,q)-spherical distributions. Based upon a suitably defined non-Euclidean arc-length measure on (p,q)-circles we prove geometric and stochastic representations of these distributions and correspondingly distributed random vectors, respectively. These representations allow dealing with the new probability measures similarly like with elliptically contoured distributions and more general homogeneous star-shaped ones. This is demonstrated at hand of a generalization of the Box-Muller simulation method. En passant, we prove an extension of the sector and circle number functions.

A multiscale (micro-macro) approach is proposed for the establishment of the full thermal and induced stress fields in cracked composites that are subjected to heat flow. Both the temperature and stresses distributions are determined by the solution of a boundary value problem with one-way coupling. In the micro level and for combined thermomechanical loading, a micromechanical analysis is employed to determine the effective moduli, coefficients of thermal expansion and thermal conductivities of the undamaged composite. In the macro level, the representative cell method is employed according to which the periodic damaged composite region is reduced, in conjunction with the discrete Fourier transform, to a finite domain problem. As a result, a boundary value problem is obtained in the Fourier transform domain which is appropriately discretized and solved. The inverse transform and an iterative procedure provide the full thermal and stress fields. The proposed method is verified by comparisons with exact solutions. Applications are given for the determination of the thermal and stress fields in cracked fiber-reinforced polymeric composite, cracked porous ceramic material and cracked periodically layered ceramic composite caused by the application of heat flow. The presented formulation admits however the application of a combined mechanical and heat flux on cracked composites.

Several specific types of ordinary and generalized separation axioms of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized separation axioms of a generalized topological space is reported herein as a starting point for more generalized classes.

The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function.Some integrals involving trigonometric,generalized Bessel function and Struve functions are also indicated as special cases of our main results.further, with the help of our main results and their special cases, we obtain two reduction formulas for the Wright hypergeometric function.

A double Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2, 3} 2 with the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for 3 which f(v) = 3 or two vertices v1 and v2 for which f(v1) = f(v2) = 2, and every vertex u for which 4 f(u) = 1 is adjacent to at least one vertex v for which f(v) ≥ 2. The weight of a double Roman dominating function f is the value w(f) = ∑u∈V(G) 5 f(u). The minimum weight over all double 6 Roman dominating functions on a graph G is called the double Roman domination number γdR(G) 7 of G. In this paper we determine the exact value of the double Roman domination number of the 8 generalized Petersen graphs P(n, 2) by using a discharging approach.

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

The main goal of this article is to demonstrate the impact of environmental data on the spreading of Covid-19. In this research, data has been collected from 70 cities/provinces that are affected by Covid-19. Here, environmental data refers to temperatures, humidity and population density in each of these cities/provinces. This data has been analyzed using statistical models such as Poisson, Quasi-Poisson and negative Binomial. It is found that a negative Binomial regression model is the best fit for our data. Our results reveal that average high temperature is the vital factor to slow down the spread of Covid-19. In addition, higher population density found to be an important factor for the quick spreading of Covid-19 where it is quite impossible to maintain the social distance and the virus can spread easily.

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.

Live fuel moisture content (LFMC) influences fire activity at landscape scale and fire behavior in laboratory experiments. However, field evidences linking LFMC to fire behavior are very limited despite numerous field experiments. In the present study, we reanalyze a shrubland fire dataset with a special focus on LFMC to explain this counterintuitive outcome. We found that this controversy might result from three reasons. First, the range of experimental LFMC data was too moist to reveal significant effect with the widespread exponential or power functions. Indeed, LFMC exhibited a strong effect below 100%, but marginal above this threshold, contrary to these functions. Second, we found that the LFMC significance was unlikely when the size of the dataset was smaller than 40. Finally, a complementary analysis suggested that 10 to 15% of random measurement error in variables could lead to an underestimation by 30 % of the LFMC effect. The effect of LFMC in field experiments is thus stronger than previously reported in the range prevailing during the actual French fire season and in accordance with observations at different scales. This highlights the need to improve our understanding of the relationship between LFMC and fire behavior to refine fire danger predictions.

Several specific types of generalized sets of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized sets of a generalized topological space is reported herein as a starting point for more generalized classes.

In financial time series modelling and forecasting, combining ARMA and GARCH models tend to produce superior and reliable models for volatility persistence, half-life volatility and backtesting (application of model in real life). In Nigeria, banking stocks are mostly traded because of its potential benefits to investors. This study modelled and forecasted the Guaranty Trust (GT) Bank daily stock returns from January 2^nd 2001 to May 8^th 2017 data set collected from a secondary source. The ARMA-GARCH models, persistence, half-life and backtesting were used to analysed the collected data using student t and skewed student t distributions, and the analyses are carried out R environment using rugard and performanceAnaytics Packages. The study revealed that using the lowest information criteria values only could be misleading rather we added the use of backtesing. The ARMA(1,1)-GARCH(1,1) models fitted exhibited high persistency in the daily stock returns while the days it takes for mean-reverting of the models ranges from 5 days to 100 days but unfortunately the models failed backtesting. The results further revealed ARMA(1,1)-eGARCH (2,2) model with student t distribution provides a suitable model for evaluating the GT bank stock returns among the competing models while it takes less than 30 days for the persistence volatility to return back to its average value of the stock returns. This study recommended that researchers should adopt backtesting approach while fitting GARCH models while GT bank stocks investor should be assured that no matter the fluctuations in the stock market, the GT bank stock returns has the ability to returns to its mean price return.

In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their "space of evolution" associated to a homogeneous symplectic manifold by a Lagrange 2-form, and defines in case of non null cohomology (non equivariance of the coadjoint action on the moment map with appearance of an additional cocyle) a Gibbs density (of maximum entropy) that is covariant under the action of dynamic groups of physics (eg, Galileo's group in classical physics). Souriau Lie Group Thermodynamics was also addressed 30 years after Souriau by R. F. Streater in the framework of Quantum Physics by Information Geometry for some Lie algebras, but only in the case of null cohomology. Souriau method could then be applied on Lie Groups to define a covariant maximum entropy density by Kirillov representation theory. We will illustrate this method for homogeneous Siegel domains and more especially for Poincaré unit disk by considering SU(1,1) group coadjoint orbit and by using its Souriau’s moment map. For this case, the coadjoint action on moment map is equivariant. For non-null cohomology, we give the case of Lie group SE(2). Finally, we will propose a new geometric definition of Entropy that could be built as a generalized Casimir invariant function in coadjoint representation, and Massieu characteristic function, dual of Entropy by Legendre transform, as a generalized Casimir invariant function in adjoint representation, where Souriau cocycle is a measure of the lack of equivariance of the moment mapping.

Interval-valued functions have been widely used to accommodate data inexactness in optimization and decision theory. In this paper, we study interval-valued vector optimization problems, and derive their relationships to interval variational inequality problems, of both Stampacchia and Minty types. Using the concept of interval approximate convexity, we establish necessary and sufficient optimality conditions for local strong quasi and approximate $LU$-efficient solutions to nonsmooth optimization problems with interval-valued multiobjective functions.

Corona virus disease (COVID-19) has infected over more than 10 million people around the globe and killed at least 500K worldwide by the end of June 2020. As this disease continues to evolve and scientists and researchers around the world now trying to find out the way to combat this disease in most effective way. Chest X-rays are widely available modality for immediate care in diagnosing COVID-19. Precise detection and diagnosis of COVID-19 from these chest X-rays would be practical for the current situation. This paper proposes one shot cluster based approach for the accurate detection of COVID-19 chest x-rays. The main objective of one shot learning (OSL) is to mimic the way humans learn in order to make classification or prediction on a wide range of similar but novel problems. The core constraint of this type of task is that the algorithm should decide on the class of a test instance after seeing just one test example. For this purpose we have experimented with widely known Generalized Regression and Probabilistic Neural Networks. Experiments conducted with publicly available chest x-ray images demonstrate that the method can detect COVID-19 accurately with high precision. The obtained results have outperformed many of the convolutional neural network based existing methods proposed in the literature.

This paper is focused on the analysis of methods used to assess effectiveness and efficiency of the occupational safety and health management system (OSHMS) in a company. It reviews current Russian and international occupational safety and health standards. The paper details the method outlined in International Standard GOST 12.0.230.3-2016 “Occupational safety standards system. Management systems for occupational safety. Evaluation of effectiveness and efficiency” based on the data collected during the external audit of OSHMS function efficiency in a Russian mining company. Effectiveness and efficiency indicators were determined, and a generalized desirability coefficient was calculated. Weaknesses of the method proposed in GOST 12.0.230.3-2016 were identified and mathematical and linguistic solutions were proposed to improve it. Harrington function was used to determine a numerical and linguistic score. The performed calculation demonstrated that the company needed strategic management decisions to improve the current situation. Practical approaches were offered to enhance the company's systems-based occupational safety and health performance..

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.

In this paper we introduce the New/Generalized two parameter Gamma function and Pochhammer symbol. We named them, as Generalized p - k Gamma Function and Generalized p - k Pochhammer symbol and denoted as $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ respectively. We prove the several identities for $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ those satisfied by the classical Gamma function. Also we provide the integral representation for the $ _{p}^{a}\Gamma_{k}(x) $

High-performance motor drives that operate in harsh conditions require an accurate and robust angular position measurement to correctly estimate the speed and reduce the torque ripple produced by angular estimation error. For that reason, a resolver is used in motor drives as a position sensor due to its robustness. A resolver-to-digital converter (RDC) is an observer used to get the angular position from the resolver signals. Most RDCs are based on angle tracking observers (ATOs). On the other hand, generalized predictive control (GPC) has become a powerful tool in developing controllers and observers for industrial applications. However, no GPC-based RDC with zero steady-state error during constant speed operation was proposed. This paper proposes an RDC based on a second-order difference GPC (SOD-GPC). In SOD-GPC, the second-order difference operator is applied to design a GPC model with two embedded integrators. Thus, the SOD-GPC is used to design a type-II ATO whose steady-state angle estimation error tends to zero during constant speed operation. Simulation and experimental results prove that the proposed RDC system has better performance than other literature approaches.

This study investigated the trends of registered Death and Birth in Nigeria using Generalized Linear Models. Annual data on Death and Birth was collected from National Population Commission for the period of 2004 to 2017. The Natural increase calculated revealed a positive trend in the natural increase in Nigeria from 2004 to 2017. Evidence from summary statistics revealed some level of over dispersion (variance > mean). This study explored Poisson Regression Models and Negative Binomial Regression Models using two links (identity and log). The results revealed a positive increase in registration of birth and death rates in Nigeria and among the competing the models, Negative Binomial regression model with identity link emerged as the best model for modeling birth and death rates registration in Nigeria. Data on numbers of deaths and causes of death are essential if countries are to determine priorities, formulate and monitor policies for public health care as well as other government policies that may be based on such data

In this paper, we prove some random fixed point theorems for generalized random $\alpha-\psi-$contractive mappings in a Polish space and, as some applications, we show the existence of random solutions of second order random differential equation.

Let G[F,Vk, Huv] be the graph with k pockets, where F is a simple graph of order n ≥ 1,Vk= {v1,v2,··· ,vk} is a subset of the vertex set of F and Hvis a simple graph of order m ≥ 2,v is a specified vertex of Hv. Also let G[F,Ek, Huv] be the graph with k edge pockets, where F is a simple graph of order n ≥ 2, Ek= {e1,e2,···ek} is a subset of the edge set of F and Huvis a simple graph of order m ≥ 3, uv is a specified edge of Huvsuch that Huv− u is isomorphic to Huv− v. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of G[F,Vk, Hv] and G[F,Ek, Huv] in terms of the resistance distance and Kirchhoff index F, Hv and F, Huv, respectively.

A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of those of 1-type in the usual sense and pointwise 1-type. We classify ruled surfaces with generalized 1-type Gauss map as part of a plane, a circular cylinder, a cylinder over a base curve of an infinite type, a helicoid, a right cone and a conical surface of $G$-type.

Background: Periodontitis is a disease that leads to serious functional and aesthetic dysfunctions resulting in impairment of life quality; it exists in different forms and its etiology is related with multiple component causes. Angiogenesis, together with inflammatory infiltrate, are two key processes in the evolution of inflammatory processes involving gingival tissues. The aim of this study was to evaluate their alterations in relation to some important periodontal diseases-associated factors (i.e. smoke, sex, age, plaque, pus, probing pocket depth) in patients with diagnosis of Generalized Aggressive Periodontitis (GAP). Methods: Eighteen subjects with GAP were enrolled for this study. Percentage of inflammatory cells and vascular area were measured and evaluated in relation with each periodontal diseases-associated factor. Results: The results showed a significant decrease of the percentage of vascular area in association with almost all the periodontal diseases-related factors (smoke, age, PPD, plaque) and not significant differences in the percentage of inflammatory cells. Conclusions: Data suggest that, even if these factors are often commonly related to worsening of periodontal status, they did not affect inflammatory and vascular pattern, as we can assume. For the future, additional studies, aimed to evaluated each singular factor in a wider sample size, should be planned.

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.

Several specific types of generalized maps of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized maps of a generalized topological space is reported herein as a starting point for more generalized classes.

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.

The Simplified Spherical Harmonic (SPN) approximation was first introduced as a three-dimensional (3-D) extension of the plane-geometry Spherical Harmonic (PN) equations. A third order SPN (SP3) solver, recently implemented in the Nodal Expansion Method (NEM), has shown promising performance in the reactor core neutronics simulations. This work is focused on the development and implementation of the transport corrected interface and boundary conditions in NEM SP3 solver, following recent published work on the rigorous SPN theory for piecewise homogeneous regions. A streamlined procedure has been developed to generate the flux zero and second order/moment discontinuity factors (DFs) of the generalized equivalence theory to eliminate the error introduced by pin-wise homogenization. Moreover, several color set models with varying size and configuration are later explored for their capability of generating DFs that can produce results equivalent to that using the whole-core homogenization model for more practical implementations. The new developments are tested and demonstrated on the C5G7 benchmark. The results show that the transport corrected SP3 solver shows general improvements to power distribution prediction compared to the basic SP3 solver with no DFs or only zero order/moment DFs. The complete equivalent calculations using the DFs can almost reproduce transport solutions with high accuracy. The use of equivalent parameters from larger size color set models show better prediction in the whole-core calculations. By coupling different color set models DFs can offer the best accuracy at both eigenvalues and power distributions.

The aim of this paper is to obtain Karush-Kuhn-Tucker optimality conditions for weakly efficient solutions to vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient solutions to the constrained vector optimization problem are presented. As well as some examples. The results presented in this paper generalize results obtained by Gong (2008) and Wei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces and real Banach spaces to Hadamard manifolds, respectively.

This study addresses the latent construct of attitudes towards environmental conservation based on study participant’s responses. We measured and evaluated the latent scale based on an 18-item scale instrument, over four experimental strata (N=945) in the US Virgin Islands and the Caribbean. We estimated the latent scale reliability and validity. We further fitted multiple alternative two-parameter logistic (2PL) and graded response models (GRM) from Item-Response Theory. We finally constructed and fitted equivalent structural and generalized structural equation models (SEM/GSEM) for the attitudinal latent scale. All scale measures (composite, alpha-based, IRT-based and SEM-based) were consistently and reliably valid measures of the study participants’ latent attitudes toward conservation. We found statistically significant differences among participant’s attributes relating to socio-demographic, physical and core environmental characteristics of participants. We assert that the nature of relationship between cognitive attitudes and individual as well as social behavior related to environmental conservation.

Land Surface Temperature (LST) estimation has been studied for several purposes, while the optimal method of estimating the LST has not been criticized yet. This research explores the optimum method in Land Surface Temperature (LST) estimation using LANDSAT-8 imagery data. Four different LST retrieval approaches, the Radiative Transfer Equation-based method (RTE), the Improved Mono-Window method (IMW), the Generalized Single-Channel method (GSC), and the Split-Window algorithm (SW), were calculated to present the LSTs over Buriram Town Municipality, Thailand. The calculated LSTs from these four methods were compared with the ground-based temperature data, taken on the same date and time of the employed LANDSAT-8 images. For this reason, the optimum method of the LST calculation was justified by considering the lowest normalized root means square error (NRMSE) values. As a result, the SW algorithm presents an optimum method in LST estimation. Regarding the SW, this algorithm requires not only the atmospheric profiles during satellite acquisition but also the retrieval of several coefficients. Besides, the LST retrieval method based on the SW algorithm is sensitive to water vapor content and coefficients. Although the SW algorithm is an optimum method explored in this study, it is emphasized that the adjustable values of coefficient response to the atmospheric state may be recommended. With these conditions, the SW algorithm can generate the land-surface temperature over the mixed land-use and land cover on the LANDSAT-8 images.

Working capital management requires a careful attention by the corporate managers because it plays an important role in corporate stability. Social belongingness of managers induced them to learn from their society, colleagues and from overall industrial movement. They also learn from their peers which have more strategical efficiency. In line with these arguments, the objective of current study is to explores the peer influence on corporate working capital management practices. To making analysis, ten-years data (2009-2018) of non-financial publicly listed firms at PSX were collected and the cash conversion cycle (CCC) uses as a proxy variable of working capital management (WCM). To estimate the regression, an econometric technique named the Generalized Method of Moments (GMM) was used. The empirical findings suggest the significant impact of peer WCM on corporate WCM. It also suggests the significant impact of other variables that determine the WCM. This study recommends social learning policy to corporate managers. They can learn from their peers to manage the working capital. Most previous studies discuss the peer influence on investment decisions, corporate cash holding and financing policy, etc., but no study explores such a relationship specifically in the Pakistani non-financial sector data set.

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

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudrayshov method for the exact analytical solution. The modified Kudrayshov method converts the nonlinear partial differential equation to algebraic equations, as a result of various steps, which on solving the so obtained equation systems yields the analytical solution. By this way various exact solutions including complex structures are found and drawn their behaviour in complex plane by Maple to compare the uniqueness of solutions.

The morphology and the activity of a submarine caldera, Avyssos, at the northern part of Nisyros volcano in the South Aegean Sea (Greece), has been studied by means of remotely operated underwater vehicle dives. The recorded time series of temperature and conductivity over the submarine volcano have been analyzed in terms of the Generalized Moments Method. The findings of the mathematical analysis shed light on the volcanic activity, but also on the morphology (shape) of the submarine volcano. The conductivity time series indicates the volcano is at rest in agreement with other types of observations. On the other hand, temperature fluctuations, which in general describe a multifractal process, show that the submarine caldera operates as an open system that interacts with its surroundings. This type of analysis can be used as an indicator for the state of activity and the morphological structure (closed or open system) of a submarine volcano.

In this article, author performs computational analysis for the generalized zeta functions by using computational software Mathematica. To achieve the purpose recently obtained difference equations are used. These difference equations have a computational power to compute these functions accurately while they can not be computed by using their known integral represenations. Several authors investigated such functions and their analytic properties, but no work has been reported to study the graphical representations and zeors of these functions. Author performs numerical computations to evaluate these functions for different values of the involved parameters. Taylor series expansions are also presented in this research.

Generalized stacking fault energies of palladium alloys were calculated using the density functional theory. The stacking fault energy of palladium alloys is correlated with the valence electron of the transition metal element. The twinning tendency is also modified by the presence of an alloying element in the plane of deformation. The obtained results suggest that Pd –transition metal alloys with elements such as Cr, Mo, W, Mn, Re are expected to exhibit high work hardening rate due to the tendency to emit of the partial dislocations and mechanical twins, which results in increased strength and ductility.

Several specific types of ordinary and generalized connectedness in a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new type of generalized connectedness in a generalized topological space is reported herein as a starting point for more generalized types.

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.

By generalizing the notion of pointwise 1-type Gauss map, the generalized 1-type Gauss map has been recently introduced. Without any assumption, we classified all possible ruled surfaces with generalized 1-type Gauss map in a 3-dimensional Minkowski space. In particular, null scrolls do not have the proper generalized 1-type Gauss map. In fact, it is harmonic.

Several specific types of generalized compactness of generalized topological spaces have been defined, investigated and related to compactness in ordinary topological spaces from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized compactness in a generalized topological space is reported herein as a starting point for more generalized classes.

In a generalized topological space Tg = (Ω, Tg), generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, are merely two of a number of generalized primitive operators which may be employed to topologize the underlying set Ω in the generalized sense. Generalized exterior and generalized frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, are other generalized primitive operators by means of which characterizations of generalized operations under g-Intg, g-Clg : P (Ω) −→ P (Ω) can be given without even realizing generalized interior and generalized closure operations first in order to topologize Ω in the generalized sense. In a recent work, the present authors have defined novel types of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in Tg and studied their essential properties and commutativity. In this work, they propose to present novel definitions of generalized exterior and generalized frontier operators g-Extg, g-Frg : P (Ω) −→ P (Ω), respectively, a set of consistent, independent axioms after studying their essential properties, and established further characterizations of generalized operations under g-Intg, g-Clg : P (Ω) −→ P (Ω) in Tg.

In a generalized topological space Tg = (Ω, Tg), ordinary interior and ordinary closure operators intg, clg : P (Ω) −→ P (Ω), respectively, are defined in terms of ordinary sets. In order to let these operators be as general and unified a manner as possible, and so to prove as many generalized forms of some of the most important theorems in generalized topological spaces as possible, thereby attaining desirable and interesting results, the present au- thors have defined the notions of generalized interior and generalized closure operators g-Intg, g-Clg : P (Ω) −→ P (Ω), respectively, in terms of a new class of generalized sets which they studied earlier and studied their essen- tial properties and commutativity. The outstanding result to which the study has led to is: g-Intg : P (Ω) −→ P (Ω) is finer (or, larger, stronger) than intg : P (Ω) −→ P (Ω) and g-Clg : P (Ω) −→ P (Ω) is coarser (or, smal ler, weaker) than clg : P (Ω) −→ P (Ω). The elements supporting this fact are reported therein as a source of inspiration for more generalized operations.

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.

This paper addresses a variant of the product for the Dirichlet $L$--functions. We propose a completely detailed proof for the truth of the generalized Riemann conjecture for the Dirichlet $L$--functions, which states that the real part of the nontrivial zeros is $1/2$. The Wang and Hardy--Littlewood theorems are also discussed with removing the need for it. The results are applicable to show the truth of the Goldbach's conjecture.

In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n=4) of the sets of H-points of rank 2, which is indicated by P42.

Reverse order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product $AB$ is $(AB)^{(i,\ldots,j)} = B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, where $(\cdot)^{(i,\ldots,j)}$ denotes an $\{i,\ldots, j\}$-generalized inverse of matrix. Because $\{i,\ldots, j\}$-generalized inverse of a singular matrix is unique, the relationships between both sides of the reverse order law can be divided into four situations for consideration. This paper provides a thorough coverage of the reverse order laws for $\{i,\ldots, j\}$-generalized inverses of $AB$, from the development of background and preliminary tools to the collection of miscellaneous formulas and facts on the reverse order laws in one place with cogent introduction and references for further study. We begin with the introduction of a linear mixed model $y = AB\beta + A\gamma + \epsilon$ and the presentation of two least-squares methodologies to estimate the fixed parameter vector $\beta$ in the model, and the description of connections between the two types of least-squares estimators and the reverse order laws for generalized inverses of $AB$. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$, as well as necessary and sufficient conditions for $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$ to be invariant with respect to the choice of $B^{(s_2,\ldots,t_2)}A^{(s_1,\ldots,t_1)}$. We then present a unified approach to the 512 matrix set inclusion problems associated with the above reverse order laws for the eight commonly-used types of generalized inverses of $A$, $B$, and $AB$ through use of the definitions of generalized inverses, the block matrix method (BMM), the matrix rank method (MRM), the matrix equation method (MEM), and various algebraic calculations of matrices.

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 ${}_3 F_2$.

We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient solutions of vector optimization problems in constrained and unconstrained scenarios on Hadamard manifolds. This implies the need to extend different concepts, such as the Karush--Kuhn--Tucker vector critical points and generalized invexity functions, to Hadamard manifolds. The relationships between these quantities are clarified through a great number of explanatory examples. Second, we present an economic application proving that Nash's critical and equilibrium points coincide in the case of invex payoff functions.

Probabilistic inference problems have very broad practical applications. To solve this kind of problems under conditions of certainty, an effective mathematical apparatus has been developed. In real situations, obtaining deterministic estimates of relevant probabilities is often difficult; therefore, problems with handling uncertain estimates of probabilities appear. This paper examines the problem of probabilistic inference with probability trees provided that the initial probabilities are given in the form of intervals of their possible values.

This paper analyzes the robust dissipativity of uncertain stochastic generalized neural networks (USGNNs) with Markovian jumping parameters and time-varying delays. In practical applications most of the systems refer to uncertainties, hence, the norm-bounded parameter uncertainties and stochastic disturbance are considered. Then, by constructing an appropriate Lyapunov-Krasovskii functional (LKF) and by employing integral inequalities LMI-based sufficient conditions of the considered systems are established. Numerical simulations are given to show the merit of the presented results.

The non-linear analysis of hollow-core concrete slabs requires the use of advanced numerical techniques, proper constitutive models both for concrete and steel as well as particular computational skills. If prestressing, cracking, crack opening, material softening, etc. are also to be taken into account, then the computational task can far exceed the capabilities of an ordinary engineer. In order for the calculations to be carried out in a traditional design office, simplified calculation methods are needed. Preferably based on the linear finite element (FE) method with a simple approach that takes into account material nonlinearities. In this paper the simplified analysis of hollow-core slabs based on the generalized nonlinear constitutive law is presented. In the proposed method a simple decomposition of the traditional iterative linear finite element analysis and the non-linear algebraic analysis of the plate cross-section is used. Through independent analysis of the plate cross-section in different deformation states, a degraded plate stiffness can be obtained, which allows iterative update of displacements and rotations in the nodes of the FE model. Which in turn allows to update the deformation state and then correct translations and rotations in the nodes again. The results obtained from the full detailed 3D nonlinear FEM model and from the proposed approach are compared for different slab cross-sections. The obtained results from both models are consistent.

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.

One of the typical forms of linear matrix expressions (linear matrix-valued functions) is given by $A + B_1X_1C_1 + \cdots + B_kX_kC_k$, where $X_1, \ldots, X_k$ are independent variable matrices of appropriate sizes, which include almost all matrices with unknown entries as its special cases. The domain of the matrix expression is defined to be all possible values of the matrix expressions with respect to $X_1, \ldots, X_k$. I this article, we approach some problems on the relationships between the domains of two linear matrix expressions by means of the block matrix method (BMM), the matrix rank method (MRM), and the matrix equation method (MEM). As application, we discuss some topics on the relationships among general solutions of some linear matrix equations and their reduced equations.

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.

The simultaneous evaluation of heat/mass transference procures momentous significance in the polymer industry and engineering activities. Extensive utilization of such aspects includes propylene flares, heat exchangers, energy transfiguration in chilling towers, and amputation of post fortuitous heat in nuclear reactors. Owing to such prospective demands, we interpreted the Jeffrey liquid reactive flow under non-linear convection. We scrutinized the transference of heat/mass under generalized Fourier-Fick relations. Thermal conductivity depends on temperature while mass diffusivity is dependent on concentration. Besides, heat source along with first-order chemical reaction aspects are accounted for. Relevant transformations are exerted to achieve non-linear differential systems that are solved through the homotopy scheme. Influences of divers factors are exhibited via graphical benchmark.

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, the geometry of pseudoparallel, Ricci-generalized pseudoparallel and 2-Ricci-generalized pseudoparallel invariant submanifolds of an almost $\alpha$-cosymplectic $(\kappa,\mu,\nu)$ space has been searched under the some conditions. We also give some characterizations for such submanifolds. I think that obtained new results contribute to differential geometry.

In this work, generalized geometry of second-order tangent groups and affine configuration complexes is proposed. Initially, geometry for higher weights n=4 and weights n=5 is presented through some interesting and suitable homomorphisms, finally, this geometry is extended and generalized for any weight n.

The paper presents a modified finite element method for nonlinear analysis of 2D beam structures. To take into account the influence of the shear flexibility, a Timoshenko beam element was adopted. The algorithm proposed enables using complex material laws without the need of implementing advanced constitutive models in finite element routines. The method is easy to implement in commonly available CAE software for linear analysis of beam structures. It allows to extend the functionality of these programs with material nonlinearities. By using the structure deformations, computed from the nodal displacements, and the presented here generalized nonlinear constitutive law, it is possible to iteratively reduce the bending, tensile and shear stiffnesses of the structures. By applying a beam model with a multi layered cross-section and generalized stresses and strains to obtain a representative constitutive law, it is easy to model not only the complex multi-material cross-sections, but also the advanced nonlinear constitutive laws (e.g. material softening in tension). The proposed method was implemented in the MATLAB environment, its performance was shown on the several numerical examples. The cross-sections such us a steel I-beam and a steel I-beam with a concrete encasement for different slenderness ratios were considered here. To verify the accuracy of the computations, all results are compared with the ones received from a commercial CAE software. The comparison reveals a good correlation between the reference model and the method proposed.

This article has two objectives. Firstly, we will use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of Vector Optimization Problem within the novel field of the Hadamard manifolds. Previously, we will introduce the concepts of generalized approximate geodesic convex functions and illustrate them with examples. We will see the minimum requirements under which critical points, solutions of Stampacchia and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we will show an economical application, using again solutions of the variational problems to identify with Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions.

In a generalized topological space T_g = (Ω, T_g) (T_g-space), the g-topology T_g : P (Ω) −→ P (Ω) can be characterized in the generalized sense by specifying the generalized open, generalized closed sets (g-T_g-open, g-T_g-closed sets), generalized interior, generalized closure operators g-Intg, g-Cl_g : P (Ω) −→ P (Ω) (g-T_g-interior, g-T_g-closure operators), or generalized derived, generalized coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω) (g-T_g-derived, g-T_g-coderived operators), respectively. For very many T_g-spaces, the δ^th-iterates g-Der_g^(δ), g-Cod_g^(δ) : P (Ω) −→ P (Ω) of g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, defined by transfinite recursion on the class of successor ordinals are also themselves g-T_g-derived, g-T_g-coderived operators for new g-topologies in the generalized sense on Ω. Thus, the use of novel definitions of g-T_g-derived, g-T_g-coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, based on a very clever construction, together with their δ^th-iterates g-T_g-operators g-Der_g^(δ), g-Cod_g^(δ) : P (Ω) −→ P (Ω), defined by transfinite recursion on the class of successor ordinals, will give rise to novel generalized g-topologies on Ω. The present authors have been actively engaged in the study of g-T_g-operators in T_g-spaces. The study of the essential properties and the commutativity of novel definitions of g-T_g-interior and g-T_g-closure operators g-Int_g, g-Cl_g : P (Ω) −→ P (Ω), respectively, in T_g has formed the first part, and the study of the essential properties and sets of consistent, independent axioms of novel definitions of g-T_g-exterior and g-T_g-frontier operators g-Ext_g, g-Fr_g : P (Ω) −→ P (Ω), respectively, has formed the second part. In this work, which forms the last part on the theory of g-T_g-operators in T_g-spaces, the present authors propose to present novel definitions and the study of the essential properties of g-T_g-derived and g-T_g-coderived operators g-Der_g, g-Cod_g : P (Ω) −→ P (Ω), respectively, and their δ^th-iterates, and the notions of g-T_g-open and g-T_g-closed sets of ranks δ in T_g-spaces.

Prior studies have focused on the overall behavior of randomly moving particle swarms. However, the characteristics of the stochastic-constrained particles that form ubiquitously within these swarms remain oblivious. This study demonstrates a generalized diffusion equation for stochastic-constrained particles that considers the velocity and location aggregation effects observed from their parent particle swarm (i.e., a completely random particle swarm). This equation can be approximated as the form of Schr\"odinger equation in the microcosmic case (low relative density) and describe the dynamics of the total mass distribution in the macrocosmic case (high relative density). The predicted density distribution of the particle swarm in the stable aggregation state is consistent with the total mass distribution of massive, relaxed galaxy clusters (at least in the range of r < r_s), preventing cuspy problems in the empirical Navarro-Frenk-White (NFW) profile. This study opens a window to observe the dynamics of stochastic-constrained particles from a third perspective, from which the aggregation effect of particles without gravitation can be saw.

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.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, Most of important methodological advancements in more than half century of molecule modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science based on force fields parameterization by coarse graining, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but no transferability is available. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science and a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

In this paper, we give explicit asymptotic formulas for some sums over primes involving generalized alternating hyperharmonic numbers of types I, II and III. Analogous results for numbers with $k$-prime factors will also be considered.

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

The goal of this work is to show that the underlying symmetries of effective field theory can be traced to the onset of self-similarity. In particular, we argue that the scale-free structure of fractal geometry lies at the heart of invariance principles in classical and Quantum Field Theory.

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.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.