Successful fertilization treatments targeted to improve stand productivity while reducing operational complexities and cost depend on a clear understanding of soil nutrient availability under varying environmental conditions. Soil nutrient data collected from 154 forest sites throughout the Inland Northwest, USA were analyzed to examine soil nutrient characteristics on different geologic soil parent materials and to rank soil fertility. Results show that soil parent material explains significant differences in soil nutrient availability. Soils developed from volcanic rocks have the highest CEC and are relatively high in P, K, S, Mg, Cu, Ca, and B, but generally poor in N. Forest soils developed from plutonic rocks exhibit the lowest CEC and are low in N, S, K, Mg, Cu, and Ca, but higher in P. Some soils located on mixed glacial till are low only in K, Cu, Mg, and Ca, but many glacial soils are relatively rich in other nutrients, albeit the second lowest CEC. Soils developed from metasedimentary and sedimentary rocks are among those with lowest soil nutrient availability for P and B. Sulfur was found to have the highest concentrations in metasedimentary influenced soils and the least in sedimentary derived soils. Our results should be useful in designing site-specific fertilizer and nutrient management prescriptions for forest stands growing on soils developed from these major geologies within the Inland Northwest region of the United States.

Legendre’s equation is key in various branches of physics. Its general solution is a linear function space, spanned by the Legendre functions of first and second kind. In physics however, commonly the only acceptable members of this set are the Legendre polynomials. Quantization of the eigenvalues of Legendre’s operator is a consequence of this. We present and explain a stand-alone, in-depth argument for rejecting all solutions of Legendre’s equation, but the polynomial ones, in physics. We show that the combination of the linearity, the mirror symmetry and the signature of the regular singular points of Legendre’s equation is quintessential to the argument. We demonstrate that the evenness or oddness of the Legendre polynomials is a consequence of the same ingredients.

The time symmetry of T_c = CT is redefined based on the 4-D Euclidean space. The time inversion symmetry of T_c = CT changes the signs of the charge (q) and absolute time (ct) of the particle. The P symmetry changes the signs of the space momenta and handedness of the particle. The T_c symmetry changes the signs of the time momentum (P_t=E/c) and charges. The handedness are classified as the left-handedness and right-handedness on the 3-D space. The charges (|q| = cDt) and energies (E= cDtDV) of the particles are originated from the upward warping (q>0) and downward warping (q<0) of the particles along the time axis. The evolution of our matter universe with P_t > 0 since the big bang can be interpreted based on the CTP symmetry with the partner antimatter universe with p_t < 0. The photon space is called as the vacuum space. Then the E and M waves are the space fluctuations, and the gravitational G wave is the time fluctuations. And the E, M and G fields are newly explained. The zero E and M fields of the photon space indicates that the photon space and gamma ray are the 2EM waves. The rest mass energy of the particle is the 4-D space volume of the warped photon space. In the present work, the quantum wave function is considered as the 4-D vector with the space wave function and time axis wave function in the 4-D Euclidean space. The warped photon space corresponds to the squared wave function which is the probability density. It is concluded that, in the quantum mechanics, the imaginary number concept is introduced in the quantum wave functions instead of the time axis component of the 4-D wave function vector. The left-handed neutrino puzzle is explained from the handedness partner relation with the right-handed dark matters. Finally, the modified Lorentz transformations derived in the 4-D Euclidean space are compared with the Lorentz transformations of the special and general relativity theories in the 4-D Minkowski space.

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.

Executive functions comprise top-down cognitive processes that exert control over information processing, from acquiring information to issuing a behavioural response. These cognitive processes of inhibition, working memory and shifting underpin complex cognitive skills, such as episodic memory and planning, which have been repeatedly investigated in several bird species in recent decades. Until recently, avian executive functions were studied in relatively few bird species, but have gained traction in comparative cognitive research following MacLean and colleagues’ large-scale study (2014). Therefore, in this review paper, relevant previous findings are collected and organized to facilitate further investigations of these core cognitive processes in birds. This review can assist in integrating findings from avian and mammalian cognitive research and further current understanding of executive functions’ significance and evolution.

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.

This paper considers the solution of the equations for ruin probabilities in infinite continuous time. Using the Fourier Transform and certain results from the theory of complex functions, these solutions are obtained as com- plex integrals in a form which may be evaluated numerically by means of the inverse Fourier Transform. In addition the relationship between the re- sults obtained for the continuous time cases, and those in the literature, are compared. Closed form ruin probabilities for the heavy tailed distributions: mixed exponential; Gamma (including Erlang); Lognormal; Weillbull; and Pareto, are derived as a result (or computed to any degree of accuracy, and without the use of simulations).

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.

Footprints are powerful indicators for evaluating the impact of the bioeconomy of a country on environmental goods, domestically and abroad. In this study, we apply a hybrid approach combining a Multi-Regional Input-Output model and land use modelling to compute the agricultural land footprint (aLF). Furthermore, we added information on land-use change to the analysis and allocated land conversion to specific commodities. The German case study shows that the aLF abroad is larger by a factor of 2.5 to 3 than the aLF in Germany. In 2005 and 2010, conversion of natural and semi-natural land-cover types abroad allocated to Germany due to import increases was 2.5 times higher than the global average. Import increases to Germany slowed down in 2015 and 2020, reducing land conversion attributed to the German bioeconomy to the global average. The case study shows that the applied land footprint provides clear and meaningful information for policymakers and other stakeholders. The presented methodological approach can be applied to other countries and regions covered in the underlying database EXIOBASE. It can be adapted, also for an assessment of other ecosystem functions, such as water or soil fertility.

Kinetic parameters of SO2 adsorption on unburned carbons from lignite fly ash and activated carbons based on hard coal dust were determined. The model studies were performed using the linear and non-linear regression method for the following models: pseudo first and second-order, intraparticle diffusion, and chemisorption on a heterogeneous surface. The quality of the fitting of a given model to empirical data was assessed based on: R2, R, Δq, SSE, ARE, χ2, HYBRID, MPSD, EABS, and SNE. It was clearly shown that it is the linear regression that more accurately reflects the behaviour of the adsorption system, which is consistent with the first-order kinetic reaction – for activated carbons (SO2+Ar) or chemisorption on a heterogeneous surface – for unburned carbons (SO2+Ar and SO2+Ar+H2O(g)+O2) and activated carbons (SO2+Ar+H2O(g)+O2). Importantly, usually, each of the approaches (linear/non-linear) indicated a different mechanism of the studied phenomenon. A certain universality of the χ2 and HYBRID functions has been proved, the minimization of which repeatedly led to the lowest SNE values for the indicated models. Fitting data by any of the non-linear equations based on the R or R2 functions only, cannot be treated as evidence/prerequisite of the existence of a given adsorption mechanism.

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.

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.

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.

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

In recent years, data providers are generating and streaming a large number of images. More particularly, processing images that contain faces have received great attention due to its numerous applications, such as entertainment and social media apps. The enormous amount of images shared on these applications presents serious challenges and requires massive computing resources to ensure efficient data processing. However, images are subject to a wide range of distortions in real application scenarios during the processing, transmission, sharing, or combination of many factors. So, there is a need to guarantee acceptable delivery content, even though some distorted images do not have access to their original version. In this paper, we present a framework developed to estimate the images' quality while processing a large number of images in real-time. Our quality evaluation is measured using an integration of a deep network with random forests. In addition, a face alignment metric is used to assess the facial features. Experimental results have been conducted on two artificially distorted benchmark datasets, LIVE and TID2013. We show that our proposed approach outperforms the state-of-art methods, having a Pearson Correlation Coefficient (PCC) and Spearman Rank Order Correlation Correlation Coefficient (SROCC) with subjective human scores of almost 0.942 and 0.931 while minimizing the processing time from 4.8ms to 1.8ms.

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

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.

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.

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 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.

The 32CA reactions of a series of pairs of bent three-atom-components (B-TACs) and linear TACs (L-TACs) towards electrophilic dicyanoethylene (DCE) have been studied within the Molecular Electron Density Theory in order to understand their different reactivity. ELF analysis indicates that while pseudodiradical B-TACs change their electronic structure to pseudoradical or carbenoid L-TACs upon dehydrogenation, zwitterionic B-TACs experience no remarkable change. Analysis of the CDFT indices indicates that five of the nine studied TACs have a strong nucleophilic character, thus participating in polar reactions towards electrophilic ethylenes. The activation energies of the 32CA reactions of the nine TACs towards electrophilic DCE range from 0.6 to 22.0 kcal·mol-1, which are by between 2.0 and 10.1 kcal·mol-1 lower than those involved in the non-polar 32CA reactions with ethylene. In general, B-TACs are more reactive than their L-TAC counterparts. A change of the regioselectivity is found in these polar 32CA reactions; in general, while B-TACs are meta regioselective, L-TACs are ortho regioselective. Analysis of the geometrical parameters indicates that at all TSs, the formation of the single bond involving the most electrophilic C4 carbon of DCE is more advanced than that involving the C5 one. A change of the asynchronicity in the reactions involving B-TACs and L-TACs is also found.

A random variable X that is base b Benford will not in general be base c Benford when c is not equal to b. This paper builds on two of my earlier papers and is an attempt to cast some light on the issue of base dependence. Following some introductory material, the “Benford spectrum” of a positive random variable is introduced and known analytic results about Benford spectra are summarized. Some standard machinery for a “Benford analysis” is introduced and combined with my method of “seed functions” to yield tools to analyze the base c Benford properties of a base b Benford random variable. Examples are generated by applying these general methods to several families of Benford random variables. Berger and Hill's concept of “base-invariant significant digits” is discussed. Some potential extensions are sketched.

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.

This study examined the effect of an educational hybrid physical education (PE) intervention on cognitive performance and academic achievement in adolescents. A 9-month group-randomized controlled trial was conducted in 150 participants (age: 14.63 ± 1.38) allocated into control group (CG, n = 37) and experimental group (EG, n = 113). Inhibition, verbal fluency, planning and academic achievement were assessed. Significant differences were observed in the post-test for cognitive inhibition, verbal fluency in animals, and the average from verbal fluency in favour of the EG. With regard to the intervention, verbal fluency in animals, verbal fluency in vegetables, the average of verbal fluency, cognitive inhibition, language, the average of all subjects, the average of all subjects except PE, and the average from the core subjects) increased significantly in the EG. The last five variables (the academic ones and cognitive inhibition) also increased in the CG, in addition to mathematics. This study contributes to the knowledge by suggesting that both methodologies produced improvements in the measured variables, but the use of a hybrid program based on TPSR and gamification strategies produce improvements in cognitive performance, specifically through the cognitive inhibition and verbal fluency.

We present a new Multiple-Observations (MO) helper data scheme for secret-key binding to an SRAM PUF. This MO scheme binds a single key to multiple enrollment observations of the SRAM PUF. Performance is improved in comparison to classic schemes which generate helper data based on a single enrollment observation. The performance increase can be explained by the fact that the reliabilities of the different SRAM cells are modeled (implicitly) in the helper data. We prove that the scheme achieves secret-key capacity for any number of enrollment observations, and, therefore it is optimal. We evaluate performance of the scheme using Monte Carlo simulations, where an off-the-shelf LDPC code is used to implement the linear error-correcting code. Another scheme that models the reliabilities of the SRAM cells is the so-called Soft-Decision (SD) helper data scheme. The SD scheme considers the one-probabilities of the SRAM cells as an input, which in practice are not observable. We present a new strategy for the SD scheme that considers the binary SRAM-PUF observations as an input instead and show that the new strategy is optimal and achieves the same reconstruction performance as the MO scheme. Finally, we present a variation on the MO helper data scheme that updates the helper data sequentially after each successful reconstruction of the key. As a result, the error-correcting performance of the scheme is improved over time.

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 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.

We give three new authentication schemes without secrecy. The first two on finite fields and Galois rings, using Gray map for this link. The third construction is given on Galois rings. The main achievement in this work is to obtain optimal impersonation and substitution probabilities in the schemes. Additionally, in the first and second scheme, we simplify the source space and bring a better relationship between the size of the message space and the key space than the given in [8]. Finally, we provide a third scheme on Galois rings, which generalizes the scheme over finite fields constructed in [9].

Forest ecosystems are important providers of ecosystem functions and services belonging to four categories: supporting, provisioning, regulating, and cultural ecosystem services. Forest management, generally focused on timber production, has consequences on the ability of the system to keep providing services. Silviculture, in fact, may affect ecological structures and processes from which services arise. In particular, the removal of biomass causes a radical change in the stocks and flows of energy characterizing the system. Aiming at the assessment of differences in stored natural capital and ecosystem functions and services provision, three differently managed temperate forests of common beech (Fagus sylvatica) were considered: (1) a forest in semi-natural condition, (2) a forest carefully managed to get timber in a sustainable way and (3) a forest exploited without management. Natural capital and ecosystem functions and services are here accounted in biophysical terms. Specifically, all the resources used up to create the biomass (stock) and maintain the production (flow) of the different components of the forest system were calculated. Both stored emergy and empower decrease at increasing human pressure on the forest, resulting in a loss of natural capital and a diminished ability of the natural system to contribute to human well-being in terms of ecosystem services provision.

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.

A theoretical model to translate the evolution over time, in early stages, of growth and accumulation of biofilm bacterial mass is introduced. The model implies the solution of a system of differential-difference master equations. The application of an algorithm like Miller´s tree term recurrence, already known for Bessel functions of first kind, allows an exact calculation of the solutions of such equations, for a wide range of parameters values and time. For biofilm model a five term recurrence is deduced and applied in a backwards computation. A suitable normalisation condition completes the reach of the solution.

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.

The non-inertial effects on spin-0 scalar particle that interacts with scalar potentials of Cornell-type in cylindrical system and Coulomb-type in the magnetic cosmic string space-time using Kaluza-Klein theory is analyzed. We show that the energy eigenvalue and eigenfunction depend on the global parameters characterizing the space-time, and the gravitational analogue of the Aharonov-Bohm effect for bound states is observed.

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 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.

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.

Abstract: The article proposes to consider the possibility of connecting the problems of engineering synthesis of frequency control systems for asynchronous electric drives with the basic provisions of the theory of identification of asynchronous electric motors based on the equations of a generalized AC electric machine.The article presents the results of experimental studies of load parrying processes in asynchronous electric drives with vector and scalar controls. These results indicate the absence of fundamental advantages as processes in a drive with vector control. This advantage should have manifested itself in a more efficient formation of the moment and fast transients. It is suggested that the reason for this is in too significant errors, assumptions and simplifications of the equations adopted in the derivation of vector control and which are its theoretical basis. A method is proposed for describing asynchronous electric motors by nonlinear transfer functions, which made it possible to formulate the principle of correction of electric drives and a method for assessing their efficiency.The article shows. that the correction based on the proposed nonlinear transfer functions of the induction motor is much more efficient than the traditional vector control, which was confirmed by detailed experiments and modeling. The results of the most important of which are given in the article. An assumption was made. that the advantage in efficiency is due to a more accurate identification of the dynamics of an asynchronous electric motor with a gear function instead of vector equations.

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

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.

In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, and other techniques, the author finds necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic.

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.

The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modelling and forecasting. The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epidemic outbreaks, yet for decades it evaded the efforts of the community to derive explicit solution. The present work demonstrates that this is a non-trivial task. Notably, it is proven that the explicit solution of the model requires the introduction of a new transcendental special function, related to the Wright's Omega function. The present manuscript reports new analytical results and numerical routines suitable for parametric estimation of the SIR model. The manuscript introduces iterative algorithms approximating the incidence variable, which allows for estimation of the model parameters from the numbers of observed cases. The numerical approach is exemplified with data from the European Centre for Disease Prevention and Control (ECDC) for several European countries in the period Jan 2020 -- Jun 2020.

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.

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps subordinated to a (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a “well-scaled” diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the ‘state density kernel’ solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time fractional Mittag-Leffler process. The approach of construction of good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

In this paper, we introduce a new type of degenerate poly-Fubini polynomials and numbers, are called degenerate poly-Fubini polynomials and numbers, by using the degenerate polylogarithm function and derive several properties on the degenerate poly-Fubini polynomials and numbers. In the last section, we also consider the degenerate unipoly-Fubini 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.

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.

In this paper, we construct the degenerate poly-Fubini polynomials, called the type 2 degenerate poly-Fubini polynomials, by using the modified degenerate polyexponential function and derive several properties on the degenerate poly-Fubini polynomials and numbers. In the last section, we introduce type 2 degenerate unipoly- Fubini polynomials attached to an arithmetic function, by using the modified degenerate polyexponential function and investigate some identities for those polynomials. Furthermore, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

In this paper, our goal is to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate $\eta$-convexity conditions for locally Lipschitzian functions

In this paper, we consider a new class of polynomials which is called the multi-poly-Euler polynomials. Then, we investigate their some properties and relations. We provide that the type 2 degenerate multi-poly-Euler polynomials equals a linear combination of the degenerate Euler polynomials of higher order and the degenerate 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-Euler polynomials and degenerate Whitney numbers.

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.

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.

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.

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).

In this paper, we construct the degenerate poly-Frobenius-Genocchi polynomials, called the type 2 degenerate poly-Frobenius-Euler polynomials, by means of polyexponential function. We derive explicit expressions and some identities of those polynomials. In the last section, we introduce type 2 degenerate unipoly-Frobenius-Genocchi polynomials by means of unipoly function and derive explicit multifarious properties.

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.

Kim-Kim [20] studied the type 2 degenerate poly-Bernoulli numbers and polynomials by using modified degenerate polylogarithm function. In this paper, we construct the new type of degenerate poly-Cauchy polynomials and numbers of the second kind, called the new type of 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.

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.

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.

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.

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 provide alternative proofs to some results proposed in the article "New inequalities involving circular, inverse circular, hyperbolic, inverse hyperbolic and exponential functions" authored by Yogesh J. Bagul.

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.

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 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.

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.

We calculate the spectral function of a boson ladder in an artificial magnetic field by means of analytic approaches based on bosonization and Bogoliubov theory. We discuss the evolution of the spectral function at increasing effective magnetic flux, from the Meissner to the Vortex phase, focussing on the effects of incommensurations in momentum space. At low flux, in the Meissner phase, the spectral function displays both a gapless branch and a gapped one, while at higher flux, in the Vortex phase, the spectral function displays two gapless branches and the spectral weight is shifted at a wavevector associated to the underlying vortex spatial structure which can indicate a 8 supersolid-like behavior. While the Bogoliubov theory, valid at weak interactions, predicts sharp delta-like features in the spectral function, at stronger interactions we find power-law broadening of 10 the spectral functions due to quantum fluctuations as well as additional spectral weight at higher 11 momenta due to backscattering and incommensuration effects. These features could be accessed in 12 ultracold atom experiments using radio-frequency spectroscopy techniques.

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

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

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

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.

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.

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.

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

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/

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.

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.

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.

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.

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.

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

In this paper, we 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 ).

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.

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 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.

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.

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 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.

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.

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 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.

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.

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 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 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.

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.

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).

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 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.

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.

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.