In the last years, a recent growing line of research has been developed with fruitful results by using fractional and conformable derivatives in the iterative procedures of classical methods for solving nonlinear equations. In that sense, the use of conformable derivatives has shown better behavior than fractional ones, not only in the theory, but also in the practice. In this work, we adapt the approximation of conformable derivatives in order to design the first conformable derivative-free iterative schemes to solve nonlinear equations: a Steffensen’s type method and a Secant type method; the latter with memory. Convergence analysis is made, preserving the order of classical cases, and the numerical performance is studied in order to confirm the results in the theory. It is shown that these methods can present some numerical advantages versus their classical partners, with wide sets of converging initial estimations.

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.

With the current rapid spread of COVID-19, global health systems are increasingly overburdened by the sheer number of people that need diagnosis, isolation and treatment. Shortcomings are evident across the board, from staffing, facilities for rapid and reliable testing to availability of hospital beds and key medical-grade equipment. The scale and breadth of the problem calls for an equally substantive response not only from frontline workers such as medical staff and scientists, but from skilled members of the public who have the time, facilities and knowledge to meaningfully contribute to a consolidated global response. Here, we summarise community-driven approaches based on Free and Open Source scientific and medical Hardware (FOSH) currently being developed and deployed to bolster access to personal protective equipment (PPE), patient treatment and diagnostics.

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

Shell-like, double curved and thus above-average performance structures, are usually produced monolithically on site. For industrial advancement, however, they must be divided into transportable modules which can be assembled on the construction site (design for assembly). Models are lattice shells made of steel and glass, in which predominantly flat sub-surfaces (modules) are used. Therefore, the main question is: Which modularizations are suitable for flow production with mineral building materials? In this paper designed free-form surface is going to be discretized as PQ circular mesh system, suitable modules for 3D concrete printing. Moreover, the multi-criteria optimization is done with Response Surface Methodology (RSM) in order to get optimal final shape. The goal is to start from the arbitrary shape, that can be generated from two curves, with possible two-way division into modules and compare it with the resulted discretized PQ circular mesh system, realized with new algorithm. The comparison can be defined through two main criteria: geometrical and structural.

This paper introduces new improvements to the modified version of the BIRECT (BI secting RECTangles) algorithm referred to as BIRECTv. We explore various approaches, by first including a grouping strategy for hyper-rectangles having almost the same sizes by categorizing them into different classes. Therefore constraining them not to exceed a certain pre-defined threshold (a small positive value to define the tolerance level). This approach allows for more efficient computation and can be particularly useful when dealing with a large number of hyper-rectangles with varying sizes. To avoid over-sampling, and preventing redundant or excessive sampling, at some shared vertices in descendant subregions, a particular vertex database is used to limit the number of samples taken within each subregion to two. The experimental investigation shows that these improvements have a positive impact on the performance of the BIRECTv(imp.) algorithm and the proposal is a promising global optimization algorithm compared to the original BIRECTv algorithm and its variants. Additionally, the BIRECTv(imp.) algorithm showed particular efficacy in solving high-dimensional problems.

The duality is one of the most interesting properties of the Laplace and Fourier transforms associated to the integer order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier transforms. The scale and nabla derivatives are used.

This paper proposes an optimal trading algorithm based on a novel application of the conventional Control Engineering (CE). We consider a fundamental CE concept, namely, the feedback control and apply it to the Algorithmic Trading (AT). The concrete feedback control strategy is designed in a form of the celebrated Proportional-Integral-Derivative (PID) model. The highly fluctuating nature of the modern financial markets has led to the adoption of a model-free realisation of the generic PID framework. The control theoretical methodology we propose is combined with the advanced statistics for the historical market data. We obtain a specific log-normal probability distribution function (pdf) associated with the specific quantities associated with the available stock data. The empirical log-normal pdf mentioned above makes it possible the necessary PID gains optimization. For this aim, we apply the data-driven optimization approaches and consider the corresponding Monte Carlo solution procedure. The optimized PID trading algorithm we propose is also studied in the Fourier analysis framework. This equivalent frequency domain representation involves a new concept in the financial engineering, namely, the "stock market energy" concept. For the evaluation, we implement the proposed PID optimal trading algorithm and develop a Python based prototype software. We finally apply the corresponding prototype software to a dataset from the Binance BTC / USDT stock market. The experimental result illustrates the implementability of the proposed optimal PID trading scheme and also shows the effectiveness of the proposed CE methods in the modern AT.

Bacteria a Microscopic organisms are the most inexhaustible and flexible of microorganisms and constitute a huge division of the whole living earthly biomass, certain microorganisms were found to amass metallic components at a high limit Was Known as Bacterial Bio-sorption Due to their little size, capacity to become under controlled conditions, and their Accommodation to an extensive variety of ecological situations; Potent metal bio-sorbents among microorganisms, at low pH esteems, cell divider ligands are protonated and contend essentially with metals for official. With expanding pH, more ligands, such as amino and carboxyl groups, could be exposed, leading to attraction between these negative charges and the metals, and consequently increment bio-sorption onto the cell surface. Starting with Isolation and identification of heavy metal-resistant bacteria from rock Ore. Studying Factors Affecting Uranium Bio-sorption, Optimization of bacterial growth conditions and optimum for metal uptake by free and immobilized bacterial cells and Desorption ratio of uranium ions adsorbed by Coli. /alginate, All this evidence suggest that functions groups Represented in our study are responsible for metal uptake in our bacterial biomass beside change in peaks position which assigned for it's groups confirm bio-sorption of metal ions from waste due to ions charge interaction comparing with immobilized we found increase in no of binding sites indicate that immobilized bacterial have high efficiency for metal up take which also change in peaks position which assigned for its groups confirm bio-sorption of metal ions from waste due to ions charge interaction, Where the high bio-sorption yield obtained by bacteria, the Uranium & heavy metal bioremediation process expects microorganisms to be joined to a strong surface.

This study aims at the sustainable valorization of eggshells (ES) from different countries of origin in cement concrete as a cement replacement for Hong Kong. For this purpose, sixteen different eggs from different regions across the world were selected from the local market. Firstly, the extent of uniformity in the weight and mineral content of sampled eggshells were assessed by a specific gravity test and thermogravimetric analysis (TGA), respectively. It was found that specific gravity varies between 2.02 and 2.39, with an average value of 2.20 ± 0.01, whereas CaCO₃ varies between 94.65% and 97.23%, with an average value of 96.33%. These values were a bit lower than those of extra-pure limestone (LS) because of the organic part and the porous structure of eggshells. Secondly, three different eggshells were selected for cement replacement in cement concrete, both in the uncalcined and calcined states, based on having the highest, medium, and lowest CaCO₃ content, respectively. To get the calcined eggshells, the eggshells were calcined at 800^oC for three hours. It was found that the strength of eggshells varies with CaCO₃, but the variation was acceptable. The calcined eggshells showed comparatively more compressive strength and were close to the LS because of the free CaO and the absence of an organic part. In general, the variation in the basic properties of eggshells from different regions across the world is negligible and suitable to use as a cement replacement with acceptable variation in strength in Hong Kong.

This paper aims to unify q-derivative/q-integral and h-derivative/h-integral in a single definition, this will be called q−h-derivative/q−h-integral. These notions are further extended on finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities are studied for q−h-integrals which are directly connected with well known results. In diverse fields of science and engineering the theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified by using the concept of q−h-derivative/q−h-integral.

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.

The polysaccharide-based chiral stationary phase (CSP) columns for high-performance liquid chromatography (HPLC) were applied in the separation of liquid crystalline racemic mixtures obtained based on (R,S)-2-octanol and were found to be highly effective in recognizing isomers of minor structural differences. The mobile phase (MP), which consists of acetonitrile (ACN)/water (H2O) at different volume ratios, was used. All measurements were made at room temperature. The order of the elution was also determined. The chromatographic parameters such as resolution - (Rs), selectivity - (α), and the number of theoretical plates, i.e., column efficiency - (N), were determined. The polysaccharide-based CSP columns have unique advantages in separation technology, and this study has shown the potential usefulness of the CSP columns in separating liquid crystalline racemic mixtures belonging to the same homologous series.

Bio-based packaging materials and efficient drug delivery systems are gaining attention, carboxymethyl cellulose (CMC) is one of the most soluble cellulose derivatives, is a good candidate material due to its biocompatibility, biodegradability, and reproducibility. However, CMC-based films are lack of sufficient mechanical properties, limiting its widespread application. In this paper, the molecular interactions between CMC and additives with different molecular structures have been studied with rheological method. The additives are chitosan and cellulose derivatives including O-carboxymethylated chitosan (O-CMCh), N-2-hydroxypropyl-3-trimethylammonium-O-carboxymethyl chitosan (HTCMCh), hydroxypropyltrimethyl ammonium chloride chitosan (HACC), cellulose nanofibers (CNC), and cellulose nanofibers (CNF). The influencing factors, such as molecular structure, concentration of additives and temperature on the rheological properties were studied, which results revealed the information intermolecular interactions. Based on the rheological properties, several systems were selected to prepare films, which show very good transparency, wettability, mechanical properties, biodegradability, and cytotoxicity. These good characteristics of the selected films also proved the good biocompatibility of CMC and chitosan and cellulose derivatives. This work will provide an idea to prepare CMC-based food packaging and effective drug delivery materials with specific properties.

The material derivative is important in continuum physics. This Letter shows that the expression $\frac{d }{dt}=\frac{\partial }{\partial t}+(\bm v\cdot \bm \nabla)$, used in most literature and textbooks, is incorrect. The correct expression $ \frac{d (:)}{dt}=\frac{\partial }{\partial t}(:)+\bm v\cdot [\bm \nabla (:)]$ is formulated. The solution existence condition of Navier-Stokes equation has been proposed from its form-solution, the conclusion is that "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

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 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

The current study aims to study the optimal fermentation conditions for producing microbial bioactive compounds. The microwave parameters consist on 2450 MHz, and 500-watt for 20, 30, and 40 seconds. The solubility of solvents was tested for the extraction of antioxidant compounds from fermented rice (Koji) by A. flavus, Ethyl acetate was the best solvent used for extraction purposes. Antioxidant properties were differentiated by blocking the oxidation of the linoleic acid with an inhibition rate of 73.13% at a concentration of 200 mg/mL, in addition to increasing its effectiveness for free radical extraction and reduction strength by increasing concentrations gradually. The bond ability to irons was lower compared to the EDTA-2Na, in addition to the obtained total content corresponding to phenolic compounds in the ethyl acetate extract of fermented rice (Koji) by A. flavus was 232.11 mg, on the basis of galic acid/mg. The stability of the antioxidant compounds of the ethyl acetate extract of fermented rice (Koji) by A. flavus was also studied; showing stability under neutral conditions, as well as at high temperatures (185 °C during two hours). However, no stability was obtained under acidic and alkaline conditions.

We show the tensor properties of joint probabilities on a Riemannian parametric manifold. Initially we develop a binary data matrix for parameter measurements of a large number of particles confining in a closed system in order to retrieve the joint probability densities of related parameters. By introducing a new generalized inner product as a multilinear operation on dual basis of parametric space, we extract the set of joint probabilities and prove them to meet contravariant tensor properties in a general Riemannian parametric space. We show these contravariant tensors reduce to classical ordinary partial derivatives definition in ordinary Euclidean parametric space. Finally we prove by a theorem that symmetrized iterative contravariant derivative of cumulative probability function on Riemannian manifold gives the set of joint probabilities in those manifold. We bring some examples for compatibility with physical tensors.

Creating self-learning algorithms, developing deep neural networks and improving other methods that "learn" for various areas of human activity is the main goal of the theory of machine learning. It helps to replace the human with a machine, aiming to increase the quality of production. The theory of artificial neural networks, which already have replaced the humans in problems of detection of moving objects, recognition of images or sounds, time series prediction, big data analysis and numerical methods remains the most dispersed branch of the theory of machine learning. Certainly, for each area of human activity it is necessary to select appropriate neural network architectures, methods of data processing and some novel tools from applied mathematics. But the universal problem for all these neural networks with specific data is the achieving the highest accuracy in short time. Such problem can be resolved by increasing sizes of architectures and improving data preprocessing, where the accuracy rises with the training time. But there is a possibility to increase the accuracy without time growing, applying optimization methods. In this survey we demonstrate existing optimization algorithms of all types, which can be used in neural networks. There are presented modifications of basic optimization algorithms, such as stochastic gradient descent, adaptive moment estimation, Newton and quasi-Newton optimization methods. But the most recent optimization algorithms are related to information geometry, for Fisher-Rao and Bregman metrics. This approach in optimization extended the theory of classic neural networks to quantum and complex-valued neural networks, due to geometric and probabilistic tools. There are provided applications of all introduced optimization algorithms, what delighted many kinds of neural networks, which can be improved by including any advanced approaches in minimization of the loss function. Afterwards, we demonstrated ways of developing optimization algorithms in further researches, engaging neural networks with progressive architectures. Classical gradient based optimizers can be replaced by fractional order, bilevel and, even, gradient free optimization methods. There is a possibility to add such analogues in graph, spiking, complex-valued, quantum and wavelet neural networks. Besides the usual problems of image recognition, time series prediction, object detection, there are many are other tasks for modern theory of machine learning, such as solving problem of quantum computations, partial differential and integro-differential equations, stochastic processes and Brownian motion, making decisions and computer algebra.

Research on the lead halide-based perovskite solar cells have obtained considerable interest in photovoltaic industry owing to their higher efficiency, easy manufacturing, light-weight and low cost. However, these lead halide-based solar cells are not suitable to manufacture commercially because of the toxicity of lead-based materials. In this context, a lead-free perovskite, cesium-bismuth iodide (Cs₃Bi₂I₉) is considered as a potential alternative to the lead halide-based cell due to their non-toxicity and stability, but this perovskite cannot be matched with random hole transport layer (HTL) and electron transport layer (ETL) materials compared to lead halide-based perovskite because of their crystal structure and band gap. Therefore, in this study, performance comparison of different ideal HTL and ETL materials for Cs₃Bi₂I₉ perovskite layer were studied using SCAPS-1D device simulation on the basis of open circuit voltage, short circuit current, power conversion efficiency (PCE) and fill factor (FF) as well as several novel PSC configuration model were designed that can direct for further experimental research for PSC device commercialization. Results from this investigation reveals that the maximum efficiency of 20.96% is obtained for the configuration ITO/WS₂/Cs₃Bi₂I_9­/NiO/Au with optimized parameters such as thickness 400 nm, band gap 2.1eV, absorber layer defect density 10¹² cm^-3, donor density of ETL 10¹⁸ cm^-3 and the acceptor density of HTL 10²⁰ cm^-3.

In this manuscript a new approach into analyzing the local stability of equilibrium points of non-linear Caputo fractional planar systems is shown. It is shown that the equilibrium points of such systems can be a stable focus or unstable focus. In addition, it is proposed that previous results regarding the stability of equilibrium points have been incorrect, the results here attempt to correct such results. Lastly, it is proposed that a Caputo fractional planar system cannot undergo a Hopf bifurcation, contrary to previous results prior. Though, it is shown that such systems can undergo a Hopf bifurcation (topologically).

In option pricing, we often deal with options whose payoffs depend on multiple factors such as foreign exchange rates, stocks, etc. Usually, it leads to a knowledge of the joint distributions and complicated integration procedures. The paper develops an alternative approach that converts the option pricing problem to a dual one and presents a solution to the problem in the optional semimartingale setting. The paper contains several examples which illustrate results in terms of the parameters of models and options.

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.

Sirtuins are a family of Class III epigenetic modifying enzymes involved in regulating cellular processes through the removal of acetyl groups from proteins. They rely on NAD+ as a coenzyme in contrast with classical HDACs (Class I, II, and IV) that depends on Zn+ for their activation, linking their function to cellular energy levels. There are seven mammalian sirtuin isoforms (SIRT1-7), each located in different subcellular compartments. Sirtuins act as master regulators of cellular homeostasis, responding to changes in nutrient availability and energy status. They play vital roles in diverse physiological and pathological conditions, making them promising therapeutic targets for various diseases, including cancer, neurodegenerative disorders, and metabolic diseases. High levels of SIRT6 are involved in the cancer progression of many tumor types and our previous studies revealed that sirtuin 6 was highly expressed in NSCLC cells and its inhibition potentially favored apoptosis and cell cycle arrest. Sirt6 emerged as a promising target and inhibitors of natural and synthetic sources are highly warranted. Imidazole derivatives are often investigated as sirtuin regulators due to their ability to interact with the binding site and modulate their activity. Imidazole bestows many possible substitutions on its ring and neighboring atoms, to design and synthesize derivatives with specific target selectivity and improved pharmacokinetic properties, optimizing drug development. We recently developed imidazole-based derivatives that potentially inhibited classical HDAC enzymes. Therefore, we evaluated the Sirtuin inhibition activity of our in-house compound comprised of imidazole derivatives and the strongest inhibition was observed with Ethyl 2-[5-(4-chlorophenyl)-2-methyl-1-H-Imidazole-4-yl) acetate against Sirt6 by in-silico and protein expression studies. Our results suggested that Ethyl 2-[5-(4-chlorophenyl)-2-methyl-1-H-Imidazole-4-yl) acetate could be a potential novel sirt6 inhibitor.

The development of biosensors with high sensitivity and low-detection limits provides a new direction for medical and personal care. Graphene and graphene derivatives have been used to prepare various types of biosensors due to their excellent sensing performance (e.g. high specific surface area, extraordinary electronic properties, electron transport capabilities and ultrahigh flexibility). This perspective review focuses on graphene-based biosensors for quantitative detection of cancer related biomarkers such as DNA, miRNA, small molecules and proteins by integrating with different signal outputting approaches including fluorescent, electrochemistry, surface plasmon resonance, surface enhanced Raman scattering etc. The article also discussed their challenges and potential solutions along with future prospects.

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

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.

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.

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.

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.

In this paper we investigate some properties of square-free numbers. In particular, we study a function that counts the number of square-free numbers no larger than the given number n. We show that this function has asymptotics consistent with the predictions of the Riemann hypothesis and use this to obtain new and better estimates of the density of square-free numbers. Finally, we present a well-known generalization of the concept of a square-free number to monoids and research on square-free factorizations.

This paper explores the suppression of ideas within academic scholarship by academics, either by self-suppression or because of the efforts of other academics. Legal, moral, and social issues distinguishing freedom of speech, freedom of inquiry, and academic freedom are reviewed. How these freedoms and protections can come into tension is then explored by an analysis of denunciation mobs who exercise their legal free speech rights to call for punishing scholars who express ideas they disapprove of and condemn. When successful, these efforts, which constitute legally protected speech, will suppress certain ideas. Real-world examples over the past five years of academics who have been sanctioned or terminated for scholarship targeted by a denunciation mob are then explored.

In this study, we investigate spectral structure of conformable Sturm-Liouville problems and with this end, we obtain representation of solutions under different initial conditions and asymptotic formulas for eigenfunctions, eigenvalues, norming constants and normalized eigenfunctions. Consequently, we prove the existence of infinitely many eigenvalues. Also, we compare the solutions with graphics with different orders, different eigenvalues, different potentials and so, we observe the behaviors of eigenfunctions. We give an application to the α-orthogonality of eigenfunctions and reality of eigenvalues for conformable Sturm-Liouville problems defined by [15] in the last section.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

The use of salt rock for underground radioactive waste disposal facilities requires a comprehensive analysis of creep-damage process in salt rock. A computer-controlled creep setup is employed to carry out a creep test of salt rock lasted as long as 359 days under a constant uniaxial stress. The AE space-time evolution and energy releasing characteristics during creep test are studied in the meantime. A new creep-damage model is proposed on the basis of fractional derivative by combining the AE statistical regularity. It indicates that the AE data in non-decay creep process of salt rock can be divided into three stages. Furthermore, the parameters of new creep-damage model are determined by Quasi-Newton method. The fitting analysis suggests that the creep-damage model based on fractional derivative in this paper provides a precise description of full creep regions in salt rock.

Pollution caused by copper is one of the key factors of environment contamination. As one of heavy metals, copper is hard to decompose in nature, the biological enrichment of which may lead to severe damage to health. Cu²⁺ detection, thus, possesses a bright application prospect both in environment protection and in human health. In this paper, a dual-functional fluorescence-magnetic composite nano-platform has been designed to sensitively detect, meanwhile capture and remove Cu²⁺ in the solution of water and ethanol (1:1, v/v). The core-shell structure nanoparticle synthesized by using Fe₃O₄ as core and SiO₂ as shell, is covalently bonded with rhodamine derivatives on the silica layer to construct the nano-platform. The emission is increased upon the addition of Cu²⁺, showing fluorescence turn on effect for the detection, and the limit of detection which was as low as 1.68 nM. Meanwhile, Cu²⁺ ions are captured by the coordination with rhodamine derivatives, and can be removable with the help of magnetic field.

The objective of this study was to develop an ultrasonic-assisted procedure for the extraction of total phenolics from Citrus aurantium L. blossoms (CAB) and evaluate the free radical scavenging activity, anti-HMG-CoA reductase activity of total phenolics. In this work, a Box-Behnken design based on the single-factor experiments was used to explore the optimum extraction process. Under the optimum conditions (extraction solvent 70.31% ethanol, extraction temperature 61.94 °C, extraction time 51.73 min and liquid-to-solid ratio 35.63 mL/g), the extraction yield of total phenolics was 95.84 mg gallic acid equivalents (GAE)/g dry matter (DM), which was highly consistent with the theoretical value (96.12 mg GAE/g DM). The total phenolic extract showed excellent free radical scavenging properties against DPPH·, ABTS+·, ·OH and ·O2-, with the IC50 values of 197.007, 83.878, 218.643 and 158.885 μg/mL, respectively, and the extracts also showed good inhibition of HMG-CoA reductase activity, with the IC50 value of 117.165 μg/mL. Total phenolics from CAB could be a potential source of natural free radical scavenger and HMG-CoA reductase inhibitor.

Cell free systems are a widely used research tool in systems and synthetic biology and a promising platform for manufacturing of proteins and chemicals. In the past, cell free biology was primarily used to better understand fundamental biochemical processes. Notably, E. coli cell free extracts were used in the 1960s to decipher the sequencing of the genetic code. Since then, the transcription and translation capabilities of cell free systems have been repeatedly optimized to improve energy efficiency and protein yield. Today, cell free systems, in combination with the rise of synthetic biology, have taken on a new role as a promising technology for just in time manufacturing of therapeutically important biologics and high-value small molecules. They have also been implemented in an industrial scale for the production of antibodies and cytokines. In this review, we discuss the evolution of cell free systems, advancements in cell free protein synthesis, and cell free metabolic engineering, and conclude with discussing the importance and feasibility of mathematical modeling in cell free systems.

Underwater Sensor Networks (UWSNs) can enable a broad range of applications such as resource monitoring, disaster prevention, and navigation-assisted. It is especially relevant for sensor nodes location in UWSNs. Global Positioning System (GPS) is not suitable for using in UWSNs because of the underwater propagation problems. Hence some localization algorithms based on the precise time synchronization between sensor nodes have been proposed which are not feasible for UWSNs. In this paper, we propose a localization algorithm called Two-Phase Time Synchronization-Free Localization Algorithm (TP-TSFLA). TP-TSFLA contains two phases, namely, range-based estimation phase and range-free evaluation phase. In the first phase, we address a time synchronization-free localization scheme base on the Particle Swarm Optimization (PSO) algorithm to decrease the localization error. In the second phase, we propose a Circle-based Range-Free Localization Algorithm (CRFLA) to locate the unlocalized sensor nodes which cannot obtain the location information through the first phase. In the second phase, sensor nodes which are localized in the first phase act as the new anchor nodes to help realize localization. Hence in this algorithm, we use a small number of mobile beacons to help achieve location without any other anchor nodes. Besides, to improve the precision of the range-free method, an extension of CRFLA by designing a coordinate adjustment scheme is updated. The simulation results show that TP-TSFLA can achieve a relative high localization ratio without time synchronization.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

The fungus Xylaria sp. Z184, harvested from the leaves of Fallopia convolvulus (L.) Á. Löve, has been isolated for the first time. Chemical investigation of the methanol extract of this strain’s culture broth led to the discovery of three new pyranone derivatives fallopiaxylaresters A-C (1–3) and a new bisabolane-type sesquiterpenoid named fallopiaxylarol A (4), along with the first complete set of spectroscopic data for the previously-reported pestalotiopyrone M (5). Known pyranone derivatives (6–11), sesquiterpenoids (12–14), isocoumarin derivatives (15–17), and an aromatic allenic ether (18) were co-isolated. Their structures were elucidated by the interpretation of HRESIMS, 1D, 2D NMR spectroscopy and quantum chemical computation method. The antimicrobial, anti-inflammatory, and α-glucosidase inhibitory activities of selected compounds and crude extract were evaluated in vitro. The extract inhibited nitric oxide (NO) production induced by lipopolysaccharide (LPS) in murine RAW264.7 macrophage cells, with an inhibition rate of 77.28 ± 0.82% at a concentration of 50 μg/mL. The compounds 5, 7 and 8 displayed weak antibacterial activity against Staphylococcus areus subsp. aureus at a concentration of 100 μM.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

Based on the marine natural products piperafizine B, X334 and our previously reported compound 4m, fourteen novel 3,6-diunsaturated 2,5-diketopiperazine (2,5-DPK) derivatives (1-2, 4-6, 8-16), together with two known ones (3 and 7), were designed and synthesized as anticancer agents against cell lines A549 and Hela. The MTT assay results showed that the derivatives 6, 8-12 and 15 had moderate to good anticancer capacities with the IC50 values ranging from 0.7 to 8.9 μM. Among them, compound 11 with naphthalen-1-ylmethylene and 2-methoxybenzylidene functions at the 3- and 6-positions of 2,5-DPK ring, respectively, displayed good inhibitory activities to both cancer cells A549 (IC50 = 1.2 μM) and Hela (IC50 = 0.7 μM). It could also induce apoptosis and obviously block the cell cycle progression at G2/M phase in both cells at 1.0 μM. The electron withdrawing functions might not be favorable for the derivatives with high anticancer activities. Additionally, compared to piperafizine B and X334, these semi-N-alkylated derivatives have high liposolubilities (> 1.0 mg•mL-1). Compound 11 can be further developed aiming to the discovery of novel anticancer candidate.

The quest for accurate and more efficient methods for solving periodic/oscillatory problems is gaining more attention in recent time. This paper presents the construction and implementation of a family of exponentially–fitted Obrechkoff methods. A single–step Obrechkoff method involving terms up to the fourth derivatives was used as the base method. We also present the stability and convergence properties of the constructed family of methods. Two numerical examples were use to illustrate the performance of the constructed methods.

In this paper, a two-link manipulator system stability performance is designed and analyzed using Optimal control technique. The manipulator system is highly nonlinear and unstable. The system is modelled using Lagrangian equation and linearized in upward unstable position. The closed loop system is designed using optimal sliding mode controller. The system is compared with a known PID controller with an impulse applied and disturbance torques and a promising results has been obtained.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

Alzheimer’s disease is the most common neurodegenerative disease and affects persons of all races, ethnic groups, and sexes. The disease is characterized by neuronal loss leading to cognitive decline and memory loss. There is no cure and the effectiveness of existing treatments is limited and depends on the time of diagnosis. The long prodromal period, during which patients’ ability to live a normal life is not affected despite neuronal loss, often leads to a delayed diagnosis because it can be mistaken for normal aging of the brain. In order to make a substantial impact on AD patients, early diagnosis may provide a greater therapeutic window for future therapies to slow AD-associated neurodegeneration. Current gold standards for disease detection include magnetic resonance imaging and positron emission tomography scans, which visualize amyloid β and phosphorylated tau depositions and aggregates. Liquid biopsies, already an active field of research in precision oncology, are hypothesized to provide early disease detection through minimally or non-invasive sample collection techniques. Liquid biopsies in Alzheimer’s disease have been studied in cerebrospinal fluid, blood, ocular, oral, and olfactory fluids. However, most of the focus has been on blood and cerebrospinal fluid due to biomarker specificity and sensitivity attributed to the effects of the blood-brain barrier and inter-laboratory variation during sample collection. Many studies have identified amyloid β and phosphorylated tau levels as putative biomarkers, however, advances in next-generation sequencing-based liquid biopsy methods have led to significant interest in identifying nucleic acids species associated with Alzheimer’s disease from liquid tissues. Differences in cell-free RNAs and DNAs have been described as potential biomarkers for AD and hold the potential to affect disease diagnosis, treatment, and future research avenues.

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.

Synergy, emerges from synchronized reciprocal positive feedback loops between a network of diverse actors. For this process to proceed, compatible information from different sources synchronically coordinates the actions of the actors resulting in a nonlinear increase in the useful work or potential energy the system can manage. In contrast noise is produced when incompatible information is mixed. This synergy produced from the coordination of different agents achieves non-linear gains in free energy and in information (negentropy) that are greater than the sum of the parts. The final product of new synergies is an increase in individual autonomy of an organism that achieves increased emancipation from the environment with increases in productivity, efficiency, capacity for flexibility, self-regulation and self-control of behavior through a synchronized division of ever more specialized labor. Examples that provide quantitative data for this phenomenon are presented. Results show that increases in free energy density require decreases in entropy density. This is proposed as a law of thermodynamics.

Raw materials used for producing concrete, such as sand and gravel, are in short supply worldwide. It has been reported that the production of cement, one of the main constituents of concrete, results in the emission of a large amount of CO₂, accounting for 8% of total global CO₂ emissions. In this study, we developed a method to produce a construction material using only sand as the solid raw material. By utilizing a technique to produce organic silicon material from sand, we placed sand, alcohol, and catalyst in a closed vessel and heated it to 240 °C. After 24 h, the sand particles were bonded to each other, and a hardened body was formed. A tradeoff in production conditions, such as temperature, time, and the amount of sand, was confirmed.

Development of methods and algorithms to predict the effect of mutations on protein stability, protein-protein, and protein-DNA/RNA binding is necessitated by the needs of protein engineering and for understanding the molecular mechanism of disease-causing variants. The vast majority of the leading methods are either methods with adjustable parameters or machine learning algorithms, both requiring a database of experimentally measured folding and binding free energy changes. These databases are collections of experimental data taken from scientific investigations typically aimed at probing the role of particular residue on the above-mentioned thermodynamics characteristics, i.e., the mutations are not introduced at random and do not necessarily represent mutations originating from single nucleotide variant (SNV). Thus, the reported performance of the leading algorithms assessed on these databases or other limited cases, may not be applicable for predicting the effect of SNVs seen in the human population. Indeed, we demonstrate that the SNVs and non-SNVs are not equally presented in the corresponding databases and the distribution of the free energy changes are not the same. Furthermore, the Pearson correlation coefficients (PCCs) obtained on cases involving SNVs are less impressive than for non-SNVs, indicating that caution should be used in applying them to reveal the effect of human SNVs. All methods are found to underestimate the energy changes by roughly a factor of 2.

Abstract: — management of the Continuous Stirred Tank Reactor (CSTR) operation has proven to be a difficult undertaking due to the complex and ever-changing nature of its behavior, which is both nonlinear and dynamic, which is further compounded by its instability. Attempts have been made to use Proportional-Integral-Derivative (PID) controllers for such processes, but the performance is often poor due to the inherent limitations of the controllers. In contrast, heuristic algorithms have been employed to tune the controllers, but these methods can only provide optimal performance for a restricted range of parameter variations. This paper presents a novel approach that involves using a conventional gain scheduling PID controller in combination with a fuzzy gain scheduling (FGS) controller method to calibrate set-point weighted PID controllers for the CSTR process. The paper outlines the design of the controllers and evaluates their performance by subjecting them to varying input signals within the given bandwidth.

In this study, we investigate the existence of positive solutions within a system of Riemann-Liouville fractional differential equations that incorporate the (r1,r2,r3)-Laplacian operator while being subject to three-point boundary conditions. These equations incorporate various fractional derivatives and are influenced by parameters represented as (ψ1,ψ2,ψ3). Our approach involves employing techniques such as cone expansion and compression of the functional type, in conjunction with the Leggett-Williams fixed point theorem, to establish the existence of positive solutions. To emphasize the practical significance of our findings in the realm of fractional differential equations, we provide two illustrative examples.

The continuing public health issue known as COVID-19 (the 2019 Novel Corona virus infection) has a global emphasis. Despite (or perhaps because of) the fact that there are significant gaps in our understanding of COVID-19 epidemiology, transmission dynamics, research methods, and management breakout poses a new kind of global hazard. The good news is that there is currently enough knowledge about the epidemic process to allow for the creation of mathematical forecasting models. We modify a conventional SEIR epidemic model to the unique dynamic compartments and epidemic features of COVID 19 as it spreads in a population with a diverse age structure. Although many US states and other nations around the world followed lockdown and reopening processes, we perform some analysis on using some techniques of the epidemic course. A new perspective of fractional calculus known as piecewise derivatives of fractional order is used to study the proposed model. Sufficient conditions are established to show the existence theory. In addition, a numerical scheme based on Newton’s polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Some real data results are also shown with comparison of the numerical results.

NAD⁺ is known classically as a metabolite that participates in catabolic and anabolic pathways throughout the metabolism that is taught to students in introductory biochemistry courses. However, non-classical studies starting over a decade ago found that NAD⁺ is also involved in higher order functions, in part because of its involvement in the activation of SIRTs and the support of the mitochondrial unfolded protein response. Many studies since have suggested that NAD⁺ is involved in an extensive spectrum of human pathologies, including neurodegenerative disorders, cardiomyopathy, obesity, and diabetes, Further, healthy aging and longevity appear to be closely related to NAD⁺ and its related metabolites, including NAR and NMN. Together, these studies show that this system has value as a dietary supplement to improve general health overall, as well as mitigating specific disease conditions. Accordingly, many are now recommending the consumption of materials in this system as dietary supplements. Nicotinamide riboside (NAR) appears to have special value in this regard. It appears to be better tolerated than other molecules in this system, as well as better pharmacodynamics and greater potency. Unfortunately, NAR is a reactive molecule, often unstable during its manufacturing, transport, and storage. Indeed, HPLC analyses of many commercial samples of NAR shows that they contain substantial amounts of material that are not, in fact, NAR. In some of these commercial preparations, NAR is a minority component. Therefore, more stable derivatives of NAR that are easily converted upon consumption into NAR are therefore desired. Recently work related to prebiotic chemistry provided the borate derivative of NAR. NARB is considerably more stable than NAR itself. However, immediately upon consumption, the borate dissociates from NARB, and is lost in the body through dilution and binding to other species, notably carbohydrates such as fructose and glucose. The NAR left behind is expected to behave pharmacologically in ways identical to NAR itself. This review provides a comprehensive summary (through Q1 of 2023) of literature that makes the case for the consumption of NAR as a dietary supplement. It then summarizes the challenges of delivering quality NAR to consumers using standard synthesis, manufacture, shipping, and storage approaches. It concludes by outlining the advantages of NAR-borate in these processes.

Multicore magnetic nanoparticles of manganese ferrite were prepared using carboxymethyl-dextran and melamine as agglutinating agents. The nanoparticles prepared using melamine exhibit a flower-shape structure, a saturation magnetization of 6.16 emu/g and good capabilities for magnetic hyperthermia. Magnetoliposome-like structures containing the multicore nanoparticles exhibit sizes in the range 250 – 400 nm. A new antitumor thienopyridine derivative was loaded in these nanocarriers with a high encapsulation efficiency of 98% ± 2.6%. Release profiles in absence and presence of an AMF indicate a transport by diffusion, with a maximum compound release of 31% under the AMF. A sustained and controlled drug release in anticipated from the results, pointing to suitable characteristics of the magnetoliposomes for dual cancer therapy (combined magnetic hyperthermia and chemotherapy).

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.

Relapsed leukemia following initial therapeutic response and remission is difficult to treat and causes high patient mortality. Leukemia relapse is due to residual quiescent leukemia cells that escape conventional therapies and later reemerge. Eliminating not only growing but quiescent leukemia cells is critical to effectively treating leukemia and preventing its recurrence. Such therapeutic agents, however, are lacking in the clinic. Here we report that a 4-arylmethyl derivative of the natural anticancer compound curcumin demonstrates a dual effect in eliminating both growing and quiescent leukemia cells. This curcumin derivative, C212, on the one hand, inhibits growing leukemia cells at a higher efficacy than curcumin by inducing apoptosis and cell cycle arrest; it, on the other hand, kills quiescent leukemia cells that are resistant to conventional chemotherapy drugs. Furthermore, C212 drives leukemia cells into and kills them at deep quiescence, avoiding the potential risk associated with awaking therapy-resistant subpopulation of quiescent leukemia cells. Lastly, we show that C212 induces apoptosis and drives cells into deep dormancy at least partially by binding to and inhibiting Hsp90, leading to client protein degradation and protein aggregation. Further elucidating the molecular mechanisms underlying the dual function of C212 in eliminating both growing and quiescent leukemia cells will aid the development of novel therapies against leukemia relapse.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

The search for graphene or few layer graphene production methods that are simple, allow mass production and yield good quality material continues to provoke intense investigation. The present work contributes through the study of the aqueous exfoliation of four types of graphene sources, namely graphite and graphite nanoflakes with different morphologies and geographical origin. The exfoliation was achieved in an aqueous solution of a soluble pyrene derivative that was synthesized to achieve maximum interaction with the graphene surface at low concentration (5 x 10-5 M). The yield of bilayer and few layer graphene obtained was quantified by Raman spectroscopic analysis and the adsorption of the pyrene derivative on the graphene surface was studied by thermogravimetric analysis and X-ray diffraction. The whole procedure was rationalized with the help of molecular modeling.

TTF1-NP(5,2′,4′-trihydroxy-6,7,5′-trimethoxyflavone nanoparticles), derived from the traditional Changbai Mountain medicinal plant Sorbaria sorbifolia (SS), has been showedits anti-cancer effect in various liver cancer cell types and tissues. The present study was designed to evaluate the antitumor mechanism of the TTF1-NP against HepG2 hepatoma cells and HepG2 cells-induced hepatocarcinoma (HCC) in nude mouse model. Here we demonstrated that TTF1-NP inhibits tube formation of HUVECs and HepG2 cell migration and invasion, and inhibits tumor growth in nude mice implanted with HepG2 cells through the downregulation of STAT3 protein and activation, along with VEGF, KDR, bFGF, MMP2 and MMP9 levels. We further revealed that TTF1-NP decreased the DNA-binding capacity of STAT3. Together our results provide a mechanism by which TTF1-NP suppresses cancer cell migration, invasion and angiogenesis through the action of STAT3 and suggests TTF1-NP as a potential therapy for hepatocellular cancer treatment.

Facebook (FB) is the most popular online networking platform. There are several FB pages dedicated to spreading awareness about the Celiac disease (CD). To get the latest information, a huge number of CD patients follow Celiac disease Facebook (CD-FB) pages. Such pages frequently post beneficial information. However, very less is known if they provide appropriate information to CD patients. We conducted this study to know if CD-FB pages spread misleading information to CD patients. CD-FB pages from three celiac-influenced countries were explored using the FB platform and Google search engine. From October 2021 to April 2022, a total of 147 CD-FB, Italy (n=63), the USA (n=46), and India (n=38), were found eligible. Of them, 13% of pages (followers Mean±SD; Italy 2478±2011; USA 12635±12486; India 667±313) shared misleading information, particularly about gluten-free ingredients, and treatment of CD. In total,16% of CD-FB pages discussed alternative treatments option. Surprisingly, 7% of pages (followers Mean±SD; USA 23800±10465; India 628±333) supported alternative treatments for CD. CD-FB pages are useful for disseminating celiac-related information. While most of such pages provide useful information, a few pages sometimes contain misleading information. CD patients must consult their treating unit before following any uncertain information posted on CD-FB pages.

The antioxidant activity of molecules constitutes an important factor for the regulation of redox homeostasis and reduction of oxidative stress. Cells affected by oxidative stress can undergo genetic alteration, causing structural changes and promoting the onset of chronic diseases, such as cancer. The in silico study performed here was developed to evaluate the antioxidant potential of two molecules, ZINC08706191 (Z91) and ZINC08992920 (Z20), with recognized epithelial anticancer potential. Molecular docking, chemical-quantum calculations and Pearson's correlation were performed. The Z91 and Z20 molecules showed lower binding free energy (ΔG) values for the receptor-ligand interaction than the reference molecules (caffeine – CAF and ascorbic acid – AA), and better results for values of molecular descriptors correlated with ΔG, resulting in a decrease of ΔG. Strong correlations were observed between ΔG values for the five receptors evaluated and ΔG values of the potential epithelial anticancer activity available in literature. These results attest to the significant antioxidant potential of the Z91 and Z20 molecules and their strong relation with the potential epithelial anticancer activity and may be indicated for further analysis in relation to the control of oxidative stress and epithelial anticancer activity.

Lead halide perovskite has become a promising candidate for high-performance photodetector (PD) applications due to its attractive optical and electrical properties such as high optical absorption coefficient, high carrier mobility, and long carrier diffusion length. However, the presence of highly toxic lead in these devices has limited their practical applications and even hindered their progress toward commercialization. Therefore, the scientific community has been committed to searching for low-toxic and stable perovskite-type alternative materials. Lead-free double perovskite materials, which are still in the preliminary stage of exploration, have achieved inspiring results in recent years. In this review, we mainly focused on two types of lead-free double perovskite based on different Pb substitution strategies, including A2M(I)M(Ⅲ)X6 and A2M(IV)X6. We reviewed the research progress and prospects of lead-free double perovskite photodetectors in the past three years. And more importantly, from the perspective of optimizing inherent defects in materials and improving device performance, we proposed some feasible pathways and made an encouraging perspective for the future development of lead-free double perovskite photodetectors.

In cancer, the lymphatic system is hijacked by tumor cells to escape from primary tumor and to metastasize to the sentinel lymph nodes. Tumor lymphangiogenesis is stimulated by the vascular endothelial growth factors-C (VEGFC) after binding to its receptor VEGFR-3. However, how VEGFC cooperates with other molecules to promote lymphatic neovessels growth is not fully determined. Here, we found that tumor lymphangiogenesis developed in tumoral lesions and in their surrounding adipose tissue (AT). Interestingly, lymphatic vessel density correlated with an increase of circulating free fatty acids (FFA) in the lymph from tumor-bearing mice. We found that adipocyte-released FFA are uploaded by lymphatic endothelial cells (LEC) to stimulate their sprouting. Lipidomic analysis identified the monounsaturated oleic acid (OA) as the major circulating FFA in the lymph in tumoral context. OA transporters FATP-3, -6 and CD36 were only upregulated on LEC in the presence of VEGFC showing a collaborative effect of these molecules. OA released from adipocytes is taken up by LECs to stimulate the fatty acid β-oxidation, leading to increase adipose tissue lymphangiogenesis. Our results provide new insights on the dialogue between tumors and adipocytes via the lymphatic system and identify a key role for adipocyte-derived FFA in the promotion of lymphangiogenesis, revealing novel therapeutic opportunities for inhibitors of lymphangiogenesis in cancer.

It has been recognized for some time that even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel-Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features.

The resonance spectrum of surface resistance derivative in quasi-two dimensional layered organic conductors has been calculated numerically for the out-of-plane and in-plane magnetic field. Not all but some of the resonances in a given series of transitions are present in the spectra. They are observed at the positions corresponding to the maxima in the surface resistance derivative curve and are in a good agreement with previously calculated magnetic field resonance positions. For tilted magnetic fields, there are more resonances present in the spectrum than in the case of a non-tilted field. Apart from the resonances corresponding to the transitions between the adjacent surface states there also appear resonances involving the transitions between the more distant surface states. This is correlated with the specific topology of Fermi surface of the organic conductors. The presented calculations will allow correct interpretation of the experimental curves for the resonance spectrum, and also to obtain information on the surface properties of these materials for their possible implementation in fabrication of devices based on organic molecular conductors.

As an option to deal with the insulin-dependent disease, a recent commuted PD control strategy is designed and carefully analyzed for different clinic diabetic patients. This controller approach is mainly conceived to stabilize the glucose blood concentration in a diabetic patient around its basal value, hence avoiding extreme situations such as hypoglycemia and hyperglycemia. This control strategy receives two inputs carefully tuned to actuate when the measured variable is out of a prescribed healthy zone. Therefore, one of these variables is invoked to decrease the glucose concentration to insulin injection, and the other is employed to increase the glucose absorption, both by using a proper PD controller. According to our numerical experiments, our controller approach performs well, even when there is an external disturbance in the controlled system.

Epilepsy is a neurological disorder that affects approximately 1% of the world's population. To diagnose and estimate the occurrence of epilepsy, the analysis of recorded brain activity is performed by a neurologist, which is not only time-consuming and tedious but also occasionally accompanied by human error. Therefore, in recent decades, researchers have aimed to unravel an approach for designing and building an automated method for diagnosing and estimating the occurrence of epilepsy. Accordingly, the present study proposed two new-fangled ways based on brain signals and a convolutional neural network (CNN). Moreover, this research implements a CNN with a sequential three-layer structure. Numerous experiments were performed, and the accuracy of estimating epilepsy using the developed methods was achieved at 95% without feedback and 97% with feedback. The proposed methods were proven to be more accurate than the previous techniques and can be employed as a physician's assistant once entering the field of operation.

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 &amp; 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 main objective of this present paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. Also, we give some results related to the newly defined fractional operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

In Philadelphia chromosome positive B-cell (Ph+) acute lymphoblastic leukemia (LLA), growing evidence has ac-cumulated about the efficacy of low-intensity and chemo-free regimens. Our objective was to analyze all recent trials evaluating these treatments and to compare them in terms of efficacy. We applied the Shiny method, an artificial intelligence technique, to analyze Kaplan-Meier curves and reconstruct patient-level data. Reconstructed patient data were then evaluated through standard survival statistics and subjected to indirect head-to-head treatment comparisons. The endpoint was progression-free survival (PFS). Based on 848 reconstructed patients, 9 trials were analyzed. The survival data from these trials were pooled into three types of treatments: i) treatments based on ty-rosine kinase inhibitors (TKIs) combined with reduced-intensity chemotherapy (denoted as TKICHE); ii) TKIs as-sociated to steroids with no chemotherapy (TKISTE); iii) chemotherapy-free combinations of blinatumomab plus TKIs (TKIBLI). According to the Shiny method, the three PFS curves were reported in a single Kaplan-Meier graph and subjected to survival statistics. In terms of PFS, TKIBLI ranked first, TKICHE second, and TKISTE third; the differences between these three regimens were statistically significant. This multi-treatment Kaplan-Meier graph, generated through the Shiny method, summarized the current evidence on these treatments in both qualitative and quantitative terms.

: In Philadelphia chromosome positive B-cell (Ph+) acute lymphoblastic leukemia (LLA), growing evidence has accumulated about the efficacy of low-intensity and chemo-free regimens. Our objective was to analyse all recent trials evaluating these treatments and to compare them in terms of efficacy. We applied the Shiny method, an artificial intelligence technique, to analyse Kaplan-Meier curves and reconstruct patient-level data. Reconstructed patient data were then evaluated through standard survival statistics and subjected to indirect head-to-head treatment comparisons. The endpoint was progression-free survival (PFS). Based on 562 reconstructed patients, 8 trials were analyzed. The survival data from these trials were pooled into three types of treatment: i) treatments based on tyrosine kinase inhibitors (TKIs) combined with reduced-intensity chemotherapy (denoted as TKICHE); ii) TKIs associated to steroids with no chemotherapy (TKISTE); iii) chemotherapy-free combinations of blinatumomab plus TKIs (TKIBLI). According to the Shiny method, the three PFS curves were reported in a single Kaplan-Meier graph and subjected to survival statistics. In terms of PFS, TKIBLI ranked first, TKICHE second, and TKISTE third; the differences between these three regimens were statistically significant. In conclusion, the multi-treatment Kaplan-Meier graph generated in this study has effectively summarized the current evidence on these treatments in comparative terms.

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially we develop a binary data matrix to record variables' values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle oriented coordinate and generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar field in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of cumulative probability function defined on Riemannian manifold also gives the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and gives the formal definition of joint probabilities by partial derivatives of cumulative distribution function. The equivalence between symmetrized covariant derivative and generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated. Usually, such two-component integrable nonlinear evolutionary equations are considered, the form of which does not depend on the replacement of one component with another. In this paper, we propose for consideration and usage a new hierarchy of two-component integrable nonlinear equations, which have an important difference from the already known equations. Among the hierarchy equations there are analogues of the two-component nonlinear Schrödinger equation (second equation from hierarchy) and the two-component modified Korteweg-de Vries equation (fourth equation from hierarchy). The third equation of the hierarchy is a combination of the nonlinear Schrödinger equation for one component and the modified Korteweg-de Vries equation for the second component. The equations for the individual components are very different from each other, even if they have the same order. Let us note that even hierarchy equations can be reduced to well-known variants of the scalar derivative nonlinear Schrödinger equations, and odd equations can’t be reduced. To construct the hierarchy equations, we use the monodromy matrix method, first proposed by B.A. Dubrovin. Knowledge of the monodromy matrix makes it possible to construct spectral curves of multiphase solutions, as well as to find stationary equations that these solutions satisfy. The last section presents the simplest solutions in the form of solitons and periodic one-phase waves, as well as spectral curves corresponding to these solutions.

We investigate the behavior of the partial derivative approach to the change of scale formula and prove relationships among the analytic Wiener integral and the analytic Feynman integral of the partial derivative for the function space integral.

In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?

Wastewater contaminated with antibiotics is a major environmental challenge. We developed here the green synthesis of bio-graphenes by using natural precursors (Xanthan, Chitosan, Boswellia, Tragacanth). The use of these precursors can act as templates to create 3D doped graphene structures with special morphology. Also, this method is a simple method for in-situ synthesis of doped graphenes. The elements present in the natural polymers (N) and other elements in the natural composition (P, S) are easily placed in the graphene structure and improve the catalytic activity due to the structural defects, surface charges, increased electron transfers, and the high absorption. In this mechanism, O2 dissolved in water absorbs onto the positive charged C in doped graphenes to create oxygenated radicals, which enables the degradation of antibiotic molecules. Light irradiation increases the amounts of radicals and rate of antibiotic removal. The results have shown that the hollow cubic Chitosan-derived graphene has shown the best performance due to the doping of N, S, and P. The Boswellia-derived grapheme shows the highest surface area, but lower catalytic performance, which indicates the more effective role of doping in the catalytic activity. The effect of oxygen and light were also studied to accelerate the degradation process.

An imbalance in any metabolic system can be traced to its homeostasis. When homeostatic environment is not attainable then there will be a response from the body. A new shift has emerged, “the negative feedback effect of high fructose consumption;” more pain than gain. The human metabolic system daily combat fructose sugar metabolism which emanates from high consumption. This inadvently lead to a chronological series of complications arising from the feedback. These feedbacks play pivotal roles in skeletal muscle damage and other body frameworks, it also fosters toxic advanced glycation end products (AGEs), factors that impose and inflict damaging effects to the body`s energy currency and serious threat to health. These damages are missed or overlooked because of early nonspecific physiological symptoms. High level of fructose has both long- and short-term effects on human metabolic processes. These effects which are majorly through the production of reactive oxygen species (ROS) and other free radicals, are felt in the disruption of biomolecules such as causing DNA mutation, lipid peroxidation etc. these effects in turn lead to various diseases such as cancer, diabetes, atherosclerosis, and other health issues. In this review, we will focus on the damaging effects this sugar has on human health and the present solutions being applied. We will also look at the next step in combatting and controlling these negative feedbacks.

Background: Traditional omic analysis relies on p-value and fold change as selection criteria. There is an ongoing debate on their effectiveness in delivering systemic and robust interpretation, due to their dependence on assumptions of conformity with various parametric distributions.Here, we propose a threshold-free selection method based on robust, non-parametric statistics, ensuring independence from the statistical distribution properties and broad applicability. Such methods could adapt to different initial data distributions, contrary to statistical techniques based on fixed thresholds. Methods: Our work extends the Rank Products methodology with a neutral selection method of high information-extraction capacity. We introduce the calculation of the RP distribution’s entropy to isolate the features of interest by their contribution to the distribution’s information content. The aim is a methodology performing threshold-free identification of the differentially expressed features, which are highly informative about the phenomenon under scrutiny. Conclusions: Applying the proposed method on microarray (transcriptomic and DNA methylation) and RNAseq count data of varying sizes and noise presence, we observe robust convergence for the different parameterisations to stable cutoff points. Functional analysis through BioInfoMiner and EnrichR was used to evaluate the information potency of the resulting feature lists. Overall, the derived functional terms provide a systemic description highly compatible with the results of traditional statistical hypothesis testing techniques. The methodology behaves consistently across different data types. The feature lists are compact and information-rich, indicating phenotypic aspects specific to the tissue and biological phenomenon i nvestigated. Selection by information content measures efficiently addresses problems, emerging from arbitrary thresholding, thus facilitating the full automation of the analysis.

Considering Games with the broad definition proposed by Juul (Juul, 2010), consequences outside of the magic circle can be negotiated. This definition opens up the possibility to define serious games, games developed with an utilitarian goal in mind, in addition to fun. The entertaining and utilitarian objectives may however be contradictory, leading serious games to be, more often than not, less than optimal in at least one of the two dimensions. Another way to play with the boundaries of games is to consider pervasive games, which include alternate reality games, and crossmedia games (Montola, 2005). We question here the limit between game, play and toy in the context of a mixed reality serious game. ‘Pangu’ is a game designed for bachelor students, with biochemistry as the utilitarian objective, and the origin of life as a game theme. The students are asked to play the game on their smartphone, which in turn ask them to build molecules with a tangible balls-and-sticks model typically used in chemistry classes. Pictures taken from the models allow users to ‘scan’ these models and progress in the game. The use of the game was observed in four opportunities. An unanticipated observation is that, in addition to expected behaviors, some students used briefly the models like a toy rather than in the context of the game. It is therefore tempting to speculate that the pervasive nature of the game is blurring the game/non game boundary and, in the context of this serious game, opens a door for fun.

Despite the uptake of tobacco smoking declining in the UK, smoking is still the leading cause of preventable poor health and premature death. While improved approaches to smoking cessation are necessary, encouraging and assisting smokers to switch by using substantially less toxic non-tobacco nicotine products may be a possible option. To date few studies have investigated the rates of smoking cessation and smoking reduction associated with the free provision of electronic-cigarettes (e-cigarette) to smokers. In this study the Blu Pro e-cigarette was given to smokers for use in place of tobacco for 90 days. The rates of smoking abstinence and daily smoking patterns were assessed at baseline 30 days, 60 days and 90 days. The response rate was 87%. After 90 days, the complete abstinence rate was 36.5% from 0% at baseline. Frequency of daily smoking reduced from 88.7% to 17.5% (P<0.001) and median consumption of cigarettes/day from 15 to 5 (P<0.001). Median days per month participants smoked also dropped from 30 to 13 after 90-days (P<0.001). On the basis of these results there may be value in smoking cessation services and other services ensuring that smokers are provided with e-cigarettes at zero or minimal costs for at least a short period of time.

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.

The time interval set approach depends on results for radiation propagation from star sources, ie spherically symmetric, where properties relate to propagation sphere surfaces, finite for any realistic event and measurement. In contrast the usual vector and one moment time set approach from Newton’s laws, applies to stationary parallel radiation. A time interval only description necessarily has to start from it's own definitions, and properties for time intervals have to be defined with time intervals. This paper is devoted to deriving time interval only set properties commutation, addition and multiplication and derivative, and to define how these can correspond consistently to one moment time set properties. Time development within the time interval description equilibrium depends on the well-known ‘mean velocity theorem’ (MVT) and the time interval version of the Legendre transform, defined in earlier papers. Radiation propagation ‘away from’ and gravitation ‘towards’ the star source can be part of the description. In the discussion parts these properties are applied within astrophysics. Included is a integral derivation of star source radiation energy for both zero and non zero wave particle mass. The time interval set is not one of the usual sets encountered. However it’s non-linearity or non-commutativity property can be related to Noether charges and structure constants, that equal the radiation wave group-velocity, for photons the light velocity c, and, different from the usual derivative to one moment time, to specifics of the time interval only set derivative to time intervals.

Enterococcus faecalis is a bacterium that can develop a multidrug resistance profile associated with the community as well as nosocomial-acquired infections. Among the treatment options for these infections are aminoglycosides combined with bacterial cell wall inhibitors such as beta-lactams, since E. faecalis is intrinsically resistant to aminoglycosides. One of its most representative resistance mechanisms is the expression of aminoglycoside-modifying enzymes, such as the aminoglycoside phosphotransferase type IIIa of E. faecalis (EfAPH(3')-IIIa). This enzyme acts by phosphorylating aminoglycosides in an ATP-dependent reaction, modifying the 3' position of hydroxyl groups of these antibiotics. Considering this scenario, 3,092 natural products obtained from the ZINC22 database were analyzed to select molecules with the highest affinity for the nucleotide-binding pocket of EfAPH(3')-IIIa, which could be potential aminoglycoside adjuvants. The molecules that showed the best-score results obtained from ensemble docking-based virtual screening were ZINC000000952700 (BS-1), ZINC000014793040 (BS-2) and ZINC000015498603 (BS-3). The most promising results were for BS-2, a flavone derivative, due to its improved stability profile in molecular dynamics simulation (average values of RMSD of 0.23 nm, and Rg of 1.94 nm), binding free energy calculations (average ΔG total of -35.3 nm), as well as better toxicological profile (lower probability of hepatotoxicity, carcinogenic, immunotoxicity, mutagenicity, and cytotoxicity effects), compared to BS-1 and BS-3. These results allow us to propose that a flavone derivative may act as an adjuvant to aminoglycosides in the treatment of E. faecalis infections, acting as an inhibitor in the nucleotide-binding pocket of EfAPH(3')-IIIa.

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.

In this paper, the design of a low cost portable ventilator with performance analysis have been done to solve the scarcity of respiratory ventilators for COVID-19 patients. The materials used to build the system are: DC motor, rotating disc and pneumatic piston. The system input is the patient heart beat and the output is volume of air to the patient lung with adjusted breathing rate. This ventilator adjusts the breathing rate to the patient depending on his heart beat rate. The performance analysis of this system have been done using Proportional Integral Derivative (PID) and Full State Feedback H2 controllers. Comparison of the system with the proposed controllers have been done using a step change and a random change of the patient heart beat and a promising result have been analyzed successfully.

The article is devoted to infinitesimal transformations. We have obtained that LCK-manifolds do not admit nontrivial infinitesimal projective transformations. Then we study infinitesimal conformal transformations of LCK-manifolds. We have found the expression for the Lie derivative of a Lee form. Also we have obtained the system of partial differential equations for the transformations, and explored its integrability conditions. Hence we have got the necessary and sufficient conditions in order that the an LCK-manifold admits a group of conformal motions. Also we have calculated the number of parameters which the group depends on. We have proved that a group of conformal motions admitted by an LCK-manifold is isomorphic to a homothetic group admitted by corresponding K\"{a}hlerian metric. We also established that an isometric group of an LCK-manifold is isomorphic to a some subgroup of homothetic group of the coresponding local K\"{a}hlerian metric.

In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.

Quercetin is a flavonoid with a low molecular weight that belongs to the human diet's phenolic phytochemicals and non-energy constituents. Quercetin has a potent antioxidant capacity, being able to capture Reactive Oxygen Species (ROS), reactive nitro-gen species (RNS), and Reactive Chlorine Species (ROC), which act as reducing agents by chelating transition metal ions. Its structure has five functional hydroxyl groups, which work as electron donors and are responsible for capturing free radicals. In addition to its antioxidant capacity, it was described different pharmacological properties of Quercetin, such as carcinostatic properties, antiviral, antihypertensive, anti-inflammatory, protection of Low-Density Lipoprotein (LDL) oxidation, and inhibi-tion of angiogenesis are developed in this review.

Pancakes are fast food snacks that are generally made with the basic ingredients of wheat flour, which is an imported commodity and detrimental for people who are allergic to gluten. To reduce the use of wheat, alternative raw materials derived from local commodities are used, such as modified cassava flour (mocaf), arrowroot flour, and suweg flour. The experiment was carried out by mixing mocaf flour, arrowroot flour, and suweg flour to produce composite flour with a ratio of 70:15:15 (CF1), 70:20:10 (CF2), and 70:20:5 (CF3). The result showed that the ratio of mocaf flour, arrowroot flour, and suweg flour had a significant effect on pasting temperature, peak viscosity, hold viscosity, breakdown viscosity, setback, L*, a*, hue, whiteness, ∆E, as well as swelling volume and solubility on the characteristics of the composite flour It also had a significant effect on the texture characteristics of hardness, adhesiveness, chewiness, color characteristics L*, a*, whiteness, ∆E, and preference for the flavor of gluten-free pancake products. It is known that the best formulation for the resulting pancake product is P1, with the addition of a 70% ratio of mocaf flour, 15% ratio of arrowroot tuber flour, and 15% ratio of suweg flour.

Background: Free-living amoebas (FLA), also amebas, are eukaryotic and mitochondrial microorganisms that are capable of growing in any environment, aquatic or terrestrial. These free-living amoebas are mostly non-pathogenic to humans. However, there exist some highly pathogenic species, such as Acanthamoeba — mainly T-4 genotype —, Naegleria fowleri (known as brain-eating amoeba), and Balamuthia mandrillaris. They can be called "brain-eating amoebas” because of their ability to cause substantial destruction of brain tissue. There is no standard treatment; immunological processes which predispose humans to acquire and infection and, then, a disease are unknown. In addition, there are other species of free-living amoebas such as, Sappinea pedata, Vermamoeba vermiformes, Vanellas sp,Vahlkampfia sp., and, more recently, Paravahlkampfia francinae, which is less virulent and aggressive than the first three mentioned above. Methods: All CSF samples were evaluated in our laboratory under the microscope. Monoxenic and axenic cultures were negative as well as the presence of cysts or exponential growth. PCR was negative using the FLA primers. Results: Under close observation of sterile CSF, we can see mobile forms of non-human cells. None of the observed forms has the morphotype of Acanthamoeba, Naegleria sp. or Balamuthia mandrillaris. Conclusions: Due to these findings, we know these structures can be observed in the CSF and many of them do not form cysts as others do. In addition, these microorganisms are uncultivable in conventional medium culture to FLA and impossible to detect even when using molecular tools such as PCR, using the primers for EUK A/B or 18s RNAr gene as a target.

Consciousness is usually perceived as a state of being aware of one’s environment as well as self. Despite its omnipresence in our life, understanding this concept is challenging. This has given rise to several theories attempting to explain the nature of consciousness, as well as hard and soft problems of consciousness. In fact, the boundaries of consciousness defined by these theories are a topic of continued discussion, particularly in light of the recent advances in artificial intelligence (AI). Some of these theories consider consciousness as a simple integration of information while others purport the need for an agency in the process of integration for an entity to be considered conscious. Some theories consider consciousness as a graded entity and some equate consciousness with content of awareness. In this work, major theories of consciousness are reviewed and compared, focusing on awareness, attention, and sense of self. These findings are interpreted in relation to AI in order to ascertain what makes AI distinct from natural intelligence.

Consciousness is usually interpreted as a state of being aware of one’s environment as well as self, while awareness is understood as knowledge of something. Despite their semantic differences, in philosophy, these terms are often used interchangeably, as is the case of the hard problem of consciousness proposed by Chalmers, which in fact is the hard problem of awareness. Trilogy paradigm of consciousness (or simply “trilogy”) offers a new paradigm where consciousness is the result of a unique interaction between awareness and the decision-making process. By conferring the input of awareness to the decision-making process, a new mental function of awareness-based choice selection (ABCS) or true free will emerges. Likewise, application of the power of decision-making to the process of awareness gives rise to discretionary selection of information for awareness (DSIA) or intentional attention. The intertwined actions of ABCS and DSIA comprise “I” which is the faculty of our consciousness and is what sets natural intelligence (NI) apart from artificial intelligence (AI). Based on trilogy, mind is an unconscious compilation of all mental function excluding ABCS and DSIA that are the essence of consciousness. As humans, we are a union of “I,” our minds, and our bodies.

Endometriosis occurs when endometrial-like tissue grows outside the uterine cavity, leading to pelvic pain, infertility, and increased risk of ovarian cancer. The present study describes the optimization and characterization of cellular spheroids as building blocks for Kenzan scaffold-free method biofabrication and proof-of-concept models of endometriosis and the endometriotic microenvironment. The spheroid building blocks must be a specific diameter (~500 m), compact, round, and smooth to withstand Kenzan biofabrication. Under optimized spheroid conditions for biofabrication, the endometriotic epithelial-like cell line, 12Z, expressed high levels of estrogen-related genes and secreted high amounts of endometriotic inflammatory factors that were independent of TNF stimulation. Heterotypic spheroids, composed of 12Z and T-HESC, an immortalized endometrial stromal cell line, self-assembled into a biologically relevant pattern, consisting of epithelial cells on the outside of the spheroids and stromal cells in the core. 12Z spheroids were biofabricated into large three-dimensional constructs alone, with HEYA8 spheroids, or as heterotypic spheroids with T-HESC. These three-dimensional biofabricated constructs containing multiple monotypic or heterotypic spheroids represent the first scaffold-free biofabricated in vitro models of endometriosis and the endometriotic microenvironment. These efficient and innovative models will allow us to study the complex interactions of multiple cell types within a biologically relevant microenvironment.

Transition-metal-free synthesis of 4-pyrones via TfOH-promoted nucleophilic addition/cyclization of diynones and water has been developed. This transformation is simple, atom economical and environmentally benign, providing rapid and efficient access to substituted 4-pyrones.

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