This paper uses the $\exp(-\Phi(\xi))$-Expansion method to investigate solitons to the M-fractional nonlinear Schrödingers equation with cubic nonlinearity. The results obtained are dark solitons, trigonometric function solutions, hyperbolic solutions and rational solutions. Thus, the constraint relations between the model coefficients and the traveling wave frequency coefficient for the existence of solitons solutions are also derived.

This research paper is about to obtain new soliton solutions to the M-fractional (1+1)-dimensional nonlinear Westervelt model by utilizing $\exp_a$ function and modified simplest equation techniques. The gained solutions involving dark, bright, periodic, dark-bright and other solitons. These results have many applications in wave propagation of sound waves, high amplitude in medical imaging and therapy. Achieved results are verified by Mathematica tool and the effect of M-fractional derivative on the solutions is explained through 2-Dimensional, 3-Dimensional and contour plots. At the end, these techniques are simple, fruitful and effective to deal with nonlinear FPDEs.

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

Let R be a commutative ring and m, n be positive integers. We define a proper submodule N of an R-module M to be (m,n)-closed if for r∈R and b∈M, r^{m}b∈N implies rⁿ∈(N:_{R}M) or b∈N. This class of submodules lies properly between the classes of prime and primary submodules. Many characterizations, properties and supporting examples concerning this class of submodules are provided. The notion of (m,n)-modules is introduced and characterized. Furhermore, the (m,n)-closed avoidance theorem is proved. Finally, the (m,n)-closed submodules in amalgamated modules are studied.

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illsutrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

This experimental research presents an easier model for fitting experimental results that can be simulate the dynamical behaviour of a single degree freedom system, SDFS, subjected in a forced vibration in a shaking table. The fractional damping using a Kelvin-Voigt fractional derivative rheological model, KVFRdm, to represent a fractional oscillator and compare with the experimental model.

Power series expansions are useful in approximation theory and mathematical physics. The manuscript presents several types of fractional Taylor expansions of sufficiently smooth functions. This is achieved by employing an incremental regularization procedure to the computation of the derivative. The series are constructed in an algorithmic way, which allows for its implementation in computer algebra systems.

The current paper provides a cutting-edge information data length- theoretic approach to the transient M/M/Infinity queueing system. This is a first time ever investigation that unifies information data length and queueing theories. The significant impact of both time and the number of states for the transient M/M/ Infinity queue on both the upper and lower bounds of the obtained information data length is observed and noted. The paper concludes with some challenging open problems, combined with concluding remarks and future research pathways.

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

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

The space time fractional Korteweg-de Vries equation, modified Equal Width equation and Benney-Luke Equations are solved by using simple hyperbolic tangent Ansatz method. A simple compatible wave transformation in one dimension is employed to reduce the governing equations to integer ordered ODEs. Then, the ansatz approximation is used to derive exact solutions. Some illustrative examples are presented for some particular choices of parameters and derivative orders.

Human tuberculosis (TB) is caused mainly by Mycobacterium tuberculosis (MTB) and M. africanum (MAF) remains a major global health threat. The varying response of different host to contact with the TB bacteria, indicates the importance of host genetics in susceptibility to TB disease. We explored the association among selected human/host genomic variants and disease caused by the two causative pathogens in Ghana through a case control study. MTBC isolates (323) recovered from pulmonary TB patients recruited between 2016 and 2018 were genotyped using spoligotyping. A selection of 29 SNPs from MTB-related genes with high frequency among African populations were genotyped using a TaqMan® SNP Genotyping Assay and iPLEX Gold Sequenom Mass Genotyping Array. Associations between MTBC lineages and host variables were assessed using univariate and multivariate logistic regression. The prevalence of MTB and Maf among the participants were 79% and 21% respectively. Association analysis between the controls and MAF showed that rs2695342 variant on the SIC11A1 gene have the propensity to confer susceptibility to MAF infections (P = 0.093, OR = 8.35, 95% CI = 0.70 – 99.24) whilst the rs17048476 (P = 0.088, OR = 1.57, 95% CI = 0.93 – 2.63) and rs1482868 (P = 0.095, OR = 0.60, 95% CI = 0.33 – 1.09) were observed to be only suggestive. Our findings implicate SLC11A1 as a potential susceptibility gene of substantial interest for TB caused by MAF which is an important pathogen in West Africa and highlight the need for in-depth host pathogen studies in West Africa.

The bilateral tempered fractional derivatives are introduced generalising previous works on the one-sided tempered fractional derivatives and the two-sided fractional derivatives. An analysis of the tempered Riesz potential is done and showed that it cannot be considered as a derivative.

In this paper, the new optical wave solutions of truncated M-fractional perturbed Kundu-Eckhaus model with full non-linearity are obtained by utilizing the expa function technique and modified extended tanh expansion function technique. The solutions are in the form of dark soliton, bright soliton, singular solitons and other form of solutions. The gained solutions are helpful for the further development of concerned model. The obtained results have also been presented graphically in both two-dimensional and three-dimensional formats to discuss the dynamical features as well as the parametric dependence of the constructed solutions. The study offers a highly spectacular and acceptable techniques to combine various intriguing wave demonstrations for more sophisticated models of the modern day.

This paper analyzes the potential strategies for a bank merger from a Sustainable Development Goals (SDG) perspective, focusing on three key criteria: profitability, market share, and service quality. In the short-term, the merged bank should prioritize optimizing financial performance through cost management, revenue stream identification, and risk management practices. Market share expansion can be achieved through targeted customer acquisition and retention efforts, market research, and competitive analysis. Service quality can be enhanced through improved customer service, efficient complaint resolution processes, and leveraging technology. These short-term plans align the merged bank's operations with the identified criteria and promote responsible banking practices that contribute towards the SDGs. In the long-term, the merged bank should focus on diversifying revenue streams, expanding its customer base, and optimizing cost structure. Long-term strategies should include establishing a strong brand presence, customer loyalty programs, and continuous improvement in service quality. The paper emphasizes the importance of monitoring progress, making necessary adjustments, and aligning with SDGs for sustained profitability and long-term success in the marketplace. The findings of this study provide valuable insights for banks considering a merger and highlight the significance of considering SDGs in their strategic planning.

In this paper, we propose to explore a nonlinear fractional mathematical model of HFMD- Hand Foot Mouth Disease with vaccinated compartment. Firstly, we prove the non negativity and boundedness for the fractional order dynamical model. The system’s existence and uniqueness are studied using the formulation of the Caputo derivative operator. The fixed-point approach was used to get results indicating the presence of at least one solution. In numerical simulation, we obtained the approximate solution by using fractional Euler method.

This paper deals with the analysis of the temperatures in a group of 36 African countries. By looking at the maximum, minimum and the range (the difference between the maximum and the minimum) and using a long memory model based on fractional integration and cointegration, we first show that all series display a long memory pattern, with a significant positive time trend in 29 countries for the maximum temperatures and in 33 for the minimum ones. Looking at the range, the estimated value for the order of integration is smaller than the one based on maximum or minimum temperatures in 17 countries. Performing fractional cointegration tests between the maximum and minimum temperatures, our results indicate that the two series cointegrate in the classical sense (i.e., with a short memory equilibrium relationship) in a group of 11 countries, and there is another group of eight countries displaying cointegration in a fractional sense. The remaining 17 countries with no evidence of cointegration are therefore at the very high risk of climate change due to the absence of long-term comovement in their maximum and minimum temperatures. Findings in this paper are of tremendous interpretations and relevance for the analysis and climate projections in Africa.

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.

Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.

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

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

Let R be a commutative ring with identity and m, n be positive integers. In this paper, we introduce the class of (m,n)-prime ideals which lies properly between the classes of prime and (m,n)-closed ideals. A proper ideal I of R is called (m,n)-prime if for a,b∈R, a^{m}b∈I implies either aⁿ∈I or b∈I. Several characterizations of this new class with many examples are given. Analougus to primary decomposition, we define the (m,n)-decomposition of ideals and show that every ideal in an n-Noetherian ring has an (m,n)-decomposition. Furthermore, the (m,n)-prime avoidance theorem is proved.

Tuberculosis (TB) remains a major public health threat globally, especially in sub-Saharan Africa. Both human and Mycobacterium tuberculosis (MTBC) genetic variation affect TB outcomes, but few studies have examined if and how the two genomes interact to affect disease. We hypothesize that long-term coexistence between human genomes and MTBC lineages modulate disease to affect its severity. We examined this hypothesis in our TB household contact study in Kampala, Uganda, in which we identified 3 MTBC lineages of which one, L4.6-Uganda, is clearly derived and hence recent. We quantified TB severity using the Bandim TBscore and examined the interaction between MTBC lineage and human single nucleotide polymorphisms (SNPs) genome-wide, in two independent cohorts of TB cases (N=149 and N=127). We found a significant interaction between a SNP in PPIAP2 and the Uganda lineage (combined p=4x10-8). PPIAP2 is a pseudogene that is highly expressed in immune cells. Pathway and eQTL analyses indicated potential roles between coevolving SNPs and cellular replication and metabolism as well as platelet aggregation and coagulation. This finding provides further evidence that host-pathogen interactions affect clinical presentation differently than host and pathogen genetic variation independently, and that human-MTBC coevolution is likely to explain patterns of disease severity.

In this study, we consider delta fractional Sturm--Liouville (DFSL) initial value problems in the sense of delta Caputo and delta Riemann-Liouville (R--L) operators. One of the properties of delta fractional difference operators which makes it different from nabla counterpart is to shift its domain. This feature makes it more complex than the nabla fractional operator. We obtain sum representation of solutions for DFSL initial value problems with the help of $\mathcal{Z}-$ transformation. Moreover, we get analytical solutions of homogeneous DFSL problem within Riemann-Liouville (R--L) and Caputo sense, discrete Sturm--Liouville (DSL) problem, continuous fractional Sturm--Liouville (FSL) problem in the sense of R--L and Caputo operators, and continuous Sturm--Liouville (SL) differential problem. From this point of view, we compare all the solutions with each other. Consequently, we show that all results for these four eigenvalue problems are compatible with each other and approach to each other while the orders tends to one, i.e. $\Delta^{\mu }\left( \Delta x\left( t-\mu \right) \right)\cong D_{0^{+}}^{\mu }\left( x^{\prime }\left( t\right) \right)\cong \Delta^2x(n-1) \cong x^{\prime \prime }\left( t\right) =\lambda x\left( t\right),\ \mu\rightarrow1 $ . We support our results comparatively by tables and simulations in detail.

Here are given tight probabilistic inequalities that provide nearly best estimates for the Csiszar's f-divergence. These use the right and left psi -Hilfer fractional derivatives of the directing function f. Csiszar's f- divergence or the so called Csiszar's discrimination is used as a measure of dependence between two random variables which is a very essential aspect of stochastics, we apply our results there. The Csiszar's discrimination is the most important and general measure for the comparison between two probability measures. We give also other applications.

In this paper, we pursue and investigate the solutions for fractional kinetic equations, involving Bessel-Struve function by means of their Sumudu transforms. In the process, one Important special case is then revealed, and analyzed. The results obtained in terms of Bessel-Struve function are rather general in nature and can easily construct various known and new fractional kinetic equations.

Recently, representation formulae and monotonicity properties of generalized k-Bessel functions, Wk v,c., were established and studied by SR Mondal [24]. In this paper, we pursue and investigate some of their image formulae. We then extract solutions for fractional kinetic equations, involving Wk v,c, by means of their Sumudu transforms. In the process, Important special cases are then revealed, and analyzed.

In this paper, two types of the general fractional derivatives of distributed order as well as a corresponding fractional integral of distributed type are defined and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of the one-parametric Sonin kernels with a power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann-Liouville and the Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.

Our aim in this paper is to establish some new Hermite-Hadamard- Mercer type integral inequalities by utilizing the fractional proportional-integral operators.For this purpose, Hermite-Hadamard-Mercer inequalities for di¤er- antiable mappings whose derivatives in absolute value are convex.

Fractional-time Schrödinger equation (FTSE) describes the evolution of quantum processes endowed with memory effects. FTSE manifestly breaks all consistency requirements of quantum field theory (unitarity, locality and compliance with the clustering theorem), unless the order of fractional differentiation and integration ( ) falls close to the standard index . Working in the context of the minimal fractal manifold (where , ), we confirm here that FTSE approximates the attributes of gravitational metric and provides an unforeseen generation mechanism for massive fields.

The gradient descent algorithm has become the standard algorithm for computing the extreme values of functions, but for multivariate functions this algorithm is mostly ineffective. This is because the convergence rate of each element is inconsistent in most cases. However, in this paper, we found that the gradient sign is a self-optimizing operator, ensuring that the convergence rate is consistent across all elements. This also explains, from an optimization perspective, the success of the Fast Gradient Sign Method (FGSM) in generating adversarial samples that are indistinguishable from the normal input, but can easily fool neural networks. We also found that the fractional order gradient is also self-optimizing, and that the convergence speed of this algorithm can be controlled by adjusting the order of the gradient. Experiments suggest that this algorithm not only generates adversarial samples faster than other algorithms, but that a single source image can generate many such samples. This algorithm is also more effective than others at generating adversarial samples from simple images.

A stochastic dominance (SD) relation can be defined by two different perspectives: One from the view of distributions, and the other one from the view of expected utilities. In early days, Fishburn investigated SD from the view of distributions and we refer this perspective as Fishburn’s SD. One of his many results was the development of fractional-order SD for continuous distributions. However, discrete fractional-order SD may not be generalized directly since some properties of fractional calculus do not have a discrete counterpart. In this paper, we develop a discrete analogue of fractional-order SD from the view of distributions. We generalize the order of SD by Lizama’s fractional delta operator, show the preservation of SD hierarchy, and formulate the utility classes that are congruent with our SD relations. This work brings a message that some results of discrete SD cannot be generalized directly from continuous SD. We characterize the difference between discrete and continuous fractional-order SD, as well as the way to handle them.

Fractional calculus gained a lot of attention in the last couple of years. Researchers discovered that processes in various fields follow rather fractional dynamics than ordinary integer-ordered dynamics, meaning the corresponding differential equations feature non-integer valued derivatives. There are several arguments for why this is the case, one of them being that fractional derivatives’ inherit spatiotemporal memory and/or the ability to express complex naturally occurring phenomena. Another popular topic nowadays is machine learning, i.e., learning behavior and patterns from historical data. In our ever-changing world with ever-increasing amounts of data, machine learning is a powerful tool for data analysis, problem-solving, modeling, and prediction. It further provides many insights and discoveries in various scientific disciplines. As these two modern-day topics provide a lot of potential for combined approaches to describe complex dynamics, this article reviews combined approaches of fractional derivatives and machine learning from the past, puts them into context, and thus provides a list of possible combined approaches and the corresponding techniques. Note, however, that this article does not deal with neural networks, as there already is profound literature on neural networks and fractional calculus. We sorted past combined approaches from the literature into three categories, i.e., preprocessing, machine learning & fractional dynamics, and optimization. The contributions of fractional derivatives to machine learning are manifold as they provide powerful preprocessing and feature augmentation techniques, can improve physically informed machine learning, and are capable of improving hyperparameter optimization. Thus, this article serves to motivate researchers dealing with data-based problems, to be specific machine learning practitioners, to adopt new tools and enhance their existing approaches.

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

Anyon is collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. So far, anyons with serial fractional charges only exist in fractional quantum Hall effect. It is still a challenge to find new serial of fractional charges in other physical system and develop an unified mathematical physics theory based on the same root. Here a topological path fusion theory of propagating electrons in magnetic flux lattice is proposed to explore the physical origin of fractional charges based on a generalization of Feynman's path integral theory and Thurston's train track theory. This mathematical physics theory generated the existed serial of fractional charges in fractional quantum Hall effect and predicted new serial of fractional charges. A serial of irrational charges are predicted in one dimensional lattice of magnetic fluxes. Fractionally charged anyons are also generated in two dimensional and three dimensional lattice of train tracks of electric currents, revealing an exact correspondence between knot lattice model and train track model. A new explanation for the modular symmetry of complex Hall conductance and composite fermion in fractional quantum Hall effect is also derived from this topological path fusion theory. Experimental observation of anyon in three dimensions can be realized by constructing three dimensional interlocking magnetic fluxes or mapping magnetic fluxes into forbidden zones in multi-connected space filled by solid state material. A photonic crystal with porous nano-structures is a promising system for detecting fractional charges and paves a new way for topological quantum computation.

Here we present Hilfer-Polya, psi-Hilfer Ostrowski and psi-Hilfer-Hilbert- Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and -Hilfer fractional derivatives. All estimates are with respect to norms ||.||p, 1 <_ p <_infinite. At the end we provide applications.

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.

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, some mixed type bounds on the spectral radius $\rho(A\circ B)$ for the Hadamard product of two nonnegative matrices ($A$ and $B$) and the minimum eigenvalue $\tau(C\star D)$ of the Fan product of two $M$-matrices ($C$ and $D$) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several $M$-matrices is also presented: $$ \tau(A_{1}\star A_{2}\cdots\star A_{m})\geq \min_{1\leq i\leq n}\{\prod^{m}_{k=1}A_{k}(i,i)-\prod^{m}_{k=1}[A_{k}(i,i)^{P_{k}}-\tau(A_{k}^{(P_{k})})]^\frac{1}{P_{k}}\}, $$ where $A_{1},\ldots, A_{k}$ are $n\times n$ $M$-matrices and $P_{1},\ldots, P_{k}>0$ satisfy $\sum^{m}_{k=1}\frac{1}{P_{k}}\geq 1$. Some special cases of the above result and numerical examples show that this new bound improves some existing results.

The theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations as approximations of some type of fractional nonlinear birth--death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While FDEs appear more flexible in fitting empirical data, our ODEs offered better fits to two out of three data sets. Important differences in transient dynamics between these modeling approaches are discussed.

The exact solutions in the wave form are derived for the time fractional KdV and the time fractional Burgers' equations in conformable fractional derivative sense. The fractional variable change using the fundamental properties of the conformable derivative reduces both equations to some nonlinear ODEs. The predicted solution is assumed to be a finite series form of a function satisfying a particular first-order ODE whose solution contains an exponential function in the denominator. The solutions are represented in the explicit forms and illustrated by some choices of the parameters for various fractional orders of the equations.

In this research article we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional order differential equations. To guarantee the synchronization and anti-synchronization of these systems, we use the well-known PID control theory and the Lyapunov-Krasovskii stability theory for discrete systems of variable fractional order.We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of variable fractional order with discrete time delay.

During blooms, cyanobacteria produce diverse modified peptides. Among these are the microginins, which inhibit zinc-containing metalloproteases. Ten microginins, microginins KR767 (1), KR801(2), KR835 (3), KR785 (4), KR604 (5), KR638 (6), KR781 (7), KR815 (8), FR3 (9), and FR4 (10) were isolated from the extract of a bloom material of Microcystis sp. (IL-405) collected from the Kishon Reservoir, Israel in the fall of 2009. The structures of the pure compounds were elucidated using 1D and 2D NMR techniques and high-resolution mass spectrometry. The absolute configuration of the chiral centers of the amino acids were determined by Marfey’s and advance Marfey’s methods and by comparison of ¹H and ¹³C NMR chemical shifts of the Ahda derivatives with those of known microginins. These microginins differ in sequence and absolute configuration of the chiral centers of the Ahda moieties and by N-methylation of Ahda amine group and extent of chlorination of Ahda terminal methyl group. The compounds were evaluated for inhibition of the zinc metalloprotease aminopeptidase M and exhibited low- to sub-nanomolar IC₅₀ values.

The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave(RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. The homogeneous balance procedure gives the order of the predicted polynomial-type solution that is inspired from well-known Sine-Gordon equation. The substitution of this solution follows the previous step. Equating the coefficients of the powers of predicted solution leads a system of algebraic equations. The solution of resultant system for coefficients gives the necessary relations among the parameters and the coefficients to be able construct the solutions. Some solutions are simulated for some particular choices of parameters.

Exact solutions to conformable time fractional (3+1)- dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE. The resultant polynomial equation is solved by using algebraic operations. The method works for the Jimbo-Miwa, the Zakharov-Kuznetsov and the modified Zakharov-Kuznetsov equations in conformable time fractional forms. All the solutions are expressed in explicit forms.

In the particular configuration of the scalar field K-essence in the Wheeler-DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is $\beta=\frac{2\alpha}{2\alpha - 1}$. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when $\omega_{X} \in [0,1]$, the order belongs to the interval $1\leq \beta \leq 2$, and when $\omega_{X}\in[-1,0)$, the order belongs to the interval $0<\beta \leq 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(\Omega,\phi)$ and its corresponding momenta $(\Pi_\Omega, \Pi_\phi)$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T(\tau)$, however in the dust era we found a closed solution in the gauge time $\tau$.

TThis paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann-Liouville fractional integral and fractional Caputo derivatives, enabling a comprehensive understanding of these functions. Additionally, we introduce a secondary characterization based on the Bernstein characterization of completely monotone functions. The practical significance of our study is showcased through an examination of the positivity of the fundamental solution of the space-fractional Bessel diffusion equation, highlighting the real-world applicability of the developed concepts. Through this work, we contribute to the broader understanding of radial positive definite functions and their utility in diverse mathematical and applied contexts.

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

In view of the problem of cracking easily and partial distortion of images after encryption or decryption, a novel image encryption and decryption algorithm based on Arnod Transform and fractional chaotic is proposed. To begin with, the Arnold transform is used to encrypt. So that the spatial confidence of the original image has been comprehensively disturbed. Secondly, the XOR involving the fractional order chaotic sequence is used to encrypt. The key sequence is dynamically generated to ensure the randomness and difference of key generation. When decryption is required, the first decryption is performed using the key and XOR. Then the second decryption is carried out by using the inverse Arnold transform, and finally the decrypted image is obtained. Experimental results show that the improved algorithm has achieved better performance in encryption and decryption.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long Wave-Burgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker's parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational form of an exponential function is substituted to the ODE generated from the conformable time fractional PDE by using wave transformation. The coefficients used in the finite series are determined by solving the algebraic system derived from the coefficients of the powers of the predicted solution.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of nonlocality and spatial heterogeneity of complex materials and systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such operators to complex-order counterparts. In this work, we introduce new definitions for the complex-order fractional Laplacian, fully consistent with the theory of averaging of smooth functions over fractal sets, and present tailored spectral methods for their numerical treatment. The proposed complex-order operators exhibit a dual particle-wave behaviour, with solutions manifesting wave-like features depending on the magnitude of the imaginary part of the fractional order. Reaction-diffusion systems driven by the complex-order fractional Laplacian exhibit unique spatio-temporal dynamics, such as equilibrium of diffusion in random materials by interference of scattered waves, conduction block and highly fractionated propagation, or the generation of completely novel Turing patterns. Taken together, our results support that the proposed complex-order operators hold unparalleled capabilities to advance the description of multiscale transport phenomena in physical and biological processes highly influenced by the heterogeneity of complex media.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

Background: Polycystic ovary syndrome (PCOS) is a common reproductive and endocrinological disease characterized by ovulatory dysfunction, polycystic ovaries, and hyperandrogenism. Adipokines are believed to contribute to developing PCOS and its accompanying metabolic complications such as dyslipidemia, insulin resistance, and cardiovascular diseases. Oncostatin M (OSM), a novel adipokine, plays a role in oogenesis, lipogenesis, and inflammation and may contribute to PCOS pathogenesis and its related metabolic problems. Methods: In this case-control study, the patients were grouped in a 1:1 ratio into either the PCOS (n = 32) or the control group (n = 32). Blood samples were obtained between the 3rd and 5th days of the menstrual cycle. Serum levels of fasting glucose, insulin, C-reactive protein (CRP), low-density lipoprotein, high-density lipoprotein, triglyceride, white blood cell count, thyroid-stimulating hormone, luteinizing hormone, follicle-stimulating hormone, total testosterone, prolactin estradiol, and OSM were analyzed. Results: OSM levels were significantly lower, but CRP levels were substantially higher in the PCOS group than in the control group (p = .002, p = .001, respectively). OSM was inversely correlated with total cholesterol, non-high-density lipoprotein cholesterol, fasting glucose, and the luteinizing hormone/follicle-stimulating hormone ratio (ρ = .329, p = .017; ρ = .386, p = .005; ρ = .440, p = .001; ρ = .316, p = .023, respectively). Conversely, there was no correlation between OSM and total testosterone level (ρ = .220; p = .118). In the context of inflammation and metabolic parameters, OSM was inversely correlated with CRP, Homeostatic Model Assessment for Insulin Resistance score (HOMA-IR), and low-density lipoprotein cholesterol (LDL) (ρ = .353, p = .019; ρ = .275, p = .048; ρ = .470, p &lt; .001, respectively). The performance of Oncostatin M for diagnosing PCOS showed 50% sensitivity, 75% specificity, and 63% accuracy (p = .009) in ROC curve analysis. Conclusions: Plasma OSM levels were considerably lower in patients with PCOS than in the control group, and this was inversely correlated with the hormonal and metabolic parameters of PCOS. Thus, OSM may be a novel therapeutic target for PCOS and metabolic complications.

The predominance of traffic lights in urban settings often induces fluctuations in traffic patterns and energy utilization among vehicles. To counteract the adverse effects of traffic lights on the energy efficiency of electric vehicles (EVs), a Multi-Intersections-Based Eco-Approach and Departure strategy (M-EAD) is proposed. This strategy aims to enhance vehicle energy efficiency, traffic flow, and battery longevity, all while upholding satisfactory driving comfort. The M-EAD strategy unfolds in two distinct stages: the optimization of an eco-friendly green signal window and the refinement of speed trajectories. The initial stage tackles the optimization of traffic light green signal windows, underpinned by the minimization of travel delays via solving the shortest path problem. In the subsequent stage, a receding horizon framework takes center stage, leveraging an iterative dynamic programming algorithm to tackle the speed optimization challenge. The objective here is to curtail energy consumption and reduce battery wear by finding an optimal speed trajectory. Furthermore, the real-world efficacy of this approach is substantiated through on-road vehicle tests, attesting to its viability in actual road scenarios.

Extended-spectrum β-lactamase (ESBL) mediating resistance in Enterobacterales is a global public health issue, especially in low-and middle-income countries (LMICs) such as Cameroon. ESBL-producing Enterobacterales reduce therapeutic options and lead to the use of last resort drugs such as carbapenems even in vulnerable populations like children under five years. This study aims at determining the phenotypic and genotypic characteristics of ESBL-producing Escherichia coli (ESBL-Ec) isolated from children under five years with and without diarrhoea in two health care facilities in Dschang. A cross-sectional study was conducted from 3 February to 19 May 2022 in two hospitals in the city of Dschang, Cameroon. Stool collected were cultured on Eosine Methylen Blue (EMB) medium. Enterosystem 18 R kit was used for bacterial identification. Evaluation of the resistance patterns and detection of ESBL production were performed with, the Kirby Bauer disk diffusion method and CHROMagar® ESBL medium, respectively. The genomic DNA of ESBL-Ec was extracted using the boiling method and subjected to conventional and multiplex PCRs for detection of blaSHV, blaCTX-M and blaTEM genes. Data were entered into ExcelTM 2016. Epi info and R software were used for statistical analyses with a p-value <0.05 considered statistically significant. Out of the 125 children enrolled, 67.2% (84/125) were colonized by E. coli. Among these, 57.14% (48/84) were colonized by ESBL-Ec. ESBL- Ec isolates showed high levels of resistance to amoxicillin-clavulanic acid (96.22%), cefotaxime (75.47%), ceftriaxone (73.58%), ofloxacin (67.92%), levofloxacin (56.6%) and ciprofloxacin (54.71%). Children aged between 1-3 years (47.62%, p=0.09) and those who had taken an antibiotic one week prior to collection (70.83%, p=0.04) had a higher prevalence of ESBL-Ec with statistical significance. The majority of ESBL-Ec isolates (52.83%; 28/53) were co-producers of blaCTX-M and blaTEM. Infection prevention and control measures coupled with antimicrobial stewardship strategies need to be strengthened to reduce emergence and dissemination of ESBL-Ec among this vulnerable population.

The misuse of antibiotics during the last decades led to the emergence of multidrug resistant pathogenic bacteria. This phenomenon constitutes a major public health issue. Consequently, the discovery of new antibacterials in the short term is crucial. Colicins, due to their antibacterial properties, thus constitute good candidates. These toxin proteins, produced by E. coli to kill enteric relative competitors, exhibit cytotoxicity through ionophoric activity or essential macromolecule degradation. Among the 25-colicin types known to date, colicin M (ColM) is the only one colicin interfering with peptidoglycan biosynthesis. Accordingly, ColM develops its lethal activity in E. coli periplasm by hydrolyzing the last peptidoglycan precursor, lipid II, into two dead-end products, thereby leading to cell lysis. Since the discovery of its unusual mode of action, several ColM orthologs have also been identified based on sequence alignments; all of the characterized ColM-like proteins display the same enzymatic activity of lipid II degradation and narrow antibacterial spectra. This publication aims at being an exhaustive review about what is currently known on this new family of antibacterial enzymes as well as on their potential use of food preservatives or therapeutic agents.

Cyclin dependent kinase 1 (CDK1) has been primarily identified as a key cell cycle regulator in both mitosis and meiosis. Recently, an extramitotic function of CDK1 emerged when evidence was found that CDK1 is involved in many cellular events that are essential for cell proliferation and survival. In this review we summarize the involvement of active CDK1 in the initiation and elongation steps of protein synthesis in eukaryotes. During its activation CDK1 influences the initiation of protein synthesis, promotes the activity of specific translational initiation factors and affects the functioning of a subset of elongation factors. Our review provides insights into gene expression regulation during the transcriptionally silent cell cycle/M-phase and describes quantitative and qualitative translational changes based on the extramitotic role of the cell cycle master regulator CDK1, to optimize temporal synthesis of proteins to sustain division-related processes: mitosis and cytokinesis.

M-polynomial of different molecular structures helps to calculate many topological indices. A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR) quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Zagreb indices, Randic index, Symmetric division index, Harmonic index, Inverse sum index, Augmented Zagreb index, multiple Zagreb indices etc. are correlated. In this report, we compute closed forms of M-polynomial, first Zagreb polynomial and second Zagreb polynomial of Octagonal network. From the M-polynomial we recover some degree-based topological indices for Octagonal network. Moreover, we give a graphical representation of our results.

Recent discovery of triangular boron Nanotubes makes it a competitor of carbon in many respects. Closed forms of M-polynomial of nanotubes produce closed forms of many degree-based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned nanotubes. In this report, we give M-polynomials of triangular boron nanotubes and recover many important topological degree-based indices of these nanotubes. We also plot surfaces associated to these nanotubes.

Due to the nonlinear stiffness and fractional-order damping characteristics of some real suspension systems, coupled with the presence of viscoelastic materials, fractional-order nonlinear suspension system modeling has become a focus of research in recent years. In this study, an electric oil and gas actuator based on fractional-order PID position feedback control is proposed, through which the damping coefficient of the suspension system is adjusted to realize the active control of the suspension. A fractional order PID algorithm is used to control the motor's rotational angle to realize the damping adjustment of the suspension system. In this process, the road roughness is collected by the sensors as the criterion of damping adjustment, and the particle swarm algorithm is utilized to find the optimal objective function under different road surface slopes, to obtain the optimal cornering value. According to the mathematical and physical model of the suspension system, the simulation model and the corresponding test platform of this type of suspension system are built. The simulation and experimental results show that the simulation results of the fractional-order nonlinear suspension model are closer to the actual experimental values than those of the traditional linear suspension model, and the accuracy of each performance index is improved by more than 18.5%. The designed active suspension system optimizes the body acceleration, suspension dynamic deflection, and tire dynamic load to 89.8%, 56.7%, and 73.4% of the passive suspension, respectively. Notably, the designed fractional order PID control circuit for the motor shows better control results compared to the conventional PID control circuit. This study provides an effective theoretical and empirical basis for the control and optimization of fractional-order nonlinear suspension systems.

For solving the fractional differential equations in computational fluid dynamics (CFD), it’s complicated and difficult by the Laplace and Fourier transforms. Based on the Caputo fractional derivative, the analytical solutions for unsteady unidirectional flows of a generalized Oldroyd-B fluid are deduced by the separation of variables method. Results show that the analytical solutions are given easily, and have good university. For some specific parameter values, the well-known analytical solutions for the generalized second grade fluid, the generalized Upper-Convected Maxwell (UCM) fluid as well as the ordinary Oldroyd-B fluid can be obtained.

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

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

The fractional derivatives are a generalization the derivatives of integer order and find applications in studying memory processes in various scientific fields. Numerical methods are used to solve and analyze fractional models of real world problems. In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic formula, whose generating function is the polylogarithmic function. In the paper, we prove the convergence of the approximation and derive an estimate for the error and order. We consider an application of the approximation for the construction of finite difference schemes for numerical solution of the two-term ordinary fractional differential equation and the time-fractional Black-Scholes equation for option pricing. The properties of the approximation are used to prove the convergence of the methods used for numerical solution of the fractional differential equations. The theoretical results for the error and order of the methods are illustrated by the results of numerical experiments.

In the present study, nonlinear vibration of a nanobeam resting on fractional order viscoelastic Winkler-Pasternak foundaion is studied using nonlocal elasticity theory. D'Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. Detailled parametric study is conducted, the effects of variation in different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual tank device are precisely formulated by fractional calculus. Using the accurate model, multivariable Fractional-Order Controller is designed for the nonlinear device. The merits of the fractional-order design include: 1) Control of multivariable nonlinearities, 2) Compensation of uncertainties, 3) Elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control design.

The main goal of the paper is to use a generalized proportional Riemann-Liouville fractional derivative (GPRLFD) to model BAM neural networks and to study some stability properties of the equilibrium. Initially, several properties of the GPRLFD are proved such as the fractional derivative of a squared function. Also some comparison results for GPRLFD are provided. Two types of equilibrium of the BAM model with GPRLFD are defined. In connection with the applied fractional derivative and its singularity at the initial time the Mittag-Leffler exponential stability in time of the equilibrium is introduced and studied. An example is given illustrating the meaning of the equilibrium as well as its stability properties.

Quantum Gravity is not sufficient to predict the properties of particles (baryonic and non-baryonic) to a great extent. So, we develop General Quantum Gravity (GQG), which is a renormalizable formalization of quantized gravity that emerges from General Relativity through a new scenario of Quantum Mechanics. Inside every observable $(3+1)D$ spacetime in this new scenario of Quantum Mechanics, there must contain an internal hidden $(n+1)D$ spacetime, which immediately yields extra hidden dimensions by a closed continuous mapping, so that the overall spacetime must acquire Supersymmetry. We have also found that Superstrings are inevitably natural and universal but hidden inside every $(3+1)D$ observable spacetime. Superstrings are found eleven-dimensional (rather than lower dimensional) within this quantum spacetime. Consequently, eleven-dimensional Supergravity is necessarily a natural phenomenon within the GQG spacetime. GQG is formalized here in two different aspects. The first one gives an Einstein field equation in a semi-quantum Minkowski spacetime with semi-quantum Lorentzian metric tensor, whereas, the second one yields a purely Quantum Mechanical Einstein field equation in a quantum non-Minkowski spacetime with non-Lorentzian metric tensor. Dark Energy (as well as Dark Matter) appears from GQG quite naturally. We develop here Gravitational Electroweak Dark Energy interactions, where gravity and Dark Energy are allowed to combine with electroweak symmetry. Likewise, in Gravitational Chromodynamic Dark Energy interactions, we combine QCD with gravitational and Dark Energy symmetries. In a Dark Matter gauge symmetry model, we combine Dark matter with all possible gauge symmetries. A Universal Model $SU(7)_{UM}$ combines entire baryonic and non-baryonic particle interactions all together.

ntroduction: Respiratory tract Infections are the greatest cause of death worldwide. Since its outbreak in 2019, the coronavirus pandemic (COVID-19) has been a challenge to humans in terms of treatment and prevention of this respiratory viral infection. The re-emergence of respiratory viral infections like influenza, pose a serious hazard to global public health because they occur seasonally. Creating broad-spectrum antiviral compounds for rapid action in the case of an outbreak crisis, as well as bioweapon defences, is critical. Human galectin-3 is found in high concentrations in activated T lymphocytes, epithelial and endothelial cells, and fibroblasts. ProLectin -I and ProLectin -M are both galectin antagonists. Blocking viral entry with a complex polysaccharide component "ProLectin-M" has downstream effects on viral reproduction enabling it to be used as a therapeutic tool and a safe alternative to conventional anti-viral medicines. Methods: In total, 3 cell based assays have been conducted to evaluate antiviral efficacy of ProLectin–I and ProLectin-M against SARS-CoV-2 virus, Influenza-A (H1N1), and human respiratory syncytial virus (hRSV) strain A2. ProLectin-M and ProLectin-I were evaluated for their anti-viral potency using SARS-CoV2 virus strain by viral RNA Extraction and qRT-PCR assays. The plaque assays were carried out to determine the antiviral activity of the test products (ProLectin-I and ProLectin-M) against ‘Influenza-A (H1N1)-A/PR/8/34 (TC adapted)’ and ‘Human respiratory syncytial virus (hRSV) strain A2’ in a cell based in vitro setting. As eference standard, "Oseltamivir Phosphate" and "Remdesivir" were used to determine antiviral activity of test products against H1N1 and hRSV strains respectively.Results: The IC_{50 of} ProLectin-M and ProLectin-I against SARS-CoV-2 virus was found to be 6248 ng/ml (6.2µg/ml) and 4207 ng/ml (4.2μg/ml) respectively. The CC₅₀ value was similar in both the test products i.e. >100 µg/ml. Against Influenza A (H1N1) strain, ProLectin-M exhibited 95 % reduction in the viral load at the test concentration of 21.8 µg/mL with an IC₅₀ value of 5.4 µg/mL whereas, ProLectin-I did not show any cytotoxicity till 250 µg/mL concentration. Against 'human respiratory syncytial virus (hRSV) strain A2, ProLectin-M exhibited 65 % reduction in the viral load at the test concentration of 43.75 µg/mL with an IC₅₀ value of 27.41 µg/mL whereas, ProLectin- I did not show any cytotoxicity till 250 µg/mL concentration. Conclusion: Both ProLectin-I and ProLectin-M have been reported to exhibit broad-spectrum antiviral activity in ‘in-vitro’ setting. ProLectin-M reducing influenza-A virus by 95% and hRSC strain A2 by 65%. To better understand broad spectrum antiviral activity of ProLectin-I and ProLectin-M, further pre-clinical research is warranted.

ESBL-producing E. coli is a growing public problem in healthcare settings and the community. Between 2009 and 2018, a total of 187 ESBL-producing pathogenic E. coli isolates were confirmed, and clonal complex (CC) 10 was the predominant clone. This study aimed to characterize ESBL-producing pathogenic E. coli CC10 strains obtained from diarrheal patients to improve the understanding of CC10 distribution in the Republic of Korea. A total of 57 CC10 strains were selected for molecular characterizations, such as the identification of serotype, antibiotic resistance genes, genetic environments, plasmid profiles, and the genetic correlation between CC10 strains. In the CC10 isolates, the most prevalent serotype was O25:H16, followed by O6:H16. ESBL genes were identified as blaCTX-M, and the most dominant ESBL gene was blaCTX-M-15 (56%) and blaCTX-M-14 (30%). Most blaCTX-M genes were located on plasmids, and these plasmid profiles were confirmed as IncB/O/K/Z, IncF, IncI1 and IncX1. The mobile elements located up-and down-stream mainly included ISEcp1 (complete or incomplete) and IS903 or orf477 were found, respectively. Phylogenetic analysis showed that the CC10 strains were genetically diverse and divided into several distinct lineages. In this study, we found that CC10 ESBL-producing pathogenic E. coli has been steadily isolated; particularly, CTX-M-15-producing E. coli O25:H16 isolates were the major type related with distribution in CC10 clones during the last decade. Identification of ESBL-producing pathogenic E. coli CC10 isolates highlights the possibility of the emergence of resistant isolates with epidemic potential within this CC. Therefore, continuous monitoring will be conducted to prevent further spread of resistant ESBL-producing E. coli CC10 strains.

A convenient and fast multiresidue method for the efficient identification and quantification of 72 pesticides belonging to different chemical classes in red and white grape wines have been developed. The analysis was based on gas chromatography tandem quadrupole mass spectrometric determination (GC–MS/MS). An optimization strategy involved the selection of MWCNTs amount and cleanup procedure cycle times for m-PFC was performed to achieve ideal recoveries and reduce sample matrix compounds in the final extracts. The optimized procedure obtained consistent recoveries between 70.2 and 108.8% (70.2% and 108.8% for white wine, 72.3% and 106.0% for red wine) , with relative standard deviations (RSDs) generally lower than 8.3% at three spiking levels of 0.01, 0.05 and 0.2 mg/kg. Linearity was studied in the range between 0.005 and 0.2 mg/kg using pesticide standards prepared both in pure solvent and in the presence of matrix, showing coefficients of determination (R²) higher than 0.985 for all the pesticides. To improve accuracy, matrix matched calibration curves were used for calculating the quantification results. Finally, the method was used successfully in detecting pesticide residues in commercial gape wines.

In 2007, the excavation of the M-30 ring road located in Madrid and the creation of a green corridor either side of the Manzanares river brought significant change to the metropolitan area. The corridor and linear park which it provided were designed to contribute to the regeneration of the fluvial ecosystem, establish links among residents on each side of the river and promote cultural and leisure activities. This paper provides a sustainability analysis of the excavation of the M-30 (involving the socio-economic and environmental impact) 14 years after its construction. In order to show such an impact, an analysis of the area both prior to the project and after completion, as well as a hypothetical solution that uses improved materials, has been performed. This entails use of the multi-criteria decision-making model named MIVES (initials in Spanish, modelo integrado de valor para una evaluación sostenible). The MIVES method is based on the application of value functions of sustainability indicators selected by socio-economic and environmental criteria, chosen by experts. Results from analysis showed that the excavation of the M-30 considerably improved the sustainability of the area (sustainable index 3.43 and 6.26 both before and after the excavation works). However, use of improved materials in contrast with the application of conventional materials slightly improved the sustainability of the work (Sustainability Index 6.26 and 6.74, respectively, of the conventional materials).

A variant of the von Neumann-Wigner Interpretation is proposed. It does not make use of the familiar language of wave functionsand observers. Instead it pictures the state of the physical world as a vector in a Fock space and, therefore not, literally, a functionof any spacetime coordinates. And, rather than segregating consciousness into individual points of view (each carrying with it asense of its proper time), this model proposes only unitary states of consciousness, Q(t), where t represents a fiducial time withrespect to which both the state of the physical world and the state of consciousness evolve. States in our world's Fock space areclassified as either 'admissible' (meaning they correspond to definite states of consciousness) or 'inadmissible' (meaning they donot). The evolution of the state vector of the world is such as to always keep it restricted to 'admissible' states. Consciousness istreated very much like what Chalmers calls an "M-Property." But we try to show that problems with the quantum Zeno effect do not arise from this model.

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

The Fourier Continuous Derivative ($D_C$) offers a unique perspective on fractional differentiation grounded in the theory of Fourier series. This approach has the potential to address problems across various disciplines, including physics, engineering, and mathematics. The primary insight underpinning this approach is that a convex function defined on $\mathbb{Z}$ retains its convexity on $\mathbb{R}$. This paper delves into the Fourier Continuous Derivative, compares it with traditional fractional derivatives, and outlines its possible real-world applications, such as modeling viscoelastic materials, solving wave equations, and financial data analysis.

This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

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

Pulsed-field gradient (PFG) diffusion experiments can be used to measure anomalous diffusion in many polymer or biological systems. However, it is still complicated to analyze PFG anomalous diffusion, particularly the finite gradient pulse width (FGPW) effect. In practical applications, the FGPW effect may not be neglected such as in clinical diffusion magnetic resonance imaging (MRI). Here, two significantly different methods are proposed to analyze PFG anomalous diffusion: the effective phase shift diffusion equation (EPSDE) method and an observing the signal intensity at the origin method. The EPSDE method describes the phase evolution in virtual phase space, while the method to observe the signal intensity at the origin describes the magnetization evolution in real space. However, these two approaches give the same general PFG signal attenuation including FGPW effect, which can be numerically evaluated by a direct integration method. The direct integration method is fast and without overflow. It is a convenient numerical evaluation method for Mittag-Leffler function type PFG signal attenuation. The methods here provide a clear view of spin evolution under field gradient, and their results will help the analysis of PFG anomalous diffusion.

Positive recurrence for a single-server queueing system is established under generalised intensity conditions of service which does not assume existence of the density distribution function of service but a certain integral type lower bound as a sufficient condition. Positive recurrence implies existence of the invariant distribution and a guaranteed slow convergence to it in the total variation metric.

A new set of basis functions is presented. The foundation in mathematics is established. To reconstruct a signal, it is compared to the Fourier basis functions. The M-basis functions' potential applications are also presented.

The increase in the number of firms manipulating financial reports has misled shareholders' investment decisions and resulted in an indelible blot on foreign investors’ trust. Due to earnings management (EM) practice, managers' inefficiency, and lack of transparency in Iraq companies. This study tested the influence of the corporate governance mechanisms (CG), (board independence, audit committee, meeting frequency) on EM based on agency theory, as well, to link between EM and firm's performance (FP) in Iraqi listed companies and the impact of moderating role of corporate social responsibility (CSR) based on the Stakeholder Theory. The study's sample consists of 65 companies for the 2013-2018 financial years. Data were collected mainly from the annual reports (secondary data) of the Iraqi listed firms. This study uses the M-score model to detect EM practices as practical techniques in detecting earnings manipulation practices. The panel static model estimators. Hence, this paper adds to the CG literature from the perspective of stakeholder theory using Iraq's unique industrial environment. Based on the research results, policy-makers might use the study‘s findings to recognize the essential roles of several CG mechanisms in alleviating the opportunistic practices in Iraq. Further, companies should also be encouraged to enhance the CSR disclosure quality.

Epilepsy is characterized by repeated spontaneous reactions caused by hyper-excitability and neurons firing in high synchronization in the central nervous system. It seriously affects the quality of life of epileptic patients and nearly 30% of individuals are refractory to treatment of antiepileptic drugs. Therefore, there is an urgent need to develop new medicines to manage and control the refractory epilepsy. Cannabinoid ligands including selective cannabinoid receptor subtype (CB1 or CB2 receptor) ligands and non-selective cannabinoid (synthetic and endogenous) ligands may serve as the novel candidates for this need. Cannabinoid systems appear to regulating seizure activity in the brain through the activation of CB1 and CB2 cannabinoid receptors (CB1R and CB2R). An abundant series of cannabinoid analogues have been tested in various animal models, including a rat pilocarpine model of acquired epilepsy, in vitro hippocampal neuronal culture models of acquired epilepsy and status epilepticus, a pentylenetetrazole model of myoclonic seizures in mice and a penicillin-induced model of epileptiform activity in the rats. The accumulating lines of evidence show that cannabinoid ligands exhibit significant benefits to control seizure activity in different epileptic models. For this reason, we summarize the relationship between brain CB2 receptors and seizures, and emphasize the potential mechanisms of their therapeutic effects involving affecting neurons, astrocytes, and microglia cells. The unique features of CB2Rs, such as lower expression levels under physiological conditions and high inducibility under epileptic conditions, make it an important target for future research on drug-resistant epilepsy.

Rifampicin is one of the most important chemotherapeutic agents used in the treatment of tuberculosis. M. tuberculosis clinical strains resistant to rifampicin harbor mainly mutation in an 81-base pair region of rpoB. These mutations mainly consist of single amino acid substitutions. However insertions also can be related with rifampicin resistance strains. Herein, we described an insertion of 12 nucleotides in clinical isolates of M. tuberculosis resistant to rifampicin, all obtained from inmates. To evaluate the importance this insertion in surviving and drug resistance, it were carried out fitness experimental assays as well as in silico studies of 3D structural models, molecular docking simulations and virtual screening. The medical records of the seven patients showed all were previously treated to tuberculosis. Growth curves shown that the insertion determines a biological cost when compared to wild type rpoB and katG; or the double mutated rpoB S531L and katG S315T. From docking and molecular dynamics simulations it can be inferred that the insertion does not affect the process of synthesis of RNA transcripts. On the other hand, in the mutant RNAP-RIF complex rifampicin confirmed a low affinity interaction for the mutant form. Interesting, virtual screening for potential inhibitors for wtRNAP and mRNAP using a library of 1446 compounds approved by the FDA showed that the best ligands were mainly compounds with antibiotic activity, although the targets involved in the pharmacological action are other than RNAP. In conclusion, seven strains of M. tuberculosis RIF resistant that present an insertion of four amino acids in RNA polymerase showed by growth curve assays, a biological cost. Further, bioinformatics tools had characterized the putative drug resistance dynamic as well as the maintenance of RNA polymerase activity.

Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

New exact solutions to conformable time fractional EW and modified EW equations are constructed by using Sine-Gordon expansion approach. The fractional traveling wave transform and homogeneous balance have significant roles in the solution procedure. The predicted solution is of the form of some finite series of multiplication of powers of cos and sin functions. The relation among trigonometric and hyperbolic functions in sense of Sine-Gordon expansion gives opportunity to construct the solutions in terms of hyperbolic functions.

Build a special identical equation, use its calculation characters to prove and search for solution of any odd converging to 1 equation through (*3+1)/2^k operation, change the operation to (*3+2^m-1)/2^k, and get a solution for this equation, give a specific example to verify. Thus prove the Collatz Conjecture is true. Furthermore, analysis the sequences produced by iteration calculation during the procedure of searching for solution, build a weight function model, prove it decrease progressively to 0, build a complement weight function model, prove it increase to its convergence state. Build a (*3+2^m-1)/2^k odd tree, prove if odd in (*3+2^m-1)/2^k long huge odd sequence can not converge, the sequence must outstep the boundary of the tree after infinite steps of (*3+2^m-1)/2^k operation.

Today electricity is distributed to the individual users via physical Copper connections. From the power stations, the energy is transported through transmission lines where the electricity, sinusoidally modulated at a fixed frequency of about 50 Hz, is raised up to a voltage in a range approximately variating between 30, and 110 kV. When electrons, aligned at this voltage, pass through the transmission lines, they cause coherent vibrations, sometimes even audible in the acoustic frequencies. In the spectrum of movements to which electric cables are subjected, there are also unexpected and sporadic movements caused by winds and rain. The problem of carrying out persistent, precise and spatially distributed monitoring of transmission line health is to use a large number of sensors physically distributed everywhere and somehow transmit the results to a control station. The use of synthetic aperture radar (SAR) data could be a viable solution of persistent and wide-area high-voltage vibration monitoring. In this paper we produce a comprehensive survey on how to monitor both movements in terms of vibrational displacement, due to weathering, and those due to electricity transmission, normally fixed at about 50 Hz. The results demonstrate the technical feasibility of an operational use of SAR for these purposes in the very short term. This would allow the possibility of monitoring malfunctions such as black-outs or other frequency anomalies.

A substantial spike in the need for quality healthcare has resulted from people being more cognizant of health issues. With blockchain, healthcare providers may safely share patient information electronically, which is especially important given the sensitive nature of the data contained inside them. However, flaws in the current blockchain design have surfaced since the dawn of quantum computing systems. The study proposes a novel quantum inspired blockchain system (Qchain) and constructs a unique entangled quantum medical record (EQMR)system with an emphasis on privacy and security. This Qchain relies on entangled states to connect its blocks. Automated production of the chronology indicator reduces storage capacity requirements by connecting entangled BloQ (blocks with quantum properties) with controlled activities. One qubit is used to store the hash value of each block. A lot of information regarding quantum internet is included in the protocol for the entangled quantum medical record (EQMR). EQMR can be accessed in Medical Internet of Things (M-IoT) systems may be kept private and secure, and their where-abouts can be monitored in the event of an emergency. The protocol also uses quantum authentication in place of more conventional methods like encryption and digital signatures. Mathematical research shows that the quantum converged blockchain (QCB) is highly safe against attacks such as the External attack, Intercept-Measure-Repeat attack, and Entanglement-Measure attack. The reliability and auditability evaluations of the entangled BloQ, as well as the quantum circuit design for computing the hash value, are presented. There's also a comparison between the suggested approach and several other quantum blockchain designs.

Background: Polycystic ovary syndrome is a common reproductive and endocrinological disease characterized by ovulatory dysfunction, polycystic ovaries, and hyperandrogenism. Adipokines are believed to contribute to developing polycystic ovary syndrome and its accompanying metabolic complications such as dyslipidemia, insulin resistance, and cardiovascular diseases. Oncostatin M, a novel adipokine, plays a role in oogenesis, lipogenesis, and inflammation and may contribute to polycystic ovary syndrome pathogenesis and its related metabolic problems. Methods: In this case-control study, the patients were grouped in a 1:1 ratio into either the polycystic ovary syndrome (n = 32) or the control group (n = 32). Blood samples were obtained between the third and fifth days of the menstrual cycle. Serum levels of fasting glucose, insulin, C-reactive protein, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, triglyceride, white blood cell count, thyroid-stimulating hormone, luteinizing hormone, follicle-stimulating hormone, total testosterone, prolactin, estradiol, homeostasis model assessment of insulin resistance and oncostatin M were analyzed. Results: Oncostatin M levels were significantly lower, but C-reactive protein levels were substantially higher in the polycystic ovary syndrome group than in the control group (p = 0.002, p = 0.001, respectively). Oncostatin M was inversely correlated with total cholesterol, non-high-density lipoprotein cholesterol, fasting glucose, and the luteinizing hormone/follicle-stimulating hormone ratio (ρ = -0.329, p =0 .017; ρ = -0.386, p = 0.005; ρ = -0.440, p = 0.001; ρ = -0.316, p = 0.023, respectively). Conversely, there was no correlation between oncostatin M and total testosterone level (ρ = 0.220; p = 0.118). In the context of inflammation and metabolic parameters, oncostatin M was inversely correlated with C-reactive protein, homeostatic model assessment for insulin resistance score, and low-density lipoprotein cholesterol (ρ = -0.353, p = 0.019; ρ = -0.275, p = 0.048; ρ = -0.470, p &lt; 0.001, respectively). The diagnostic performance of oncostatin M, C-reactive protein, homeostasis model assessment of insulin resistance, and non-high-density lipoprotein cholesterol for polycystic ovary syndrome is as follows: Oncostatin M, sensitivity: 50%, specificity: 75%, Accuracy: 63%, p = 0.009; C-reactive protein, sensitivity: 84%, specificity: 61%, Accuracy: 74%, p = 0.004; homeostasis model assessment of insulin resistance, sensitivity: 72%, specificity: 81%, Accuracy: 77%, p &lt; 0.001; and non-high-density lipoprotein cholesterol; sensitivity: 72%, specificity: 75%, accuracy: 73%, p &lt; 0.001. Conclusions: Plasma oncostatin M levels were considerably lower in patients with polycystic ovary syndrome than in the control group, and this was inversely correlated with the hormonal and metabolic parameters of polycystic ovary syndrome. Thus, oncostatin M may be a novel therapeutic target for polycystic ovary syndrome and its metabolic complications.

A major route for influx of calcium ions into neurons uses the STIM-Orai1 voltage-independent channel. Once cytosolic calcium ([Ca2+]i) elevates, it activates mitochondrial and endoplasmic calcium stores, to affect downstream molecular pathways. In the present study we employed a novel drug, Carbonyl Cyanide Chlorophenylhydrazone (CCCP), a mitochondrial uncoupler, to explore the role of mitochondria in cultured neuronal morphology. CCCP caused a sustained elevation of [Ca2+]i and, quite surprisingly, a massive increase in density of dendritic filopodia and spines in the affected neurons. This morphological change can be prevented in cultures ex-posed to calcium-free medium, to Orai1 antagonist 2APB, or to cells transfected with domi-nant-negative Orai1 plasmid. It is suggested that CCCP activates mitochondria through influx of calcium, to cause a rapid growth of dendritic processes

Using a simple model for internal heat evolution and mass-internal heat relations found for rocky exo planetary objects in the inner solar system we have inferred the phases of volcanism at earth ( EA) or host star ages (SA) in 52 potentially habitable rocky exo planets. We have also calculated the internal tidal heat contributions and magnetic moments of these exo planets. Based on these results we have inferred the probability of existence of life favouring geophysical conditions in the above exo planets at EA and SA. In M star associated exo planets, occurrences of super flares and long night periods may pose problems for the development of advanced life

A novel type of phosphazene containing additive that act both as catalyst and as flame retardant for benzoxazine binders is presented in this study. The synthesis of a derivative of hexachlorocyclotriphosphazene (HCP) and meta-toluidine was carried out in the medium of the latter, which made it possible to achieve complete substitution of chlorine atoms in the initial HCP. Thermal and flammability characteristics of modified compositions are revealed. The modifier catalyzes the process of curing and shifts the beginning of reaction from 222.0 C for pure benzoxazine to 205.9 C for composition with 10 phr of modifier. The additive decreases the glass transition temperature of compositions. Achievement of the highest category of flame resistance (V-0 in accordance with UL-94) is ensured both by increasing the content of phenyl residues in the composition and by the synergistic effect of phosphorus and nitrogen. Brief research of the curing kinetics disclosed the complex nature of the reaction. An accurate two-step model is obtained using extended Prout-Tompkins equation for both steps.

Land Surface Temperature (LST) is a basic parameter in energy exchange between the land and atmosphere and is frequently used in many sciences such as climatology, hydrology, agriculture, ecology, etc. LST time series data have usually deficient, missing and unacceptable data caused by the presence of clouds in images, presence of dust in atmosphere and sensor failure. In this study, Singular Spectrum Analysis (SSA) algorithm was used to resolve the problem of missing and outlier data caused by cloud cover. The region studied in the present research included an image frame of MODIS with horizontal number 22 and vertical number 05 (h22v05). This image involved a large part of Iran and Turkmenistan and Caspian Sea. In this study, MODIS LST sensor (MOD11A1) was used during 2015 with 1×1 Km spatial resolution and day/night LST data (daily temporal resolution). The results of the data quality showed that cloud cover caused 36.37% of missing data in the studied time series with 730 day/night LST images. Further, the results of SSA algorithm in reconstruction of LST images indicated the Root Mean Square Error (RMSE) of 2.95 K between the original and reconstructed data in LST time series in the study region. In general, the findings showed that SSA algorithm using spatio-temporal interpolation in LST time series can be effectively used to resolve the problem of missing data caused by cloud cover.

Objective: This study aimed to demonstrate the availability of portable devices for nasal FeNO measurement, which could replace exhaled NO measurement based on the continuous aspiration of multiple flow measurement systems. Methods: A descriptive cross-sectional study. The healthy subjects without rhinosinusis disorders (control group) and those with diagnosed allergic rhinitis (AR group) were enrolled in the study. They underwent nasal and bronchial FeNO measurements by both fixed flow NObreath® connected to nasal mask and multiple flows HypAir FeNO®. Results: A total of 153 people were recruited including 63 healthy subjects and 90 subjects with AR. There were no statistically significant differences in anthropometric characteristics between the two groups (P > 0.05). There were a significant increase in FeNO values in the AR group compared to the control group; concentrations of nasal and bronchial FeNO mearsured by NObreath® were 76.0 ± 50.7 ppb (vs 36.0 ± 28.1 ppb, P < 0.01) and 32.3 ± 15.4 ppb (vs 9.2 ± 5.6 ppb, P < 0.001), and those mearsured by NObreath® Hypair FeNO® were 1796.9 ± 523.3 ppb (vs 400.2 ± 123.1 ppb, P < 0.001) and 37.3 ± 23.0 ppb (vs 17.4 ± 18.3 ppb, P < 0.01). A weak correlation between the values measured by NObreath® and Hypair FeNO® devices was observed (r = 0.023 and r = 0.089, respectively; p < 0.05). Conclusions: The handheld NObreath® device is effective in measuring FeNO concentrations in both normal subjects and AR patients. The advantages in price and size, creating a compact, low-cost device that is convenient for use and research.

Micro and small wood-processing enterprises represent the heart of the European forest-based industries, being among the key drivers of economic growth in rural, mountainous, and poor regions. Their economic efficiency is of fundamental importance for their existence and the pro-vision of income for the local population in rural areas. Data Envelopment Analysis (DEA) is nonparametric, linear-programming-based approach, commonly used to analyse the efficiency of organizational units. This method allows estimating the economic efficiency of a certain eco-nomic system without assumptions about the functional form between resources and products. Furthermore, DEA determines the efficiency frontier and gives results of whether an enterprise, i.e., a Decision Making Unit (DMU) is efficient or not. The main objective of this study was to investigate and evaluate the economic efficiency of micro and small wood-processing enterpris-es in the EU countries and reveal the hidden inputs that facilitate efficiency generation. The eco-nomic efficiency evaluation was carried out on the basis of the official statistical data for the mi-cro and small wood-processing companies in the EU member states for the period 2015-2020 by performing a two-stage DEA analysis. The data used were standardized by value per employee. In addition to the first stage of DEA, fractional regression probit and logit models with four contextual variables were used to reveal the influence of the hidden inputs in the model. The results showed that the micro and small wood-processing enterprises can be regarded as more scale-efficient than technically-efficient entities. The only contextual variable affecting the eco-nomic efficiency was Investments per Person Employed, improving the efficiency by 2% per 1% increase of the investments.