Malaysia generates significant quantities of Oil Palm Wastes (OPW) which can be potentially valorised into sustainable bioenergy as envisaged by the National Biomass Strategy (NBS-2020). Despite significant investments, policy directives and government support, the valorisation of OPW into bioenergy has remained low exacerbating waste management challenges. Therefore, the strategies and impediments to the rapid bioenergy development and bioelectricity generation from OPW require practical assessment. Therefore, this paper examines the level of development and diffusion of the biomass innovation system in Malaysia based on the Functions of Innovations Systems (FIS) approach developed by Dutch and Swedish researchers. Furthermore, the key factors hindering biomass energy technologies implementation in Malaysia and potential solutions were identified, highlighted and examined. Based on the FIS analysis the functions; entrepreneurial activities, knowledge development, and resources mobilization functions are well established in the Malaysian biomass innovation system (BIS). However, the functions of guidance of search; creation of legitimacy; knowledge diffusion and market formation are underdeveloped resulting in the low penetration of bioenergy in Malaysia. Other factors include; fossil fuel subsidies, numerous or conflicting energy policies and weak collaboration between academia and the industry. The outlined challenges can be addressed by revising fuel subsidies, Feed-in tariffs, RETs implementation, roles of supervisory agencies, and bureaucratic procedures for access to funds for research and development of bioenergy in Malaysia.

Over the last decade the blockchain technology has emerged to provide solutions to the complexity and privacy challenges of using distributed databases. It reduces the cost for customers by eliminating intermediaries and builds the trust in peer-to-peer communications. Over this time, the concept of blockchain has shifted greatly due to its potential in business growth for enterprises and the rapidly evolving applications in a collaborative smart cities' ecosystem, healthcare, and governance. Many platforms, with different architectures and consensus protocols, have been introduced. Consequently, it becomes challenging for an application developer to choose the right platform. Furthermore, blockchain has misaligned with the goals for efficient green collaborative digital ecosystem. Therefore, it becomes critical to address this gap and to build new frameworks to align blockchain with those goals. In this paper, we discuss the evolution of blockchain architecture and consensus protocols, bringing a retrospective analysis and discussing the rationale of the evolution of the various architectures and protocols, as well as capturing the assumptions conducting to their development and contributions to building collaborative applications. We introduce a classification of those architectures helping developers to choose a suitable platform for applications and providing insights for future research directions in the field to build new frameworks.

Non-linear activation functions are one of the main parts of deep neural network architectures. The choice of the activation function can affect model speed, performance and convergence. Most popular activation functions don't have any trainable parameters and don't alter during the training. We propose different activation functions with and without trainable parameters. Said activation functions have a number of advantages and disadvantages. We'll be testing the performance of said activation functions and comparing the results with widely known activation function ReLU. We assume that the activation functions with trainable parameters can outperform functions without ones, because the trainable parameters allow the model to "select'' the type of each of the activation functions itself, however, this strongly depends on the architecture of the deep neural network and the activation function itself.

The aim of this paper is to identify and document some functions and contextsof traditional pottery within northern Ghana. The descriptive approach of the qualitative research methodology was employed. Interview and observation methods were employed as the data collection methods. They were used to ascertain reasons why some potteryare engaged in certain contexts andfor certainfunctions. The data was tabulated to include the traditional name of the pot, the function and the context. The data were then analyzed and the indications were that, the potters make interesting forms of traditional pottery for different purposes; and the local name given to each pot perfectly defines their functions and contexts within northern Ghana. On the flipside of the coin, the function and context of every pot can also be dictated by its end user. Base on this, the researchers were able to discover some functions and contexts of the indigenous pottery which were put into some groups. On the first hand, the researchers classified the functions into five groups of purpose. These included: domestic purposes, religious purposes, agricultural purposes, rites of passage purposes and traditional herbal medicinal purposes. On other hand, seven groups of contexts were also discovered at the time of the study. These included: courtyards, bedrooms, bathrooms, graveyards, kitchens, shrines, and hencoops as places where these pots can be found among the people of the Northern Ghana.

Riparian zones represent ecotones between terrestrial and aquatic ecosystems and are of utmost importance to biodiversity and ecosystem functions. Modelling/mapping of these valuable and fragile areas is needed for an improved ecosystem management, based on an accounting of changes and on monitoring of their functioning in time. In Europe, the main legislative driver behind this goal is the European Commission’s Biodiversity Strategy to 2020, on one hand aiming at reducing biodiversity loss, on the other hand enhancing ecosystem services by 2020, and restoring them as far as feasible. A model, based on Earth Observation data, including Digital Elevation Models, hydrological, soil, land cover/land use data, and vegetation indices is employed in a multi-modular and stratified approach, based on fuzzy logic and object based image analysis, to delineate potential, observed and actual riparian zones. The approach is designed in an open modular way, allowing future modifications and repeatability. The results represent a first step of a future monitoring and assessment campaign for European riparian zones and their implications on biodiversity and on ecosystem functions and services. Considering the complexity and the enormous extent of the area, covering 39 European countries, including Turkey, the level of detail is unprecedented. Depending on the accounting modus, 0.95%–1.19% of the study area can be attributed as actual riparian area (considering Strahler’s stream orders 3-8, based on the Copernicus EU-Hydro dataset), corresponding to 55,558–69.128 km². Similarly depending on the accounting approach, the potential riparian zones are accounted for about 3-5 times larger. Land cover/land use in detected riparian areas was mainly of semi-natural characteristics, while the potential riparian areas are predominately covered by agriculture, followed by semi-natural and urban areas.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

This paper includes some new investigations and results for post quantum calculus, denoted by (p,q)-calculus. A chain rule for (p,q)-derivative is developed. Also, a new (p,q)-analogue of the exponential function is introduced and some its properties including the addition property for (p,q)-exponential functions are investigated. Several useful results involving (p,q)-binomial coefficients and (p,q)-antiderivative are discovered. At the final part of this paper, (p,q)-analogue of some elementary functions including trigonometric functions and hyperbolic functions are considered and some properties and relations among them are analyzed extensively.

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.

This review paper gives Excel functions for highly precise Colebrook’s pipe flow friction approximations developed by users. All shown codes are implemented as User Defined Functions – UDFs written in Visual Basic for Applications – VBA, a common programming language for MS Excel spreadsheet solver. Accuracy of the friction factor computed using nine to date the most accurate explicit approximations is compared with the sufficiently accurate solution obtained through an iterative scheme which gives satisfying results after sufficient number of iterations. The codes are given for the presented approximations, for the used iterative scheme and for the Colebrook equation expressed through the Lambert W-function (including its cognate Wright ω-function). The developed code for the principal branch of the Lambert W-function has additional and more general application for solving different problems from variety branches of engineering and physics. The approach from this review paper automates computational processes and speeds up manual tasks.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

In this study, based on a new quantum integral identity, the authors establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures.

Continuation methods are presented that are capable of treating frequency-domain flutter equations including multiple nonlinearities represented by describing functions. A small problem demonstrates how a series of continuation processes can find all limit-cycle oscillations within a specified region with a reasonable degree of confidence. Curves of the limit-cycle amplitude variation with velocity, indicating regions of stability and instability with colors give a compact view of the nonlinear behavior throughout the flight regime. A continuation technique for reducing limit-cycle amplitudes by adjusting various system parameters is presented. These processes are economical enough to be a routine part of aircraft design and certification.

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

In this paper, some convexity properties and some inequalities for the (p,k)-analogue of the Gamma function, Г_p,k(x) are given. In particular, a (p,k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p,k)-analogue of the Riemann zeta function, ζ_p,k(x) is introduced and some associated inequalities are derived. The established results provide the (p,k)-generalizations of some known results concerning the classical Gamma function.

Bent trees have been observed during the early years in juvenile plantations (less than 5 years-old) of Tectona grandis in Costa Rica. The relationship between bending and the morphological characteristics of the trees was explored. An evaluation of bent trees was conducted in six juvenile plantations (8, 17, 27, 28, 31, and 54 months old) of Tectona grandis. Site 1 with 8-month-old plantations did not display any relationship with any tree morphological variable (diameter, height, and crown weight of tree), whereas for the sites 2, 3, and 4 with 17-, 27-, and 28-month-old plantations, respectively, all the tree morphological variables were statistically correlated with the bent trees. A multiple regression analysis showed that the most influential variables were height to crown base, crown weight, diameter, and total height of the tree. An evaluation of the bending risk factor (RF) was correlated with the height to crown base, crown weight, and form factor. The modulus of elasticity and chemical compositions of bent trees differed from those of straight trees. The causes of tree bending are complex, involving, among other factors, the morphology of the trees, plantation conditions, and other factors specific to the xylem, such as the specific gravity, modulus of elasticity, and presence of calcium and magnesium in the wood.

The main aim of this paper is to establish two generalized integral formulas involving the extended Mittag–Leffler function based on the well known Lavoie and Trottier integral formula and the obtain results are express in term of extended Wright-type function. Also, we establish certain special cases of our main result.

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.

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.

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

In this paper, we introduce a new generalization of the Hermite polynomials via (p, q)-exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, explicit formula, recurrence relation, integral representation. We also de…ne a (p, q)-analogue of the Bernstein polynomials and acquire their some formulas. We then provide some (p, q)-hyperbolic representations of the (p, q)-Bernstein polynomials. In addition, we obtain a correlation between (p, q)-Hermite polynomials and (p, q)-Bernstein polynomials.

The aim of this paper is to introduce a new methodology for the fault diagnosis of induction machines working in transient regime, when time-frequency analysis tools are used. The proposed method relies on the use of the optimized Slepian window for performing the short time Fourier transform (STFT) of the stator current signal. It is shown that for a given sequence length of finite duration the Slepian window has the maximum concentration of energy, greater than can be reached with a gated Gaussian window, which is usually used as analysis window. In this paper the use and optimization of the Slepian window for fault diagnosis of induction machines is theoretically introduced and experimentally validated through the test of a 3.15 MW induction motor with broken bars during the start-up transient. The theoretical analysis and the experimental results show that the use of the Slepian window can highlight the fault components in the current's spectrogram with a significant reduction of the required computational resources.

Many of engineering’s problems are about to optimise equations, functions and process models equations which appear on common or even complex science’s cases. Most applied optimisation methods nowadays can only be used on particular cases, so the main objective of this article is to define a computational method that can optimise or even find target values for specified objective functions and variables, by just using computer effort. Chemical plants involve many differential equations and they can be optimised with more facility now. On this paper, there are shown as example, an optimisation for a chemical reactor, which is found the optimal temperature and volumetric flow rate of feed, for the given objective function being the composition of the desired product. Named Domain’s Sweep, it is an algorithm that evaluate given(s) mathematical function(s) and/or equation(s) by varying your(s) independent variable(s) through loops with a given step size and solving it after closing the degrees of freedom, and finally, with some condition statements, store all the optimum values of given or created objective functions with its respective independent variables. In another words, the user create an objective function and this method find the function’s maximum, minimum or a certain chosen target value, even if it does not have an inflection point in the given search interval of the independent variables.

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.

In recent years, music education in Ibero-America has been losing ground within the school environment in favor of the development of curricular systems that benefit academic results in standardized tests. Despite this, several studies in the field of cognitive neurosciences have found evidence of great relevance and in which it can be observed how music education can favor cognitive development and performance in practically all stages of human development, with important results in language tasks, attention, and executive functions such as planning, inhibition, cognitive flexibility and working memory.

Bringing toghether mathematical and philosophical ideas related to transcendental numbers, this paper begins with a survey on transcendence and transcendental numbers, it then presents several properties of the transcendental numbers e and π, and then it gives the proof of a new inequality for transcendental numbers. Also, in relationship with these topics, we study solutions to the Yang-Baxter equation from hyperbolic functions and from logical implication.

We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give someof their basic properties including not only addition property, but also derivative properties and integralrepresentations. We also de.ne the Hermite based λ -Stirling polynomials of the second kind, and thenprovide some relations. Moreover, we derive several correlations and identities including the Hermite-Kampéde Fériet (or Gould-Hopper) family of polynomials, the Hermite based poly-Bernoulli polynomials with a qparameter and the Hermite based λ -Stirling polynomials of the second kind.

In this paper we establish several Hermite-Hadamard type integral inequalities for hyperbolic p-convex functions. Applications for special means are provided as well.

In this paper, we define a (p,v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81–106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results.

In this paper a dynamic relationship between the CO2 emissions in Finland, Norway and Sweden is presented. With the help of a VAR(2) model, and using the Granger terminology, it is shown that the emissions in Finland are affecting those in Norway and Sweden. Other aspects of this dynamic relationship are presented as well.

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

Sumudu transform of the Dixon elliptic function with non zero modulus a ≠ 0 for arbitrary powers sm^N(x,a) ; N ≥ 1 ; sm^N(x,a)cm(x,a) ; N ≥ 0 and sm^N(x,a)cm²(x,a) ; N ≥ 0 is given by product of Quasi C fractions. Next by assuming denominators of Quasi C fraction to 1 and hence applying Heliermann correspondance relating formal power series (Maclaurin series of Dixon elliptic functions) and regular C fraction, Hankel determinants are calculated and showed by taking a = 0 gives the Hankel determinants of regular C fraction. The derived results were back tracked to the Laplace transform of sm(x,a) ; cm(x,a) and sm(x,a)cm(x,a).

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.

In this paper, we develop the theory of the multiple q-analogue of the Heine’s binomial formula, chain rule and Leibnitz’s rule. We also derive many useful definitions and results involving multiple q-antiderivative and multiple q-Jackson’s integral. Finally, we list here multiple q-analogue of some elementary functions including trigonometric functions and hyperbolic functions. This may be a good consideration in developing the multiple q-calculus in combinatorics, number theory and other fields of mathematics.

Parts produced by laser or electron-beam powder bed fusion (PBF) additive manufacturing are prone to residual stresses, deformations, and other defects linked to non-uniform temperature distribution during the manufacturing process. Several researchers have highlighted the important role scan sequence plays in achieving uniform temperature distribution in PBF. However, scan sequence continues to be determined offline based on trial-and-error or heuristics, which are neither optimal nor generalizable. To address these weaknesses, we have articulated a vision for an intelligent online scan sequence optimization approach to achieve uniform temperature distribution, hence reduced residual stresses and deformations, in PBF using physics-based and data-driven thermal models. This paper proposes SmartScan, our first attempt towards achieving our vision using a simplified physics-based thermal model. The conduction and convection dynamics of a single layer of the PBF process are modeled using the finite difference method and radial basis functions. Using the model, the next best feature (e.g., stripe or island) that minimizes a thermal uniformity metric is found using control theory. Simulations and experiments involving laser marking of a stainless steel plate are used to demonstrate the effectiveness of SmartScan in comparison to existing heuristic scan sequences for stripe and island scan patterns. In experiments, SmartScan yields up to 43% improvement in average thermal uniformity and 47% reduction in deformations (i.e., warpage) compared to existing heuristic approaches. It is also shown to be robust, and computationally efficient enough for online implementation.

This research revealed the children with difficulties in attentional functions in healthy children attending primary school and aimed to identify the possible socio-demographic factors such as child’s age, gender and school’s grade that could influence attentive performance. The participants were 105 children aged 6-10 years (M age=8.6; SD=1.04), 57 females, attending primary schools. Family economic condition attested mostly at a medium level (63.5%) and parents had more frequently 13 years of schooling. The computerized test KiTAP was administered to children to assess attentional functions. Results showed higher frequency of omissions and false alarms and a reduced speed in Alertness, Go/No go and Sustained Attention tasks comparing to Italian norms. A series of hierarchical regression analyses were run with school grade, gender and current age as independent variables and mean reaction times (and standard deviation), number of omissions and of false alarms as dependent ones. Results showed male gender and attending a lower primary school grade impacting on lower attentional performance in several subtests. Females showed the best performances in distractibility and impulsive reaction tendencies tests, while higher school grade positively influenced the divided and sustained attention. These results could be useful to identify children with major attentional difficulties and some recommendations for futures studies and implement attention empowerment programmes were proposed.

Current-quark masses are compared to the rest masses allowed by the Helmholtz equation in a polar model. Within the uncertainty of the current u quark mass determination, the current quark mass coincides with the rest mass allowed by the Helmholtz equation in the polar model in accordance with the second root of the zero Neumann function. Current d quark mass coincides with the rest mass calculated in accordance with the third root of the Bessel zero function. On the basis of a comparison of these results with the results obtained earlier for ordinary real particles u and d quarks stability is discussed.

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

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

In this paper we obtain some inequalities of Hermite-Hadamard type for composite convex functions. Applications for AG, AH-h-convex functions, GA, GG, GH-h-convex functions and HA, HG, HH-h-convex function are given.

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. One of these is a four-parameter polynomial with a discrete spectrum. Another that appeared while solving a Heun-type equation has a mix of continuous and discrete spectra. Based on these results and on our recent study of the solution space of an ordinary differential equation of the second kind with four singular points, we introduce a modification of the hypergeometric polynomials in the Askey scheme. Up to now, all of these polynomials are defined only by their three-term recursion relations and initial values. However, their other properties like the weight function, generating function, orthogonality, Rodrigues-type formula, etc. are yet to be derived analytically. This is an open problem in orthogonal polynomials.

In this paper we obtain some inequalities of Hermite-Hadamard type for composite convex functions. Applications for AG, AH-convex functions, GA, GG, GH-convex functions and HA, HG, HH-convex function are given. Applications for p, r-convex and LogExp functions are presented as well.

Predicting how a genetic change affects a given character is a major challenge in biology, and being able to tackle this problem relies on our ability to develop realistic models of gene networks. However, such models are rarely tractable mathematically. In this paper, we propose a mathematical analysis of the sigmoid variant of the Wagner gene-network model. By considering the simplest case, that is, one unique self-regulating gene, we show that numerical simulations are not the only tool available to study such models: theoretical studies can be done too, by mathematical analysis of discrete dynamical systems. It is first shown that the particular sigmoid function can be theoretically investigated. Secondly, we provide an illustration on how to apply such investigations in the case of the dynamical system representing the one self-regulating gene.

There is a large body of research on determining the impact of field variability of soil on crop yields. In contrast, site-specific information about crop responses to agronomic treatments is less frequent. On-Farm Precision Experimentation (OFPE) brings important information to understand the spatial variation of crop response to agronomic practices and thus to improve agronomic decisions. The objective of this work was to investigate the spatial variability of corn yield responses to nitrogen and seed rates using OFPE in four fields in the US Midwest. Geographically weighted regression was applied to generate local regression coefficients, which were used to delineate response zones in each field. The results showed the existence of great potential to adjust the rates of these inputs according to the response of each zone identified by the proposed method. The results of this study can be applied to reevaluate expectations on variable rate prescriptions guided largely by soil and variability.

The developmental phase of adolescence is characterized by a multitude of neurocognitive and psychosocial changes and is therefore considered one of the most critical developmental periods of life. Experimentation on the use of substances often begins in adolescence and so does the addiction process. Most research in human subjects shows that chronic cannabis abuse is the cause of the impairment of some cognitive functions, affecting the performance on divided attention, verbal memory and working memory. In this study, we wanted to investigate how the abuse of cannabis (chronic, occasional and absence use) can influence global cognitive functioning, also through executive functions. From the statistical analyzes of our study, it emerges that the group of subjects who use chronic cannabis (group 1) has a significant drop in working memory tasks compared to the group that does not use it (group 3). In addition, the goal of future studies by our group is to verify the permanent alteration of cognitive processes affected through revaluations with calendar follow-up (controlled).

This article aims to identify the generating function of modi…ed Apostol type q-Bernoulli polynomials. With the aid of this generating function, some properties of modi…ed Apostol type q-Bernoulli polynomials are given. It is shown that aforementioned polynomials are q-Appell. Hence, we make use of these polynomials to have applications on q-Umbral calculus. From those applications, we derive some theorems in order to get Apostol type modi…ed q-Bernoulli polynomials as a linear combination of some known polynomials which we stated in the paper.

In recent years, the field of deep learning achieved considerable success in pattern recognition, image segmentation and may other classification fields. There are a lot of studies and practical applications of deep learning on images, video or text classification. In this study, we suggest a method for changing the architecture of the most performing CNN models with the aim of designing new models to be used as stand-alone networks or as a component of an ensemble. We propose to replace each activation layer of a CNN (usually a ReLu layer) by a different activation function stochastically drawn from a set of activation functions: in this way the resulting CNN has a different set of activation function layers.

In this paper we establish some weighted integral inequalities of Ostrowski, Čebyšev and Lupaş type. Applications for continuous probability density functions supported on infinite intervals with two examples are also given.

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

The majority of E-commerce transactions reveal private information such as customers' identities, order contents, and payment information during the transaction. Other personal information such as health conditions, religion, and even ethnicity may be also deduced. Even when deploying electronic cryptocurrencies such as Bitcoin, anonymity cannot be fully guaranteed. Also, many anonymous payment schemes suffer from possible double spending circumstances. E-commerce privacy is basically a difficult problem as it involves parties with concurring interests. Three major e-commerce requirements are highly difficult to resolve: anonymous purchase, anonymous delivery, and anonymous payment. This work presents a possible e-commerce system addressing all three anonymity requirements for electronic-items business on open networks. The system offers anonymous entities authentication mechanisms up to completing a fair anonymous e-commerce transaction. The system is based on deploying a physically clone-resistant hardware token for each relevant involved party. The tokens are made clone-resistant by accommodating a Secret Unknown Cipher (SUC) in each hardware-token as a digital PUF-like identity. A set of novel generic system-setups for units, protocols and e-commerce schemes is introduced. The proposed anonymization is basically attained by virtually-replacing relevant e-commerce entities by low-cost, unique and clone-resistant tokens/units using SUCs. The units act as trustable anonymous, authenticated and non-replaceable entities monitored by their acting users.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

To embrace the special theory of relativity with classical thermodynamics correct Lorentz transformations of thermodynamic state functions are formulated. All of these Lorentz transformations of state functions equally support the time dilation phenomenon which is experimentally verified fact. Relativistic Boltzmann constant proves entropy to be the Lorentz variant. Twin paradox thought experiments for heat engines prove heat flux to be Lorentz variant. Lorentz transformation of entropy and heat flux proves temperature Lorentz invariant. All thermodynamic state functions are proved to be Lorentz variant which is shown in accord with Lorentz transformation of thermodynamic work.

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.

This paper formulates a new strategy for participatory forest management consisting of encouraging public participation as long as it increases empathy among participants. The strategy requires the homogeneous representation of the opinion of a participant (i.e. to determine how they assess a forest plan and identify the best one). Utility assessments are prepared for participants through pair-comparisons between meaningful points in the territory and from value functions based on forest indicators. The best plan is designed by applying combinatorial optimization algorithms to the utility of a participant. The calculating of empathy -of one participant relative to another - is based on the equivalence of their respective utilities when the current forest plan is modified. This involves calculating the opinions that are due to systematic changes in the collective plan for those participants that each participant supposes will affect the utility of the other participants. Calculating empathy also requires knowing the interactions among participants, which have been incorporated through agent-based simulation models. Application of the above methodology has confirmed the association between increases in empathy and convergence of opinions in different scenarios: well and medium-informed participants and with and without interaction among them, which verifies the proposed strategy. In addition, this strategy is easily integrated into available information systems and its outcomes show advantages over current participatory applications.

Recently, much attention has been devoted to finding highly efficient and powerful activation functions for CNN layers. Because activation functions inject different nonlinearities between layers that affect performance, varying them is one method for building robust ensembles of CNNs. The objective of this study is to examine the performance of CNN ensembles made with different activation functions, including six new ones presented here: 2D Mexican ReLU, TanELU, MeLU+GaLU, Symmetric MeLU, Symmetric GaLU, and Flexible MeLU. The highest performing ensemble was built with CNNs having different activation layers that randomly replaced the standard ReLU. A comprehensive evaluation of the proposed approach was conducted across fifteen biomedical data sets representing various classification tasks. The proposed method was tested on two basic CNN architectures: Vgg16 and ResNet50. Results demonstrate the superiority in performance of this approach. The MATLAB source code for this study will be available at https://github.com/LorisNanni.

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 .

This paper presents an alternative constraint handling approach within a specialized genetic algorithm (SGA) for the optimal reactive power dispatch (ORPD) problem. The ORPD is formulated as a nonlinear single-objective optimization problem aiming to minimize power losses while keeping network constraints. The proposed constraint handling approach is based on a product of sub-functions that represents permissible limits on system variables and that includes a specific goal on power loss reduction. The main advantage of this approach is the fact that it allows a straightforward verification of both feasibility and optimality. The SGA is examined and tested with the proposed constraint handling approach and the traditional penalization of deviations from feasible solutions. Several tests are run in the IEEE 30, 57, 118 and 300 bus test power systems. The results obtained with the proposed approach are compared to those offered by other metaheuristic techniques reported in the specialized literature. Simulation results indicate that the proposed genetic algorithm with the alternative constraint handling approach yields superior solutions when compared to other recently reported techniques.

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.

This study mostly analyzes the pragmatic viewpoints of speech acts and language functions through Halliday’s (1975) language functions and Searle’s (1976) speech acts were adapted to analyze the functional aspects of the conversations and it was also intended to explore the teachers’ perception toward teaching and learning English as a Foreign Language (EFL) learners’ textbooks and the teacher’s components of communicative knowledge regarding the functions of language in daily activity. The participants of this paper consisted of thirteen Sunrise 10, 11, 12 grades of Kurdish teachers at high school English in Iraqi Kurdistan. Through semi-structured interview, it was found that the conversations in the mentioned textbooks are insufficient from the pragmatic point of view. Some recommendation for the textbook designers, teachers, material developer were raised to make up the shortcomings of the textbooks. The findings reveal that the conversation texts in Sunrise textbooks are not meeting the systematic standard of pragmatic competence the English language learners and the book designer must be recommended to be aware of those shortcomings of the textbook series if they are required to develop their speaking skills in both student and activity series. The implications of this paper can be helpful in comparing the results of this study with other similar studies to check if there is a universal pattern in performing the speech acts and language functions and the interest to Kimberley Education for Life learners in increasing their knowledge of pragmatics in general and the role of language functions and speech acts investigated in this study.

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.

A convenient practical model for accurately estimating the total entropy (ΣSi) of atmospheric gases based on physical action is proposed. This realistic approach is fully consistent with statistical mechanics, but reinterprets its partition functions as measures of translational, rotational and vibrational action or quantum states, to estimate the entropy. With all kinds of molecular action expressed as logarithmic functions, the total heat required for warming a chemical system from 0o K (ΣSiT) to a given temperature and pressure can be computed, yielding results identical with published experimental third law values of entropy. All thermodynamic properties of gases including entropy, enthalpy, Gibbs energy and Helmholtz energy are directly estimated using simple algorithms based on simple molecular and physical properties, without resource to tables of standard values; both free energies are measures of quantum field states and of minimal statistical degeneracy, decreasing with temperature and declining density. We propose that this more realistic approach has heuristic value for thermodynamic computation of atmospheric profiles, based on steady state heat flows equilibrating with gravity. Potentially, this application of an action principle can provide better understanding of emergent properties of many natural or evolving complex systems, including modelling of predictions for global warming.

There has been a growing interest in incorporating psychological and neuroscientific knowledge about the development of cognitive functions in educational policies and academic practices. In this paper, we argue that the current knowledge about the interactions between these functions and their neurodevelopmental characteristics should also be considered in order to develop practices that could be better suited to pupils depending on their age. To facilitate this, we review current neuroscientific knowledge on the competitive interactions between two neural circuitry underlying distinct learning functions, their developmental trajectories and how they are linked to other functions such as cognitive control. The incorporation of this knowledge in education could help improve academic outcomes.

Motivation: 16S rRNA gene amplicon based sequencing has significantly expanded the scope of metagenomics research by enabling microbial community analyses in a cost-effective manner. The possibility to infer functional potential of a microbiome through amplicon sequencing derived taxonomic abundance profiles has further strengthened the utility of 16S sequencing. In fact, a surge in 'inferred function metagenomic analysis' has recently taken place, wherein most 16S microbiome studies include inferred functional insights in addition to taxonomic characterization. Tools like PICRUSt, Tax4Fun, Vikodak and iVikodak have significantly eased the process of inferring function potential of a microbiome using the taxonomic abundance profile. A platform that can enable hosting of inferred function 'metagenomic studies' with comprehensive metadata driven search utilities (of a typical database), coupled with on-the-fly comparative analytics between studies of interest, can be a major improvement to the state of art. ReFDash represents an effort in the proposed direction. Methods: This work introduces ReFDash - a Repository of Functional Dashboards. ReFDash, developed as a significant extension of iVikodak (function inference tool), provides three broad unique offerings in inferred function space - (i) a platform that hosts a database of inferred function data being continously updated using public 16S metagenomic studies (ii) a tool to search studies of interest and compare upto three metagenomic environments on the fly (iii) a community initiative wherein users can contribute their own inferred function data to the platform. ReFDash therefore provides a first-of-its-kind community-driven frame-work for scientific collaboration, data analytics, and sharing in this area of microbiome research. Results: Overall, the ReFDash database is aimed at compiling together a global ensemble of 16S-derived Functional Metagenomics projects. ReFDash currently hosts close to 50 ready-to-use, re-analyzable functional dashboards representing data from approximately 18,000 microbiome samples sourced from various published studies. Each entry also provides direct downloadable links to associated taxonomic files and metadata employed for analysis. Conclusion: The vision behind ReFDash is creation of a framework, wherein users can not only analyze their microbiome datasets in functional terms, but also contribute towards building an information base by submitting their functional analyses to ReFDash database. ReFDash web-server may be freely accessed at https://web.rniapps.net/iVikodak/refdash/

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.

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

In the present work we study the properties of geodesic sub-$ (\alpha,b,s) $-preinvex functions on Hadamard manifolds and establish some basic properties in both general and differential cases. Further, we study sufficient conditions of optimality and proved some new inequalities under geodesic sub-($ \alpha,b,s $)-preinvexity.

Boolean functions and networks are commonly used in the modeling and analysis of complex biological systems, and this paradigm is highly relevant in other important areas in data science and decision making, such as in the medical field and in the finance industry. In a Boolean model, the truth state of a variable is either 0 or 1 at a given time. Despite its apparent simplicity, Boolean networks are surprisingly relevant in many areas of application such as in bioinformatics to model gene expressions and interactions. In the latter case, a gene is either ``on" or ``off" depending on its expression level. Despite the promising utility of Boolean modeling, in most practical applications the Boolean network is not known. Automated learning of a Boolean network and Boolean functions, from data, is a challenging task due in part to the large number of unknowns (including both the structure of the network and the functions) to be estimated, for which a brute force approach would be exponentially complex. In this paper we develop a new information theoretic methodology that we show to be significantly more efficient than previous approaches. Building on the recently developed optimal causation entropy principle (oCSE), that we proved can correctly infer networks distinguishing between direct versus indirect connections, we develop here an efficient algorithm that furthermore infers a Boolean network (including both its structure and function) based on data observed from the evolving states at nodes. We call this new inference method, Boolean optimal causation entropy (BoCSE), which we will show that our method is both computationally efficient and also resilient to noise. Furthermore, it allows for selection of a set of features that best explains the process, a statement that can be described as a networked Boolean function reduced order model. We highlight our method to the feature selection in several real-world examples: (1) diagnosis of urinary diseases, (2) Cardiac SPECT diagnosis, (3) informative positions in the game Tic-Tac-Toe, and (4) risk causality analysis of loans in default status. Our proposed method is effective and efficient in all examples.

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

This study focuses on a new class of functions called sub-b-s-preinvex, that is a generalization of sub-b-s-convex and preinvex functions, and discusses some of their properties. A new sub-b-s-preinvex programming is introduced and the sufficient conditions of optimality under this type of function is established.

Steel reinforcement in concrete has the tendency to corrode and this process can lead to structural damage. FRP reinforcement represents a viable alternative for structures exposed to aggressive environments and has many possible applications where superior corrosion resistance properties are required. The use of FRP rebars as internal reinforcements for concrete, however, is limited to specific structural elements and does not yet extend to the whole structure. The reasons for this relate to the limited availability of curved or shaped reinforcing elements on the market and their reduced structural performance. Various studies, in fact, have shown that the mechanical performance of bent portions of composite bars is reduced significantly under a multiaxial combination of stresses and that the tensile strength can be as low as 25% of the maximum tensile strength that can be developed in the straight part. In a significant number of cases, the current design recommendations for concrete structures reinforced with FRP, however, were found to overestimate the bend capacity of FRP rebar. This paper presents the state-of-the art review of the research works on the strength degradation in curved FRP composites and highlighted the performance of exiting predictive models for the bend capacity of FRP reinforcement. Recent practical predictive model based on the Tsai-Hill failure criteria by considering the material at marcromechanical level is also discussed and highlighted. The review also identifies the challenges and highlights the future directions of research to explore the use of shaped FRP composites in civil engineering applications and the trends for future research in this area.

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.

Mild Cognitive Impairment (MCI) is a clinical syndrome characterized by a moderate decline in one or more cognitive functions with a preserved autonomy in daily life activities [1]. MCI exhibits cognitive, behavioral, psychological symptoms [2]. The executive functions (EFs) are a set of key functions for everyday life and physical and mental health; and allow adapting the behavior to external changes [3-5]. Higher-level executive functions develop from basic EFs (inhibition, working memory, attentional control, and cognitive flexibility). They are planning, reasoning, problem- solving, and fluid intelligence (Gf) [3]. This systematic review investigates the relationship between higher-level executive functions and healthy and pathological aging, assuming the role of executive functions deficits as a predictor of cognitive decline. The systematic review was conducted according to the PRISMA Statement [6-7]. A total of 73 studies were identified. The results indicate that 65.8% of the studies confirm significant EFs alterations in MCI (100% problem solving, 71.4% fluid intelligence, 56.8% planning, 50% reasoning). These results seem to highlight a strong prevalence of higher-level executive functions deficits in MCI elderly than in healthy elderly.

This paper presents Chebyshev Type inequalities for the Riemann-Liouville variable-order fractional integral operator using two synchronous functions on the set of real numbers. It is the first result of its kind in the current literature using variable-order Riemann-Liouville fractional integral operator. Some special cases for the result obtained in the paper are discussed.

The paper describes a method of solving some stochastic processes using generating functions. A general theorem of generating functions of a particular type is derived. A generating function of this type is applied to a stochastic process yielding polynomial time algorithms for certain partitions. The method is generalized to a stochastic process describing a rather general linear transform. Finally, the main idea of the method is used in deriving a theoretical polynomial time algorithm to the knapsack problem.

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.

The imperfection of theoretical and methodological approaches to regulate the jump process transition when combining differentiated energy resources is a pressing issue. The goal of this paper is to develop a theory and a method to regulate the integration-balancing processes of combining diversified resources. The concept of combining integration and balancing models has been substantiated by methods of transforming multidimensional space and approximating generalized functions that represent jump-like processes. Theoretical and operational-regulatory models of economic sustainability have been developed, substantiating new concepts, patterns, properties, dependencies and indicators of the dynamics of the processes of combination; the optimality conditions for the number of approximations of generalized functions, interpreting the effects of control functions of combining resources, are determined. New methods for solving problems have been developed: the organization of the energy technology complex of facilities for enhanced resource diversification and the Center for Sustainability, improving the quality of managing dynamic processes in terms of combining and diversifying resources.

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.

This paper presents the process of designing, fabrication, assembling, programming and optimizing a prototype of a nonlinear mechatronic Ball-Plate System (BPS) as a laboratory platform for STEM engineer education. Due to the nonlinearity and complexity of BPS, task presents challenging issues, such as: 1) difficulties in controlling the stabilization of a given position point known as steady state error, 2) position resolution known as specific distance error and 3) adverse environmental effects - light shadow error, also discussed in this paper. The laboratory BPS prototype for education was designed, manufactured and installed at the Karlovac University of Applied Sciences at the Department of Mechanical Engineering, Study of mechatronics. The low-cost two degrees BPS system uses a USB HD camera for computer vision as feedback and two DC servomotors as actuators. Due to controlling problems, an advanced block diagram of control system is proposed and discussed. An open-source control system based on Python scripts that allows the use of ready-made functions from the library allows changing the color of the ball and the parameters of the PID controller, thus indirectly simplifying control system and directly the mathematical calculation. The authors will continue their research on this BPS mechatronic platform and control algorithms.

The purpose of work is to quantify the changes of the organism functional reserves during the successive phases of the human health Space-Time Continuum (STC) on the basis of postulates of reliability complex systems theory. The study is devoted to the problem of age-related human involution, which is evaluated not from the causal, but from the kinetic point of view. The analysis of 10 most important basic life support systems of human body — cardiovascular (CVS), respiratory (RS), nervous (NS), digestive (DS), endocrine (ES), immune (IS), excretory (EXS), brain (BS), musculo-skeletal (MSS), hematopoietic (HS) was carried out. Based on this analysis two levels of ensuring the reliability of organism’s work were revealed: sequential and parallel. The system of logical equations for reduced sequential system is: Ys1 = CVS ∧ RS ∧ BS, where ∧ is the notation for the conjunctions of set elements. The system of logical equations for the reduced parallel system is: Ys2 = NS ∨ DS ∨ ES ∨ IS ∨ HS ∨ EXS ∨ MSS ,where ∨ is the disjunction of the scheme elements. Visualization of human STC changes the concept of the kinetics of age-related changes in the organism and the role of determinants of health as a stable factor accompanying a uniform, smooth transition from the most pronounced functions of the body to their gradual extinction. For human STC is formulated the following regularity kinetics of involutionary processes: after 30 years of age in the human body morphological changes regress in arithmetic progression, and the functions of organs in a geometric one. Assumption of health as a state redundancy of functions is suggested.

In this paper, we study the entire or meromorphic solutions for differential-difference equations in f(z) , its shifts, its derivatives and derivatives of its shifts. and study some Hayman's results for differential-difference polynomials.

Knowledge of the agricultural soil microbiota, of the microbial consortia that comprise it, and the promotion of agricultural practices that maintain and encourage them, is a promising way to improve soil quality for sustainable agriculture and to provide food security. Although numerous studies have demonstrated the positive effects of beneficial soil microorganisms on crop yields and quality, the use of microbial consortia in agriculture remains low. Microbial consortia have more properties than an individual microbial inoculum, due to the synergy of the microorganisms that make them up. This review describes the main characteristics, ecosystem functions, crop benefits and biotechnological applications of microbial consortia composed of arbuscular mycorrhizal fungi, plant growth promoting bacteria and actinobacteria, to promote the restoration of agricultural soils and, consequently, the quality and health of agricultural crops. The aim is to provide knowledge that will contribute to the development of sustainable and sufficiently productive agriculture, which will adapt in a good way to the pace of the growing human population and to climate change.

In this work, Gaussian Tribonacci functions are defined and investigated on the set of real numbers $\mathbb{R},$ \textit{i.e}., functions $f_{G}$ $:$ $\mathbb{R}\rightarrow \mathbb{C}$ such that for all $% x\in \mathbb{R},$ $n\in \mathbb{Z},$ $f_{G}(x+n)=f(x+n)+if(x+n-1)$ where $f$ $:$ $\mathbb{R}\rightarrow \mathbb{R}$ is a Tribonacci function which is given as $f(x+3)=f(x+2)+f(x+1)+f(x)$ for all $x\in \mathbb{R}$. Then the concept of Gaussian Tribonacci functions by using the concept of $f$-even and $f$-odd functions is developed. Also, we present linear sum formulas of Gaussian Tribonacci functions. Moreover, it is showed that if $f_{G}$ is a Gaussian Tribonacci function with Tribonacci function $f$, then $% \lim\limits_{x\rightarrow \infty }\frac{f_{G}(x+1)}{f_{G}(x)}=\alpha \ $and\ $\lim\limits_{x\rightarrow \infty }\frac{f_{G}(x)}{f(x)}=\alpha +i,$ where $% \alpha $ is the positive real root of equation $x^{3}-x^{2}-x-1=0$ for which $\alpha >1$. Finally, matrix formulations of Tribonacci functions and Gaussian Tribonacci functions are given. In the literature, there are several studies on the functions of linear recurrent sequences such as Fibonacci functions and Tribonacci functions. However, there are no study on Gaussian functions of linear recurrent sequences such as Gaussian Tribonacci and Gaussian Tetranacci functions and they are waiting for the investigating. We also present linear sum formulas and matrix formulations of Tribonacci functions which have not been studied in the literature.

The aging of the global population has increased the prevalence of neurodegenerative conditions. Bacopa monnieri (BM), an herb with active compounds, such as bacosides A and B, betulinic acid, loliolide, asiatic acid, and quercetin, demonstrates the potential for brain health. Limited research has been conducted on the therapeutic applications of BM in neurodegenerative conditions. This systematic review aims to project BM's beneficial role in brain disorders. BM has anti-apoptotic and antioxidant actions and can repair damaged neurons, stimulate kinase activity, restore synaptic function, improve nerve transmission, and increase neuroprotection. The included twenty-two clinical trials demonstrated that BM can reduce Nuclear Factor-κB phosphorylation, improve emotional function, cognitive functions, anhedonia, hyperactivity, sleep routine, depression, attention deficit, learning problems, memory retention, impulsivity, and psychiatric problems. Moreover, BM can reduce the levels of pro-inflammatory biomarkers and oxidative stress. Here, we highlight that BM provides notable therapeutic benefits and can serve as a complementary approach for the care of patients with neurodegenerative conditions associated with brain disorders. This review adds to the growing interest in natural products and their potential therapeutic applications by improving our understanding of the mechanisms underlying cognitive function and neurodegeneration and informing the development of new therapeutic strategies for neurodegenerative diseases.

Inspired by the definition of degenerate multi-poly-Genocchi polynomials given by using the degenerate multi-polyexponential functions. In this paper, we consider a class of new generating function for the degenerate multi-poly-Bernoulli polynomials, called the type 2 degenerate multi-poly-Bernoulli polynomials by means of the degenerate multiple polyexponential functions. Then, we investigate their some properties and relations. We show that the type 2 degenerate multi-poly-Bernoulli polynomials equals a linear combination of the weighted degenerate Bernoulli polynomials and Stirling numbers of the first kind. Moreover, we provide an addition formula and a derivative formula. Furthermore, in a special case, we acquire a correlation between the type 2 degenerate multi-poly-Bernoulli numbers and degenerate Whitney numbers.

We propose a non-invasive approach to control the quality of spheroids and their fusion into a complex bioconstruct. The proposed method is based on the union of the nutrient concentration change calculated using Fick's law and the "reaction-diffusion" equations, taking into account absorption coefficient with specifying the exact fusion geometry using implicit Function Repre-sentation (FRep) functions. The proposed approach allows us to analyze the viability of cells within the spheroid, predict the fusion of spheroids, and accurately model complex heteroge-neous biostructures as a future task for our research. These results will significantly accelerate the development of such a promising field of additive biotechnologies as 3D bioprinting.

Poor social skills in autism spectrum disorder (ASD) are associated with reduced independence in daily life. Current interventions for improving the social skills of individuals with ASD fail to represent the complexity of real-life social settings and situations. Virtual reality (VR) may facilitate social skills training in social environments and situations proximal to real life, however, more research is needed for elucidating aspects such as the acceptability, usability, and user experience of VR systems in ASD. Twenty-five participants with ASD attended a neuropsychological evaluation and three sessions of VR social skills training, incorporating 5 social scenarios with three difficulty levels for each. Participants reported high acceptability, system usability, and user experience. Significant correlations were observed between performance in social scenarios, self-reports, and executive functions. Working memory and planning ability were significant predictors of functionality level in ASD and the VR system’s perceived usability respectively. Yet, performance in social scenarios was the best predictor of usability, acceptability, and functionality level in ASD. Planning ability substantially predicted performance in social scenarios, postulating an implication in social skills. Immersive VR social skills training appears effective in individuals with ASD, yet an error-less approach, which is adaptive to the individual’s needs, should be preferred.

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.

The objective of this work is to present the results of an investigation on the technological, pedagogical and content knowledge evidenced by mathematics teachers in the second-level of initial training (preservice) at the Universidad Nacional, from the TPACK model perspective, on the subject of functions. The research has a qualitative approach with an interpretive hermeneutical stance. A sample of 27 teachers in training who were enrolled in courses related to the three base domains of the TPACK model (pedagogical, technological and content of quadratic function) during the first semester (I cycle) of 2020 was used. A theoretical inquiry was carried out that allowed the creation of an instrument that made possible the description of the participants’ knowledge based on this model focused on the topic of quadratic function. The results show that participants possess instrumental dominance over the basic forms of knowledge underlying the model. It is concluded that, although participants have already experimented in courses related to these forms of knowledge, there is insufficient evidence to ascertain that their current knowledge would allow them to integrate technologies as a didactic resource within the teaching of the subject of quadratic function.

Fibre reinforced cementitious materials (FRC) have become an attractive alternative for structural applications. Among such FRC, steel and polyolefin fibre reinforced concrete and glass fibre reinforced concrete are the most used ones. However, in order to exploit the properties of such materials structural designers need constitutive relations that reproduce FRC fracture behaviour accurately. This contribution analyses the suitability of multilinear softening functions combined with a cohesive crack approach for reproducing the fracture behaviour of the FRC previously mentioned. The implementation performed accurately simulates the fracture behaviour while being versatile, robust and efficient from a numerical point of view.

Generation of unique identifiers extracted from the physical characteristics of the underlying hardware ensures the protection of electronic devices against counterfeiting and provides security to the data they store and process. This work describes the design of an efficient Physical Unclonable Function (PUF) based on the differences in the frequency of Ring Oscillators (ROs) with identical layout due to variations in technological processes involved in the manufacture of the integrated circuit. The logic resources available in the Xilinx Series-7 programmable devices are exploited in the design to make it more compact and achieve an optimal bit-per-area rate. On the other hand, the design parameters can also be adjusted to provide a high bit-per-time rate for a particular target device. The PUF has been encapsulated as a configurable Intellectual Property (IP) module, providing it with an AXI4-Lite interface to ease its incorporation into embedded systems in combination with soft- or hard-core implementations of general-purpose processors. The capability of the proposed RO-PUF to generate implementation-dependent identifiers has been extensively tested, using a series of metrics to evaluate its reliability and robustness for different configuration options. Finally, in order to demonstrate its utility to improve system security, the identifiers provided by RO-PUFs implemented on different devices have been used in a Helper Data Algorithm (HDA) to obfuscate and retrieve a secret key.

This paper deals with the analysis of the cognitive functions of the cerebral cortex or cortex in the evolutionary context. The triune brain model is presented given its notorious popularity in fields that are not strictly neuroscientific, and its limitations and inaccuracies are also shown. Although it is an outdated theory, this one represented the passage to a new era, because it really was the model of the movement towards understanding the brain in evolutionary terms. Next, the paper illustrates the different areas of the cortex and their functions, as well as the evolution of the brain and the cortex in vertebrates. To date, the expansion of the cortex with the amniotes was placed 300 million years ago, although recent studies place it in the lampreys more than 500 million years ago. Evolutionary changes in mammalian brain and cortex size are discussed, showing the evolution from three to six cell layers and trends in different groups of mammals. Finally, the most recent contributions in the field of research are illustrated, such as the role of neurogenesis and the evolution of the connectivity of the cortex.

The literature on substance use usually extracts conclusions from data with correlational methods. Our study shows the usefulness of complementing ordered logistic regression (OLR) and fuzzy set qualitative comparative analysis (fsQCA) to assess factors inducing cannabis consumption in a sample of 1,935 teenagers. OLR showed a significant influence of gender (odd ratio (OR) =0.383, p<0.0001), parental monitoring (OR=0.587, p=0.0201); religiousness (OR=0.476, p=0.006); parental tolerance to substance use (OR=42.01, p<0.0001) and having close peers that consume substances (OR=5.60, p<0.0001). FsQCA has allowed fitting linkages between factors from a complementary perspective. (1) Coverage (cov) and consistency (cons) attained by solutions explaining use (cons=0.808, cov=0.357) are clearly lower than by recipes of non-use (cons=0.952, cov=0.869) (2) The interaction of gender, a tolerant family to use and the attitude toward substances by peers is very consistent to explain cannabis use. (3) The most important recipe explaining resistance to cannabis is simply parental disagreement with substance consumption (cons=0.956, cov=0.861) (4) Factors as gender, religiosity, parental monitoring and age show also a relevant impact on attitude toward cannabis use. However, whereas some of them impact symmetrically on use and non-use this does not follow in factors such as parental monitoring or age.

The present study assessed the effect of abscisic acid (ABA; 25 µM) and/or nitrogen (N; 10 mM) in minimization of salinity (NaCl; 100mM)-impact on growth, photosynthetic efficiency, Rubisco activity, nitrogen and sulfur assimilation, oxidative stress (H₂O₂), lipid peroxidation measured as thiobarbituric acid reactive substances, (TBARS), osmolyte (Proline) content, and the activity of antioxidant enzymes (superoxide dismutase, SOD glutathione reductase, GR; ascorbate peroxidase, APX) in cultivar RH0-749 of Brassica juncea L. NaCl stress caused significant elevations in H₂O₂ and TBARS, and differentially modulated proline content, the activity of antioxidant enzymes, and impaired growth and photosynthetic functions. Exogenously applied 25 µM ABA negatively affected plant growth and photosynthesis in B. juncea without NaCl. In contrast, exogenously applied 25 µM ABA and 10 mM N, alone or in combination minimized oxidative stress, and maintained a fine-tuning between proline content and the activity of antioxidant enzymes, and thereby improved plant growth and photosynthetic functions in NaCl exposed B. juncea.

In the present work, we evaluate the prediction capability of six Pedotransfer functions (PTFs), reported in the literature, for the saturated hydraulic conductivity estimations (Ks). We used a database with 900 measured samples obtained from the Irrigation District 023, in San Juan del Rio, Queretaro, Mexico. Additionally, six new PTFs were construct for Ks from clay percentage, bulk density and saturation water content data. The results show, for the evaluated models, that one model present an overestimation for Ks>0.5 cm h-1 values, three models have a underestimation for Ks>1.0 cm h-1 and two models have a good correlation (R2>0.98) but are necessary more than three parameters. Nevertheless, the last two models requires from three to four parameters in order to get the optimization. By other hand, the models proposed in this work have a similar correlation with a less number of parameters: the fit is seen to be much better than using the existing ones, achieving a correlation of R2 = 0.9822 with only one variable and a R2 = 0.9901 when we use two.

Motivation by the definition of the type 2 poly-Bernoulli polynomials introduced by Kim-Kim [9], in the present paper, we consider a new class of new generating function for the Fubini polynomials, called the type 2 poly-Fubini polynomials by means of the polyexponential function. Then, we derive some useful relations and properties. We show that the type 2 poly-Fubini polynomials equal a linear combination of the classical of the Fubini polynomials and Stirling numbers of the first kind. In a special case, we give a relation between the type 2 poly-Fubini polynomials and Bernoulli polynomials of order r. Moreover, inspired by the definition of the unipoly-Bernoulli polynomials introduced by Kim-Kim [9]. We introduce the type 2 unipoly-Fubini polynomials by means of unipoly function and give multifarious properties including derivative and integral properties. Furthermore, we provide a correlation between the unipoly-Fubini polynomials and the classical Fubini polynomials.

Kim-Kim [12] introduced the new type of degenerate Bernoulli numbers and polynomials arising from the degenerate logarithm function. In this paper, we introduce a new type of degenerate poly-Euler polynomials and numbers, are called degenerate poly-Euler polynomials and numbers, by using the degenerate polylogarithm function and derive several properties on the degenerate poly-Euler polynomials and numbers. In the last section, we also consider the degenerate unipoly-Euler polynomials attached to an arithmetic function, by using the degenerate polylogarithm function and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

The concept of transformative resilience emerges from complex recent literature and represents a way to interpret the potential opportunities to change in vulnerable territories, where a socio-economic change is required. This article extends the perspective of transformative resilience to assessing of the landscape multi-functionality of inland areas, exploring the potentials to identify a network of synergies among the different municipalities able to trigger a process of territorial resilience. A Spatial Decision Support System (SDSS) for multi-functionality landscape assessment aims to support the local actors to understand local resources and multi-functional values of the Partenio Regional Park (PRP) and surrounding municipalities, in the South of Italy, stimulating their cooperation to the management of environmental and cultural sites and the co-design of new strategies of enhancement.

Floods and droughts are driven, in part, by spatial patterns of extreme rainfall. Heat waves are driven by spatial patterns of extreme temperature. It is therefore of interest to design statistical methodologies that allow the identification of likely patterns of extreme rain or temperature from observed historical data. The standard work-horse for identifying patterns of climate variability in historical data is Principal Component Analysis (PCA) and its variants. But PCA optimizes for variance not spatial extremes, and so there is no particular reason why the first PCA spatial pattern should identify, or even approximate, the types of patterns that may drive these phenomena, even if the linear assumptions underlying PCA are correct. We present an alternative pattern identification algorithm that makes the same linear assumptions as PCA, but which can be used to explicitly optimize for spatial extremes. We call the method Directional Component Analysis (DCA), since it involves introducing a preferred direction, or metric, such as `sum of all points in the spatial field'. We compare the first PCA and DCA spatial patterns for US rainfall anomalies on a 6 month timescale, using the sum metric for the definition of DCA in order to focus on total rainfall anomaly over the domain, and find that they are somewhat different. The definitions of PCA and DCA result in the first PCA spatial pattern having the larger explained variance of the two patterns, while the first DCA spatial pattern, when scaled appropriately, has a higher likelihood and greater total rainfall anomaly, and indeed is the pattern with the highest total rainfall anomaly for any given likelihood. In combination these two patterns yield more insight into rainfall variability and extremes than either pattern on its own.

In this paper we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau's symplectic model of statistical mechanics, its polysymplectic extension, Koszul model, and approaches developed in quantum information geometry. We emphasize the role of equivariance with respect to Lie group actions and the role of several concepts from geometric mechanics, such as momentum maps, Casimir functions, coadjoint orbits, and Lie-Poisson brackets with cocycles, as unifying structures appearing in various applications of this framework to information geometry and machine learning. For instance, we discuss the expression of the Fisher metric in presence of equivariance and we exploit the property of the entropy of the Souriau model as a Casimir function to apply a geometric model for energy preserving entropy production. We illustrate this framework with several examples including multivariate Gaussian probability densities, and the Bogoliubov-Kubo-Mori metric as a quantum version of the Fisher metric for quantum information on coadjoint orbits. We exploit this geometric setting and Lie group equivariance to present symplectic and multisymplectic variational Lie group integration schemes for some of the equations associated to Souriau symplectic and polysymplectic models, such as the Lie-Poisson equation with cocycle.

We address security and privacy problems for digital devices and biometrics from an information-theoretic optimality perspective, where a secret key is generated for authentication, identification, message encryption/decryption, or secure computations. A physical unclonable function (PUF) is a promising solution for local security in digital devices and this review gives the most relevant summary for information theorists, coding theorists, and signal processing community members who are interested in optimal PUF constructions. Low-complexity signal processing methods such as transform coding that are developed to make the information-theoretic analysis tractable are discussed. The optimal trade-offs between the secret-key, privacy-leakage, and storage rates for multiple PUF measurements are given. Proposed optimal code constructions that jointly design the vector quantizer and error-correction code parameters are listed. These constructions include modern and algebraic codes such as polar codes and convolutional codes, both of which can achieve small block-error probabilities at short block lengths, corresponding to a small number of PUF circuits. Open problems in the PUF literature from a signal processing, information theory, coding theory, and hardware complexity perspectives and their combinations are listed to stimulate further advancements in the research on local privacy and security.