This paper aims to demonstrate that, beyond the small world of Riemann-Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, corresponding to the different paths taken. Notions of time and scale sequences are introduced and general associated basic derivatives, namely right/stretching and left/shrinking, are defined. A general framework for fractional derivative definitions is reviewed and applied to get both known and new fractional order derivatives. Several fractional derivatives are considered, mainly: Liouville, Hadamard, Euler, bilinear, tempered, q-derivative, and Hahn.

The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

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

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η- convex function. Moreover, our results include several new and known results as special cases.

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

The 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.

This paper focuses on studying the mapping properties of singular integral operators on product spaces. The boundedness of such operators is established on Triebel-Lizorkin spaces whenever their kernel functions belong to Grafakos and Stefanov class. Our results generalize and improve some previously known results.

In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann-Liouville fractional integral. Then the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied for derivation of its properties. In particular, we characterize its domain, null-space, and projector operator, establish the interrelations between its different realisations, and present a generalized fractional Taylor formula involving the generic fractional derivative. Then we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed form formula for its unique solution, and study its complete monotonicity.

In the article, by applied the concept of strongly convex function and one known identity, we establish several Ostrowski type inequalities involving conformable fractional integrals. As applications, some new error estimations for the midpoint formula are provided as well.

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.

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

This article aims to explore the existence and stability of solutions to differential equations involving a regularized ψ−Hilfer fractional derivative, which, compared to standard ψ−Hilfer fractional derivatives, provide a clear physical interpretation when dealing with initial conditions. We discovered that the regularized ψ−Hilfer fractional derivative can be represented as the inverse operation of the ψ−Riemann–Liouville fractional integral, and used this property to prove the existence of solutions for linear differential equations with a regularized ψ−Hilfer fractional derivative. Additionally, we applied the Mönch’s fixed-point theorem and knowledge of non-compactness measures to demonstrate the existence of solutions for nonlinear differential equations with a regularized ψ−Hilfer fractional derivative, and further discussed Ulam-Hyers-Rassias stability and semi-Ulam-Hyers-Rassias stability of these solutions. Finally, we illustrated our results through case studies.

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

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

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

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

In this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.

In this paper, we extend the KdVSKR equations in (1+1)-dimension and (2+1)-dimension to fractional KdVSKR equations with modified Riemann-Liouville derivative. The (2+1)-dimensional KdVSKR equation, which is a recent extension of (1+1)-dimensional KdVSKR equation, can model the resonances of solitons in shallow water. By means of the Hirota bilinear method, finite symmetry group method and consistent Riccati expansion method, many new interaction solutions have been derived. Soliton-cnoidal interaction solution of the (1+1)-dimensional fractional KdVSKR equation has been derived for the first time. For the (2+1)-dimensional frac-tional KdVSKR equation, two-wave interaction solutions and three-wave interaction solutions, including dark-soliton-sine interaction solution, bright-soliton-elliptic interaction solution, and lump-hyperbolic-sine interaction solution, have been derived. Impact of the fractional order on the shapes of these solutions has been illustrated by figures. Three-wave interaction solutions of fractional systems have not been reported in the existing references. The research idea in this paper can be applied to other fractional differential equations.

In this paper, we consider the Cauchy problem of a time fractional nonlinear diffusion equation. According to the Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time for some sufficient conditions. We next give sufficient conditions for the existence of global solutions by using the result of Zhang and Sun. In conclusions, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.

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

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.

The general synthesis of boron-containing cyclic compounds (boracycles) necessitates toxic organotin precursors or highly reactive boron halides. Here we report the synthesis of seven- and five-membered boracycles utilizing arylboronic acid pinacol esters (ArBpins) as stable boron sources. Grignard reagents generated from 2,2′-dibromodibenzyl or 2,2′-dibromobiphenyl reacted with ArBpins, where Ar = 9-anthryl (Anth), 2,4,6-trimethylphenyl (Mes), 2,4,6-triisopropylphenyl (Tip), to give 10,11-dihydro-5H-dibenzo[b,f]borepins or dibenzoborole derivatives. This Bpin-based method was successfully applied to a one-shot double boracycle formation, providing a dihydrodibenzoborepin–anthracene–dihydrodibenzoborepin triad molecule in a good yield. The dihydrodibenzoborepin bearing the Anth group was directly converted to the unsaturated borepin by NBS/AIBN. All products were characterized by NMR, HRMS, and in some cases, single-crystal X-ray diffraction analysis. Additionally, the photophysical properties of the products are also reported.

The aim of this work is research dedicated to the search for new bactericidal systems for use in cosmetic formulations, dermocosmetics, or the production of wound dressings. Over the last two decades chitosan due to its special biological activity, has become a highly indispensable biopolymer with very wide application possibilities. Literature reports on the antibacterial effects of chitosan are very diverse, but our research has shown that they can be successfully improved through chemical modification. Therefore, in this study, results on the synthesis of new Schiff bases chitosan – dCsSB-SFD and dCsSB-PCA obtained using two aldehydes: sodium 4-formylbenzene-1,3-disulfonate (SFD) and 2-pyridine carboxaldehyde (PCA) respectively. Chitosan derivatives synthesized in this way demonstrate stronger antimicrobial activity. Carrying out the procedure of grafting chitosan with a caproyl chain allowed obtaining compatible blends of chitosan derivatives with κ-carrageenan, which are stable hydrogels with a high swelling coefficient. Furthermore, covalently bounded PCL improved the solubility of obtained polymers in organic solvents. With this respect, the Schiff base-containing polymers obtained in this study, with special hydrogel and antimicrobial properties are very promising materials for the potential use as a controlled-release formulation of both, hydrophilic and hydrophobic drugs in cosmetic products for skin health.

Continuing the investigation already started (See Farcaş, A.-A.; Bende, A. PCCP 2024, 26, 14937), the light absorption and charge-transfer properties of the dopamine (DA), dopamine zwitterion (called as dopamine-semi-quinone or DsQ) and dopamine-o-quinone (DoQ) adsorbed on the graphene nanoparticle surface have been investigated using the ground state and linear-response time-dependent density functional theories, considering the B97X-D3BJ/def2-TZVPP level of theory. In terms of the strength of molecular adsorption on the surface, the DsQ form has 50 % higher binding energy than that for the DA or DoQ cases (-20.24 kcal/mol vs. -30.41 kcal/mol). The results obtained for electronically excited states and UV-Vis absorption spectra show that the photochemical behavior of DsQ is more similar to DA than that observed for DoQ. Of the three systems analyzed, the DsQ-based complex showed the most active CT phenomenon, both in terms of the number of CT-like states and the amount of charge transferred. Of the first thirty electronically excited states computed for the DsQ case, eleven are purely CT-type and nine are mixed CT and localized (or Frenkel) excitations. By varying the adsorption distance between the molecule and the surface vertically, the amount of charge transfer obtained for DA decreases significantly as the distance increases, for DoQ it remains stable, while for DsQ there are states for which little change is observed, while for others there is a significant change. Furthermore, the mechanistic compilation of the electron orbital diagrams of the individual components cannot describe in detail the nature of the excitations inside the complex.

Artificial neural networks are highly efficient tools for numerous kinds of tasks, which include forecasting, regression, and recognizing patterns in classification and pattern recognition. An artificial neural network is a model for processing information using essential components called artificial neurons that are inspired by the human brain. Two significant aspects of delayed neural networks dynamic activity are their stability and the synchronization phenomenon. This work presents a bidirectional associative memory (BAM) incommensurate fractional-order delay neural network model. The incommensurate fractional orders are calculated within the stability region through the corresponding eigenvalues and their points of equilibrium. The involved neuron states are synchronized with each other for the calculated incommensurate stable fractional orders. The reduction of the time delay will give more relaxation time for the state variable $w_4(t)$ to be stable as compared to the state variable $w_3(t)$ due to the induction of extra activation functions. The theoretical findings of this research have significance for providing guidance and controlling the dynamic behavior of artificial neural networks.

Reactions of quinones with compounds containing an amino group can produce a wide variety of addition or substitution products that depend on reactivity of both quinone and amino derivative. 6,7-Dichloropyrido[1,2-a]benzimidazole-8,9-diones undergo selective nucleophilic substitution reaction with different benzohydrazides and α-hydroxy-p-quinone imine derivatives stabilized by strong intramolecular hydrogen bond were isolated. Synthesized compounds represent a combination of several structural motifs: benzimidazole core fused with α-hydroxy-p-quinone imine which contains a benzamido fragment. The protonation/deprotonation processes were investigated in a solution using UV-Vis spectroscopy and 1H NMR titration experiment. X-ray crystallography analysis revealed a set of weak non-covalent interactions such as intra- and intermolecular hydrogen bonds and π-π stacking. Additionally, the redox behavior of 6,7-dichloropyrido[1,2-a]benzimidazole-8,9-dione and its p-imino derivative was investigated in acidic and neutral environment using cyclic voltammetry measurements. Cathode material based on 6,7-dichloropyrido[1,2-a]benzimidazole-8,9-dione could act as potential effective active electrode in aqueous electrolyte batteries, however further optimization is required.

We present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens’ theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the curve. For simplicity, we refer to the developed method as PhaSpaSto-interpolation, which is an abbreviation for phase-space-trajectory-smoothing stochastic interpolation. The proposed approach is tested and validated with a univariate time series of the Lorenz system, five non-model data sets and tested against a cubic spline interpolation and a linear linear interpolation. We find that the criterion for smoothness guarantees low errors on known model and non-model data. Finally, we interpolate the discussed non-model data sets, and show the corresponding improved phase space portraits. The proposed method is useful for interpolating low-sampled time series data sets for, e.g., machine learning, regression analysis, or time series prediction approaches.

Fractional flow reserve (FFR) is regarded as the gold standard for assessing the functional significance of coronary artery lesions, yet it remains underutilized in clinical practice. Our objective was to investigate whether FFR results have the potential to alter treatment decisions for coronary lesions compared to visual assessments of angiographic images made by three operators at a high-volume interventional center. In this retrospective study, we aimed to reassess the angiographic images of 63 patients presenting with chronic coronary syndrome (n=39, 61.9%) and acute coronary syndrome (n=24, 38.1%) who underwent FFR. Three experienced interventional cardiologists (with >300 PCI procedures per year) reevaluated, blinded to FFR results, 105 ambiguous lesions in 63 patients to determine angiographic significance and treatment strategy. The observers reached a concordant agreement (≥2 operators made the same decision) to perform PCI in 60 (57.1%) of the lesions based on angiographic evaluation. Interestingly, 9 (15%) of these lesions were functionally non-significant (FFR >0.80). The observers agreed to defer PCI in 45 (42.9%) of the lesions; however, 4 (8.9%) of these were functionally significant (FFR ≤0.80) and required PCI. Thus, inter-observer concordance in visual-guided therapeutic decision-making is variable and not always confirmed by the functional significance of coronary lesions.

This paper focus on the modeling and time-domain analyzing method of piecewise-smooth fractional-order circuit systems. Firstly, an analytical framework is constructed based on a generalized piecewise-smooth two-port impedance network model, which takes the topological characteristics of Dickson type switched-capacitor converters (SCCs) as examples, and considers the fractional-order characteristics of class-2 X7R ceramic capacitors, which are widely used in SCCs. Secondly, the time-domain analyzing method for such a piecewise-smooth fractional-order circuit system is developed, numerical solutions are obtained, and the influence of the fractional-order capacitor on the power conversion efficiency of the system are revealed. Finally, in order to validate the analysis, both numerical simulation and experiments are provided in the work, the results of which confirm that, the proposed fractional-order analytical framework can capture the power loss mechanism of piecewise-smooth fractional-order circuit systems more effectively than the traditional integer-order based approach, thus benefiting the design of circuit systems.

We consider fractional integral operators $(I-T)^d, d \in (-1,1)$ acting on functions $g: \mathbb{Z}^{\nu} \to \mathbb{R}, \nu \ge 1 $, where $T $ is the transition operator of a random walk on $\mathbb{Z}^{\nu}$. We obtain sufficient and necessary conditions for the existence, invertibility and square summability of kernels $\tau (\mathbf{s}; d), \mathmb{s} \in \mathbb{Z}^{\nu}$ of $(I-T)^d $. Asymptotic behavior of $\tau (\mathbf{s}; d)$ as $|\mathbf{s}| \to \infty$ is identified following local limit theorem for random walk. A class of fractionally integrated random fields $X$ on $\mathbb{Z}^{\nu}$ solving the difference equation $(I-T)^d X = \varepsilon$ with white noise on the right-hand side is discussed, and their scaling limits. Several examples including fractional lattice Laplace and heat operators are studied in detail.

Pluripotent stem cells (PSCs) hold many potential research and clinical benefits due to their ability to differentiate into nearly every cell type in the body. They are often used as model systems for early stages of ontogenesis to better understand key developmental pathways, and for drug screening. However, in order to fully realise the potential of PSCs and their translational applications, a deeper understanding of developmental pathways, especially in humans, is required. Several signalling molecules play important roles during development and are required for proper differentiation of PSCs. The concentration and timing of signal activation is important, with perturbations resulting in improper development and/or pathology. Bone morphogenetic protein (BMP) is one such key signalling molecule involved in the specification and differentiation of various cell types and tissues in the human body including tooth and otic development. In this review, we describe the role of BMP signalling and its regulation, the consequences of BMP dysregulation in disease and differentiation, and how PSCs can be used to investigate the effects of BMP modulation during development, mainly focusing on otic development. Finally, we emphasise the unique role of BMP4 in otic specification and how refined knowledge in controlling its regulation could lead to the generation of more robust and reproducible human PSC-derived otic organoids for research and translational applications.

This study explores the properties and behavior of bi-close-to-convex functions, introducing new subclasses defined by their relationship with fractional differential operator and bi-univalent functions. Using the Faber polynomial technique, we derive upper bounds for the n^{th} coefficient of functions in these classes. We also investigate the erratic behavior of initial coefficients in bi-close-to-convex functions, as characterized by the (λ,q)-fractional differintegral operator. Furthermore, we address Fekete-Szegö problems and present notable findings from our investigation, contributing to the continued growth and refinement of geometric function theory, yielding new insights and practical uses.

Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.

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

We introduce a series of twisted donor-acceptor (D-A) carbazole-benzophenone based electroactive bipolar derivatives that were synthesized through the reaction of 4-fluorobenzophenone with various partially alkylated 3,3’-bicarbazoles. The comprehensive structural characterization of these compounds is provided. These amorphous materials exhibit suitable glass transition temperatures ranging from 57 to 102 °C and demonstrate high thermal stability, with decomposition temperatures reaching 400 °C. Moreover, the developed materials exhibit elevated photoluminescence quantum yields (PLQY) of up to 75.5% and favorable HOMO-LUMO levels, along with suitable triplet-singlet state energy values. Due to their good solubility and suitable film-forming properties, all the compounds were evaluated as blue emitters dispersed in 4,4’-bis(N-carbazolyl)-1,10-biphenyl (CBP) host for the fabrication of organic light-emitting diodes (OLEDs) in concentration dependent experiments. Among these experiments, the device containing 15 wt% of the guest 4-(9’-{2-ethylhexyl}-[3,3’]-bicarbazol-9-yl)benzophenone demonstrated the best characteristics, achieving maximum brightness of 3581 cd/m2, current efficiency of 5.7 cd/A, power efficiency of 4.1 lm/W and external quantum efficiency of 2.7%.

Snow cover products are primarily derived from the Moderate-resolution Imaging Spectrometer (MODIS) and Advanced Very High-Resolution Radiometer (AVHRR) datasets. MODIS achieves both snow/non-snow discrimination and snow cover fractional retrieval, while early AVHRR-based snow cover products only focused on snow/non-snow discrimination. The AVHRR Climate Data Record (AVHRR -CDR) provides a nearly 40-year global dataset that has a potential to fill a gap in long term snow cover fractional monitoring. Our study selects the Qinghai-Tibet Plateau as the experimental area, utilizing AVHRR-CDR surface reflectance data (AVH09C1) and calibrating with MODIS snow product MOD10A1. The snow cover percentage retrieval from the AVHRR dataset is performed using Surface reflectance at 0.64μm (SR1) and Surface reflectance at 0.86μm (SR2), along with a simulated Normalized Difference Snow Index (NDSI) model. Also, in order to detect the effects of land cover type and topography on snow inversion, we tested the accuracy of the algorithm with and without these influences, respectively (vanilla algorithm & improved algorithm). The accuracy of the AVHRR snow cover percentage data product is evaluated using MOD10A1、 ground snow-depth measurements and ERA5. Results indicate that the logic model based on NDSI has the best fitting effect, with R-square and RMSE values of 0.83 and 0.10, respectively. Meanwhile, the accuracy was improved after taking into account the effects of land cover type and topography. The model is validated using MOD10A1 snow-covered areas, showing snow cover area differences of less than 4% across 6 temporal phases. Improved algorithm results in better consistency with MOD10A1 than vanilla algorithm. Moreover, the RMSE reaches greater levels when the elevation is below 2,000 meters or above 6,000 meters, and is lower when the slope is between 16° and 20°. Using ground snow-depth measurements as ground truth, the multi-year recall rates are mostly above 0.7, with an average recall rate of 0.81. Results also show a high degree of consistency with ERA5. The validation results demonstrate that the AVHRR snow cover percentage remote sensing product proposed in this study exhibits high accuracy in the Tibetan Plateau region, also demonstrating that land cover type and topographic factors are important to the algorithm. Our study lays the foundation for the global snow cover percentage product based on AVHRR-CDR，furthermore lays a basic work for generating a long-term AVHRR-MODIS fractional snow cover dataset.

This paper presents a new semi-explicit algorithm for parameters estimation in a time-fractional generalization of dual-phase-lag heat conduction model with the Caputo fractional derivatives. It is shown that this model can be derived from a general linear constitutive relation for the heat transfer by conduction when the heat conduction relaxation kernel contains the Mittag-Leffler function. The model can be used to describe heat conduction phenomena in a material with power-law memory. The proposed algorithm of parameters estimation is based on the time integral characteristics method. The explicit representations of the thermal diffusivity and the fractional analogues of the thermal relaxation time and the thermal retardation are obtained via a Laplace transform of the temperature field and utilized in the algorithm. An implicit relation is derived for the order of fractional differentiation. In the algorithm, this relation is resolved numerically. An example illustrates the proposed technique.

Our recent analysis of empirical limit order flow data in financial markets reveals a power-law distribution in limit order cancellation times. These times are modeled using a discrete probability mass function derived from the Tsallis q-exponential distribution, closely aligned with the second form of the Pareto distribution. We elucidate this distinctive power-law statistical property through the lens of agent heterogeneity in trading activity and asset possession. Our study introduces a novel modeling approach that combines fractional Lévy stable motion for limit order inflow with this power-law distribution for cancellation times, significantly enhancing the prediction of order imbalances. This model not only addresses gaps in current financial market modeling but also extends to broader contexts such as opinion dynamics in social systems, capturing the finite lifespan of opinions. Characterized by stationary increments and a departure from self-similarity, our model provides a unique framework for exploring long-range dependencies in time series. This work paves the way for more precise financial market analyses and offers new insights into the dynamic nature of opinion formation in social systems.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

Starting from the fact that one of the global control strategies of the Permanent Magnet Synchronous Motor (PMSM), namely the Direct Torque Control (DTC) type control strategy, is characterised by the fact that the inner flux and torque control loop usually uses hysteresis ON-OFF type controllers and the oscillations introduced by them have to be cancelled out by the outer speed loop controller (which is usually a PI speed controller and whose performance is good around the global operating points and for relatively small variations of the external parameters and disturbances caused in particular by the load torque variation), while retaining the advantages of the DTC strategy, this paper presents the improvement of the performance of the PMSM sensorless control system using Proportional Integrator (PI), PI Equilibrium Optimizer Algorithm (EOA), Fractional Order (FO) PI, Tilt Integral Derivative (TID) and FO Lead-Lag for constant flux, and Sliding Mode Control (SMC) and FOSMC for variable flux. The performance indicators of the control system are the usual ones: response time, settling time, overshoot, steady-state error and speed ripple, plus another one given by the fractal dimension (FD) of the PMSM rotor speed signal, and the hypothesis that the FD of the controlled signal is higher when the control system provides better performance is verified. The paper also presents the basic equations of the PMSM, based on which the synthesis of integer and fractional controllers, the synthesis of an observer for estimating the PMSM rotor speed, electromagnetic torque and stator flux are presented. The comparison of the performance of the proposed control systems and the demonstration of the parametric robustness are performed by numerical simulations in Matlab/Simulink using Simscape Electrical and Fractional Order Modelling and Control (FOMCON). Real-time control based on an embedded system using a TMS320F28379D controller demonstrates the good performance of the PMSM sensorless control system based on the DTC strategy in a complete hardware-in-the-loop (HIL) implementation.

Chronic Obstructive Pulmonary Disease (COPD) is a disease characterized by local and systemic inflammation independently of the risk factor; during the exacerbations, such inflammation is accentuated and amplified. A practical inflammatory marker and one with an applicable predictive value in the follow-up has been sought. FeNO has shown an excellent performance in that respect within the context of asthma and has also been studied in tobacco-smoke COPD (COPD-TS). In Biomass-smoke COPD (COPD-BS), this, to our knowledge, has not been evaluated. Objective: To measure FeNO levels in patients with COPD-BS and to compare these with those of patients with stable COPD-TS and in healthy controls. Methods: Transversal, observational, descriptive, comparative, and analytical study. A total of 57 patients, including 23 with COPD-BS, 17 with COPD-TS, and 17 healthy control subjects. The measurement of FeNO was carried out on all of these by means of the on-line chemiluminescence technique; the values were expressed in parts per billion (ppb) for their analysis. Results: It was observed that the FeNO values were similar between COPD-BS and COPD-TS and were significantly different between the healthy and stable COPD (both groups). No correlation was found between pulmonary function and symptoms with FeNO in any of the groups. Conclusions: The level of FeNO in stable COPD is found to be increased in a similar manner in COPD-BS and COPD-TS, with a significant difference on comparing it with that of the healthy subjects.

In traditional finance, option prices are typically calculated using crisp sets of variables. However, in a proposed new approach, the assumption is made that these parameters have a degree of fuzziness or uncertainty associated with them. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. To determine the belief degree associated with a particular option price, an interpolation search algorithm was proposed recently[1]. Interpolation is a mathematical technique used to estimate values between known data points. In this case, the algorithm is applied to determine the belief degree associated with a specific option price within the range of possible prices. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions. It allows them to consider their risk preferences and beliefs about the uncertain parameters when selecting an option price. In this paper, we will review a unified framework for combining fractional Brownian motion with fuzzy processes and obtain a joint measure space. We start by constructing a product measure space that captures the randomness and fuzziness inherent in the respective processes. We begin with the usual Kolmogorov filtered probability space (Ω, F, ℙ), where ℙ represents the probability measure, Ω is the set of all possible outcomes or states that a random process can take and {Ft, t ∈ [0, T]} is an information filtration. We will review the work of Merton (1976) on option pricing when the underlying stock returns have jumps [2] and expand it to fuzzy fractional processes.

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are offered to detail such systems. Method: ASA and PATHINT/PATHTREE have been effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Applications are described for COVID-19. Results: Results of detailed calculations have led to new results and insights not previously obtained. Conclusion: These 3 applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

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

Visible-light photocatalysis, particularly in its application to organic synthesis, has experienced a big renaissance in the past decade. The rational design of new photocatalysts with designed and improved photocatalytic properties, that at the same time circumvents the necessity of using scarce and toxic transition metals, will predictably play a key role in photocatalysis in the next few years. Although free-base porphyrins were identified some years ago as a promising, easily accessible and easily tunable class of organic photoredox catalysts, a systematic study on the effect of the electronic nature and of the position of the substituents on both the ground-state and the excited-state redox potentials of these compounds is still lacking. We have prepared a set of known functionalized derivatives of meso-tetraphenyl porphyrin containing different substituents either in one of the meso-positions or at a beta-pyrrole carbon and we have determined their ground- and (singlet) excited-state redox potentials. This survey has led us to conclude that the introduction of a carbonyl group at the beta-pyrrolic position strongly increases the facility of the monoelectronic reduction of the porphyrin both in the ground state and in the singlet excited state. We have also prepared a second set of four previously unknown benzoyl derivatives of meso-tetraphenylporphyrin, and we have confirmed the validity of our conclusions.

DFT calculations on the photoisomerization reactions of pyridazine N-oxide derivatives are presented. The irradiation of 3,6-diphenylpyridazine N-oxide allowed to obtain the first excited singlet state that underwent to a ring opening reaction induced to the oxygen migration to the adjacent carbon atom, with the formation of a diazo derivative. This intermediate can give a ring closure reaction to give a pyrazole derivative, or, with a higher transition energy, it can lose nitrogen allowing the formation of 2,5-diphenylfuran. The irradiation of 3-phenylpyridazine N-oxide allowed the formation only of 2-phenylfuran. In this case, calculations allowed to explain this behavior. The first excited singlet state gave a photoisomerization reaction with the formation of the corresponding diazo intermediate. This intermediate could not be converted into the corresponding pyrazole derivative because it was converted into a N-formyl pyrazole never reported in literature. The only possible reaction is the loss of nitrogen and the formation of 2-phenylfuran.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

This paper analyzes and compares models for predicting average magnet losses in interior permanent-magnet motors with fractional-slot concentrated windings due to harmonics in the armature reaction (assuming sinusoidal phase currents). Particularly, loss models adopting different formulations and solutions to the Helmholtz equation to solve for the eddy currents are compared to a simpler model relying on an assumed eddy-current distribution. Boundaries in terms of magnet dimensions and angular frequency are identified (numerically and using an identified approximate analytical expression) to aid the machine designer whether the more simple loss model is applicable or not. The assumption of a uniform flux-density variation (used in the loss models) is also investigated for the case of V-shaped and straight interior permanent magnets. Finally, predicted volumetric loss densities are exemplified for combinations of slot and pole numbers common in automotive applications.

In this paper, we prove the existence of three solutions for a $p$-Kirchhoff problem with $\psi$-Hilfer fractional derivative. To be more precise, we use the variational method and we prove that the associated functional energy admits a critical point in each of the three constructed sets, these critical points are weak solutions for a studied problem. Moreover, by definition of these sets, one of these solutions is positive, the second is negative, and the third one change sign. At the end of this work, we present an example to validate our main results.

Almost fifty years after the introduction of antibiotics as an antimicrobial agent, we are facing an increasing number of multi-resistant microbials. The search for new antimicrobial compounds emerged as a promising alternative to treatments for diseases caused by microorganisms such as fungi and bacteria. Thus, endophytic fungi are gaining recognition for their varied metabolites that may possess antimicrobial properties. In our research, we isolated, from Calea pinnatifida, six endophytic fungi identified as Colletotrichum siamense, Colletotrichum karstii, Hypomontagnella barbarensis, Neopestalotiopsis clavispora, Nigrospora sacchari-officinarum and Annulohypoxylon moriforme. Analyses of microbial secondary metabolites by utilizing UHPLC-HR-ESI-MS/MS in conjunction with molecular networking, allowed the annotation of 9 compounds, 5 of them from GNPS spectral library match, and 4 from prediction-based on the molecular network, and allowed the isolation of two pairs of Acyl-tetronic acid derivatives distereoisomeric identified by NMR spectrum. In this sense, the present study underlines the value of endophytic fungi as a reservoir of potentially new antimicrobial agents.

The Eliezer and Gray physical interpretation of the Ermakov-Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov-Milne-Pinney equation and associated first integral. The special relativistic extension of the Ray-Reid system and invariant is obtained. General properties of the relativistic Ermakov-Milne-Pinney are analyzed. The conservative case of the relativistic Ermakov-Milne-Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered as well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov-Milne-Pinney equation has additional nonlinearities, due to the relativistic effects.

Chagas disease (CD) is a neglected tropical parasitic disease caused by the protozoan Trypanosoma cruzi. Unfortunately, the current etiological treatment for CD is unsatisfactory, due to the high toxicity and low cure efficacy of compounds, mainly during the chronic phase of this disease. Thus, the discovery of new drugs for the treatment of CD is urgent. In the present study, we report the synthesis of a series of guanidines and its evaluation in in vitro assays to determine the trypanocidal effects on the Tulahuen T. cruzi strain, transfected with a β-galactosidase reporter gene, in comparison to the cytotoxic effects on vertebrate cells. The most potent and selective compounds LQOF-G1 and LQOF-G29 were considered good drug prototypes and candidates for in vivo tests using mice. Both compounds possess an electron withdrawing group on the aniline moiety, namely a NO2 and Br group, respectively, which effectively decrease the electron density. LQOF-G29 stands out among the investigated compounds due to the replacement of the benzyl group by methyladamantane.

We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system's lifetime and explore its preservation properties in terms of established stochastic orders. Additionally, we obtain useful bounds. To aid practical applications, we propose two non parametric estimators for the fractional generalized cumulative residual entropy in these systems. The efficiency and performance of these estimators are illustrated using simulated and real datasets.

The aim of this work is to study generalizations of the notion of mean. Kolmogorov proposed a generalization based on an improper integral with a decay rate for the tail probabilities. This weak or Kolmogorov mean relates to the Weak Law of Large Numbers in the same way that the ordinary mean relates to the Strong Law. We propose a further generalization, also based on an improper integral, called the doubly weak mean, applicable to heavy-tailed distributions such as the Cauchy distribution and the other symmetric stable distributions, We also consider generalizations arising from Abel-Feynman type mollifiers that damp the behavior at infinity and alternative formulations of the mean in terms of the cumulative distribution and the characteristic function.

Diarrhea remains one of the leading causes of mortality worldwide, especially among children. Recent epidemiological studies conducted in developing countries identified Shigella species as the most predominant pathogenic bacteria responsible for diarrhea. Antimicrobial therapy is necessary for Shigella infections; however, the rapid emergence of resistance against existing antimicrobials in Shigella spp. poses a serious global health problem. To identify alternative antimicrobial compounds with activity against Shigella species, the pathogens responsible for bacterial diarrhea. In this study, we have applied antibacterial phenotypic screening to identify potent anti-Shigella compounds across a broad chemical diversity, including selected acetaminophen derivatives containing benzothiazoles backbone, and their combination with certain antibiotics. In continuation to our effort in searching potent antimicrobial compounds, we have found this time around that two acetaminophen derivatives containing benzothiazoles backbone (4a and 4b) could inhibit the growth of Shigella flexneri with common MIC value of 12.5 µg/ml. These compounds were established through a time-kill kinetics’ study to be bactericidal. Meanwhile, the 2-aminobenzothiazoles (1a and 1b) used for the synthesis of compounds 4 (a & b) were found to be poorly active (MIC: 100 µg/ml) against this pathogen. Combination studies of 4a and 4b with the least susceptible antibiotics (ceftriaxone and cotrimoxazole) demonstrated synergistic anti-Shigella activity. The present study demonstrates that the azobenzothiazole dyes 4 (a & b) can be repurposed as potential anti-Shigella compounds, which can serve as scaffolds for the development of new agents against infectious diarrhea caused by Shigella and other enteric pathogens, especially in developing countries.

This paper investigates pseudo-polymorphism in 2-pyridylmethoxy derivatives of p-tert-butylcalix[4]arene (PyC4), p-tert-butyldihomooxa-calix[4]arenes (PyHOC4), and p-tert-butylhexahomotrioxacalix[3]arenes (PyHO3C3), presenting 11 crystal structures with 15 crystallographically independent molecules. The macrocycle of PyC4 is smaller and less flexible with respect to those of PyHOC4 and PyHO3C3 and in solution, the cone conformation of these three molecules exhibit different point symmetries: C4, Cs and C3, respectively. A correlation is observed between the macrocycle's structural rigidity and the number of pseudo-polymorphs formed. The more rigid PyC4 displays a higher number (6) of pseudo-polymorphs compared to PyHOC4 and PyHO3C3, which exhibit a smaller number of crystalline forms (3 and 2, respectively). The X-ray structures obtained show that the conformation of the macrorings is primarily influenced by the presence of an acetonitrile guest molecule within the cavity, with limited impact from crystal packing and intermolecular cocrystallized solvent molecules. Notably, both calix[4]arene derivatives produce host-guest complex with acetonitrile, while the most flexible and less aromatic PyHO3C3 do not give crystals with acetonitrile as guest. Intertwined 1D and 2D solvent channel networks were observed in the PyHOC4-hexane and in the PyHO3C3-H2O-MeOH crystal structures, respectively, while the other pseudopolymorphs of PyHOC4 and PyHO3C3 and all PyC4 crystal forms exhibit a closely packed crystal structures without open channels.

Background: Forecasting nonlinear stochastic systems most often is quite difficult, without giving in to temptations to simply simplify models for the sake of permitting simple computations. Objective: Here, two basic algorithms, Adaptive Simulated Annealing (ASA) and path-integral codes PATHINT/PATHTREE (and their quantum generalizations qPATHINT/qPATHTREE) are offered to detail such systems. Method: ASA and PATHINT/PATHTREE have been effective to forecast properties in three disparate disciplines in neuroscience, financial markets, and combat analysis. Applications are described for COVID-19. Results: Results of detailed calculations have led to new results and insights not previously obtained. Conclusion: These 3 applications give strong support to a quite generic application of these tools to stochastic nonlinear systems.

5-(4-aminophenyl )-2-amino -1,3,4-thiadiazole was prepared by reaction of Thiosemicarbazide with 4-amino benzoic acid under reflux condition for 7 hours. The compound which has been synthesized successfully was subjected to addition reaction with 4-(Dimethylamino) benzaldehyde under reflux condition for 6 hours to synthesize Schiff bases. These compounds was characterized by using FTIR) and evaluated for their anticancer activity. The effect of (1, 3, 4-thiadiazole derivative) on the activity of malignant cells was studied by using different types of cell lines [Breast cancer, and human prostate cancer]. And was used the Electron microscope to show that the effect of the derivative on the cancer cells before and after 3 days of the injection time. It was found that the Schiff base of thiadiazole-1,3,4-(Dimethylamino)benzylidineamino]- [4-2-phenyl]amino was effective in reducing the size and density of malignant cells. That of 46.7 while in breast ) 145(DUprostate for growth inhibition produce of equal 85.9 µg/ml.

Based on DFT (density functional theory) using B3LYP/6-31G method, theoretical investigations applied to demonstrate the structural, electronic properties and stability of (N,Nˊ-(1,4-phenylene)bis(1,8-naphthalimide)) is more stable than the compound (N-(4-amino phenyl)1,8-naphthalimide) by (-1.2762 eV or -29.4299 Kcal.mol-1) depending on the values of HOMO, synthesis reaction of imide is spontaneous and endothermic at temperature 275˚C according to the values of ∆rS, ∆rG and ∆rH.

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

We primarily investigate the existence of solutions for fractional neutral integro-differential equations subjected to Neumann-type boundary conditions, which is crucial for understanding natural phenomena. Taking into account factors such as neutral type, fractional-order integrals, and fractional-order derivatives, we employ probability density functions, Laplace transforms, and resolvent operators to formulate a well-defined concept of a mild solution for the specified equation. Following this, by integrating fixed point theorems, we establish the existence of mild solutions under more relaxed conditions.

The unified Mittag-Leffler (ML) function is important factor in formulation of compact form of fractional integrals. In this paper estimations of integral operators, with the unified ML function as kernel are given. The Hadamard inequality in the form of fractional integrals is proved by considering refinement of convexities. These estimations provide various inequalities as refinements of recently published results.

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?

Traditional computer vision techniques aim to extract meaningful information from images but often depend on manual feature engineering, making it difficult to handle complex real-world scenarios. Fractional Calculus (FC), which extends derivatives to non-integer orders, provides a flexible way to model systems with memory effects and long-term dependencies, making it a powerful tool for capturing fractional rates of variation. Recently, Neural Networks (NNs) have demonstrated remarkable capabilities in learning complex patterns directly from raw data, automating computer vision tasks and enhancing performance. Therefore, the use of fractional calculus in neural network-based computer vision is a powerful method to address existing challenges by effectively capturing complex spatial and temporal relationships in images and videos. This paper presents a survey of Fractional Calculus Neural Network-based (FC NN-based) computer vision techniques for denoising, enhancement, object detection, segmentation, restoration, and NN compression. The survey compiles existing FFC NN-based approaches, elucidates underlying concepts, and identifies open questions and research directions. By leveraging FC's properties, FC NN-based approaches offer a novel way to improve the robustness and efficiency of computer vision systems.

Background: The identification of novel therapeutic strategies for Ovarian cancer (OC), the most lethal gynecological neoplasm, is of utmost urgency. Here, we have tested the effectiveness of the compound 2c (4-Hydroxy-2,6-bis(4-nitrobenzylidene)cyclohexanone 2). 2c interferes with cyste-ine-dependent deubiquitinating enzymes (DUBs), thus affecting the ubiquitin-proteasome de-pendent degradation of proteins. Methods: 2c phenotypic/molecular effects were studied in two OC cell lines, primary tumor cells cultured in 2D/3D and in a mouse xenograft model. We also propose an in-silico model of 2c interaction with DUBs. Finally, we tested the effect of 2c conju-gated to several linkers to generate 2c-derivatives usable for improved drug delivery. Results: 2c effectively impairs OC cell line and primary tumor cell viability in both 2D and 3D conditions. The effectiveness is confirmed in a xenograft mouse model of OC. We show that 2c impairs pro-teasome activity and triggers apoptosis most likely by interacting with DUBs; we propose a mechanism for the interaction with a model DUB via an in-silico evaluation of the en-zyme-inhibitor complex. 2c also reduces cell growth by down-regulating the level of the transcrip-tion factor E2F1. Finally, 2c activity is often retained after the conjugation with linkers. Conclu-sion: Our data strongly support the potential therapeutic value of 2c/derivatives in OC.

Fractional cointegration in time series data has been explored by several authors, but panel data applications have been largely neglected. A previous study of ours discovered that the Chen and Hurvich fractional cointegration test for time series was fairly robust to a moderate degree of heterogeneity across sections, out of the six tests considered. Therefore, this paper advances a customized version of the Chen and Hurvich methodology to detect cointegrating connections in panels with unobserved fixed effects. Specifically, we develop a test statistic that accommodates variation in the long-term cointegrating vectors and fractional cointegration parameters across observational units. The behaviour of our proposed test is examined through extensive Monte Carlo experiments under various data generating processes and circumstances. The findings reveal that our modified test performs quite well comparatively and can successfully identify fractional cointegrating relationships in panels even in the presence of idiosyncratic disturbances unique to each cross-sectional unit. Furthermore, the proposed modified test procedure established the presence of long-run equilibrium between the exchange rate and labour wage of 36 countries agricultural markets.

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.

Making sustainable business models, especially in manufacturing, is a key approach for organizations to adopt in order to create more sustainable processes. New technologies are needed to implement new policies that can minimize the economic, environmental, and social consequences of industrial activity. Sustainable maintenance is decisive to guarantee the availability, reliability, and safety of assets, surpassing traditional maintenance policies and embracing the principles of the circular economy. The main objective of Maintenance 4.0 is to increase the lifespan and availability of the equipment by preventing unplanned downtime, reducing planned shutdowns, and improving safety. This research focuses on the integration of advanced Industry 4.0 tools with conventional monitoring and control techniques in process industries. The article suggests that while complex neural networks might provide good predictions, simpler solutions can generalize well and have lower prediction errors because they can capture the underlying relationships between variables in a specific asset better. The combination of maintenance function, Industry 4.0 tools, and advanced statistical solutions to obtain sustainable processes can facilitate organizational change and aid decision-making in equipment management. These solutions seek to reduce interruptions and expenses through the unnecessary utilization of labor and spare parts. All these considerations improve communication and data processing, resulting in improved maintenance of a hydrogen compressor in the petrochemical industry.

The goal of this study is to synthesize, determine the structure, and examine the antimicrobial properties of novel metal complexes of 2,4-dithiouracil and its derivatives. These complexes were obtained by mixing aqueous solutions of the corresponding metal salts with the ligand dissolved in DMSO and aqueous NaOH, using a metal-to-ligand ratio of 1:4:2. The structures of the new compounds were analyzed by melting point determination, microwave plasma atomic emission spectrometry (MP-AES) for Cu and Au, inductively coupled plasma optical emission spectrometry (ICP-OES) for S, ATR, solution and solid-state NMR and Raman spectroscopy. The interpretation of the complex spectra was aided by data for 2,4-dithiouracil obtained from 1H-1H COSY, DEPT-135, HMBC, and HMQC spectra. Additionally, the antimicrobial activity of these complex-es and the free ligands was evaluated against Gram-positive and Gram-negative bacteria, as well as yeasts.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

Fibrosis is a ubiquitous pathology, and prior studies have indicated that various artemisinin (ART) derivatives (including artesunate (AS), artemether (AM), and dihydroartemisinin (DHA)) can reduce fibrosis in vitro and in vivo. The medicinal plant, Artemisia annua L., is the natural source of ART and is widely used, especially in underdeveloped countries, to treat a variety of diseases including malaria, while A. afra contains no ART but is also antimalarial. Using human dermal fibroblasts (CRL-2097), we compared the effects of A. annua and A. afra tea infusions, ART, AS, AM, DHA, and a liver metabolite of ART, deoxyART (dART), on fibroblast viability and expression of key fibrotic marker genes after 1 and 4 days of treatment. AS, DHA, and Artemisia tea significantly reduced fibroblast viability at 1 and 4 d post-treatment. After 4 d post treatment, AS, DHA, and A. afra tea downregulated ACTA2, and upregulated MMP3, with other genes either being unaffected or differentially affected. ART and AM had no significant effect on either fibroblast viability or fibrotic gene expression. Although A. annua contains ART, it had a significantly greater anti-fibrotic effect than ART alone. Immunofluorescent staining for smooth muscle α-actin (α-SMA) correlated well with transcriptional responses of drug-treated fibroblasts. Together, proliferation, qPCR, and immunofluorescence results show that treatment with ART, AS, DHA, and the two Artemisia teas yield differing responses, including those related to fibrosis, in human dermal fibroblasts.

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.

A number of chemical modifications were carried out in order to synthesize new compounds based on the triterpenoid betulonic acid. Triazolation reactions were carried out for the synthesis of new 1,2,3-triazole derivatives based on betulonic acid. Chemical changes were made on the carbonyl group at the C-3 position of the initial molecule and on the carboxyl and hydroxyl groups at the C-28 position. Chromatographic methods were used to separate and purify the formed products. Spectroscopic (NMR-, mass-) methods were used to establish the structure of synthesized compounds. As a result of the chemical transformations carried out, a number of new derivatives of betulonic acid were obtained. All synthesized compounds were tested for antimicrobial and cytotoxic activity. As a result, compounds with pronounced antimicrobial activity were identified.

Xanthone derivatives, a class of natural compounds abundantly found in plants such as mangosteen (Garcinia mangostana) and certain herbs, have garnered substantial interest due to their diverse pharmacological properties, including antioxidant, anti-inflammatory, and anti-cancer activities. Recent investigations have unveiled their potential as modulators of enzymatic activity, prompting exploration into their effects on hyaluronidase-mediated HA degradation, and their effects in topical treatment of telangiectasia and rosacea. Telangiectasia and rosacea are common dermatological conditions characterized by chronic skin inflammation, vascular abnormalities, and visible blood vessels, resulting in significant cosmetic concerns and impaired quality of life for affected individuals. This review aims to provide a comprehensive overview of the current understanding regarding the interplay between mechanisms of action by which xanthone derivatives exert their therapeutic effects, including the inhibition of pro-inflammatory cytokines, modulation of oxidative stress pathways, and regulation of vascular endothelial growth factors. Furthermore, we will discuss the implications of harnessing xanthone derivatives as therapeutic agents for mitigating vascular dysfunction and its associated pathologies, thereby offering insights into future research directions and therapeutic strategies in the field of vascular biology.

The ribonuclease H (RNase H) active site of HIV-1 reverse transcriptase (RT) is the only viral enzyme not targeted by approved antiretroviral drugs. Using a fluorescence-based in vitro assay, we screened 65,239 compounds at a final concentration of 10 µM to identify inhibitors of RT RNase H activity. We identified 41 compounds that exhibited 50% inhibitory concentration (i.e., IC50) values < 1.0 µM. Two of these compounds, 2-(4-methyl-3-(piperidin-1-ylsulfonyl)phenyl)benzo[d]isothiazol-3(2H)-one (1) and ethyl 2-(2-(3-oxobenzo[d]isothiazol-2(3H)-yl)thiazol-4-yl)acetate (2), which both share the same benzisothiazolone pharmacophore, demonstrate robust antiviral activity (50% effective concentrations of 1.68 ± 0.94 µM and 2.68 ± 0.54, respectively) in the absence of cellular toxicity. A limited structure-activity relationship analysis identified two additional benzisothiazolone analogs, 2-methylbenzo[d]isothiazol-3(2H)-one (3) and N,N-diethyl-3-(3-oxobenzo[d]isothiazol-2(3H)-yl)benzenesulfonamide (4), which also resulted in inhibition of RT RNase H activity and virus replication. Compounds 1, 2 and 4, but not 3, inhibited the DNA polymerase activity of RT (IC50 values ~ 1 to 6 µM). In conclusion, benzisothiazolone derivatives represent a new class of multifunctional RT inhibitors that warrants further assessment for the treatment of HIV-1 infection.

Silybin is a natural compound extensively studied for its hepatoprotective, neuroprotective and anti-cancer properties. Envisioning the enhancement of silybin potential by suitable modifications in its chemical structure, here, a series of new 7-O alkyl silybins derivatives were synthesized by Mitsunobu reaction starting from the silybins and tyrosol-based phenols, such as tyrosol (TYR, 3), 3-methoxytyrosol (MTYR, 4) and 3-hydroxytyrosol (HTYR, 5). This research sought to explore the antioxidant and anticancer properties of new eighteen derivatives and their mechanisms. In particular, the antioxidant properties of new derivatives outlined by DPPH assay, showed a very pronounced activity depending on the tyrosyl moiety (HTYR>MTYR>>TYR). A significant contribution of the HTYR moiety was observed for silybins and 2,3-dehydro-silybin based derivatives. According to the very potent antioxidant activity, 2,3-dehydro-silybin derivatives 15ab, 15a and 15b exerted the most potent anticancer activity in human prostate cancer PC-3 cells. Furthermore, flow cytometric analysis for cell cycle and apoptosis revealed that 15ab, 15a and 15b induce strong G1 phase arrest and increase late apoptotic population in PC-3 cells. Additionally, western blotting for apoptotic marker cleaved caspase-3 confirmed apoptosis induction by these silybin derivatives in PC-3 cells. These findings hold significant importance in the investigation of anticancer properties of silybin derivatives and strongly encourage swift investigation in pre-clinical models and clinical trials.

We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage of using special functions is their analytic continuation which widens the range of the parameters of the definite integral over which the formula is valid. We give as examples definite integrals of logarithmic functions times a trigonometric function. In various cases these generalizations evaluate to known mathematical constants such as Catalan’s constant and π

The study of the morphology, thermal, and chemical stability of the fluorinated compounds was performed using Becke’s three-parameter hybrid functional approach with the correlation provided by Lee, Yang, and Parr and the cc-pVTZ basis set aiming to design low sensitivity, toxicity, instability, and proneness to decomposition or degradation over a short time high-energy materials. The most stable conformers of the compounds under study were selected based on their total energy. Their thermal and chemical stability was evaluated based on the binding energy per atom, chemical hardness, and softness. The oxygen-fluorine balance is assessed to evaluate the sensitivity of these new materials. The density, detonation pressure, and velocity of the selected conformers were theoretically obtained to reveal the influence of -CF3, -OCF3, and cyclic -O(CF2)nO- fragments on the energetic properties of nitroaromatics as well as their stability and resistance to shock stimuli. The results allow us to predict new multipurpose energetic materials with a good balance between power and stability. Referring to the results obtained, we recommend CF3N2, OCF3N2, C2F6N2, 1CF2N2/O2CF2N2, and 2CF4N2/O2C2F4N2 for practical usage because these compounds possess greater stability compared to tetryl and better explosive properties than TNT.

The article proposes asymptotic methods for calculating Sommerfeld integrals, which enable us to calculate the integral using the expansion of a function into an infinite power series at the saddle point, where the role of a rapidly oscillating function under the integral can be fulfilled either by an exponential or by its product by the Hankel function. The proposed types of Sommerfeld integrals are generalized on the basis of integral representations of the Hertz radiator fields in the form of the inverse Hankel transform with the subsequent replacement of the Bessel function by the Hankel function. It is shown that the numerical values of the saddle point are complex. During integration, auxiliary or so-called standard integrals, which contain the main features of the integrand function, were used. As a demonstration of the accuracy of the technique, a previously known asymptotic formula for the Hankel functions was obtained in the form of an infinite series. The proposed method for calculating Sommerfeld integrals can be useful in solving the half-space Sommerfeld problem. An example is the expression in the form of an infinite series for the magnetic field of reflected waves, obtained directly through the Sommerfeld integral (SI).

Background: There is little clarity in the application of content related to improper integrals in university students, due to the absence of meaning, which prevents them from making a connection with everyday problem situations. Methods: we designed a mathematical modelling proposal where a specific situation involving the instrumentation, use and application of this type of integrals is experimented and solved with a population of engineering students, who learn to use them. Results: The importance of using mathematical modelling as a didactic-dynamic resource is highlighted because it helps students to reach an understanding of real situations involving improper integrals in different contexts. Conclusions: Despite the numerous errors detected in the students, this strategy made it possible to demonstrate the development of advanced mathematical thinking skills in young people.

To determine the photon emission or absorption probability for a diatomic system in the context of the semiclassical approximation it is necessary to calculate the characteristic canonical oscillatory integral which has one or more saddle points. Integrals like that appear in a whole range of physical problems, e.g. the atom-atom and atom-surface scattering and various optical phenomena. A uniform approximation of the integral, based on the stationary phase method is proposed, where the integral with several saddle points is replaced by a sum of integrals each having only one or at most two real saddle points and is easily soluble. In this way we formally reduce the codimension in canonical integrals of "elementary catastrophes" with codimensions greater than 1. The validity of the proposed method was tested on examples of integrals with three saddle points ("cusp" catastrophe) and four saddle points ("swallow-tail" catastrophe).

β-Lactams are pharmacologically important compounds because of their various biological uses, including antibiotic and so on. β-Lactams were synthesized from benzylidene-inden derivatives and acetoxyacetyl chloride. The inhibitory effect of these compounds was also examined for human carbonic anhydrase I and II (hCA I, and II) and acetylcholinesterase (AChE). The results reveal that β-lactams are inhibitors of hCA I, II and AChE. The K_i values of β-lactams (2a-k) were 0.44-6.29 nM against hCA I, 0.93-8.34 nM against hCA II, and 0.25-1.13 nM against AChE. Our findings indicate that β-lactams (2a-k) inhibit both CA isoenzymes and AChE at low nanomolar concentrations.

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.

Natural cytokinins are a promising group of cytoprotective and anti-tumor agents. In this research, we synthesized a set of novel cytokinin analogs with alkyl substituents at various positions of the aromatic moiety, as well as with oxygen-containing groups, and tested their antiproliferative activity in MDA-MB-231, A-375, and U-87 MG cell lines, and cytoprotective properties in H2O2 and CoCl2 models. Two amino-linked compounds were anti-proliferative with the ability to act synergistically with doxorubicin, and two carbamate-based ones were cytoprotective. According to the molecular docking data, anti-proliferation was based on the A2AR and APRT inhibition and cytoprotection on the CDK2 inhibition. The obtained results are promising for the development of novel anti-cancer therapeutics.

Biomaterials have been the subject of extensive research, with their applications in medicine and pharmacy expanding rapidly. Collagen and its derivatives stand out as valuable biomaterials due to their high biocompatibility, biodegradability, and lack of toxicity and immunogenicity. This review comprehensively examines collagen from various sources, its extraction and processing methods, and its structural and functional properties. Preserving the native state of collagen is crucial for maintaining its beneficial characteristics. The challenges associated with chemically modifying collagen to tailor its properties for specific clinical needs are also addressed. The review discusses various collagen-based biomaterials, including solutions, hydrogels, powders, sponges, scaffolds, and thin films. These materials have broad applications in regenerative medicine, tissue engineering, drug delivery, and wound healing. Additionally, the review highlights current research trends related to collagen and its derivatives. These trends may significantly influence future developments, such as using collagen-based bioinks for 3D bioprinting or exploring new collagen nanoparticle preparation methods and drug delivery systems.

Indole is a versatile pharmacophore widely distributed in bioactive natural products. This privileged scaffold has been found in a variety of molecules isolated from marine organisms such as algae and sponges. Among these, indole alkaloids represent one of the biggest, most promising family of compounds, having shown a wide range of pharmacological properties, including anti-inflammatory, antiviral and anticancer activities. The aim of this review is to show the current scenario of marine indole alkaloid derivatives, covering not only the most common chemical structures, but also new synthetic routes developed during the last years as well as promising therapeutic applications.

Biodiesel has several drawbacks, such as being prone to oxidation, having reduced stability, and having limited storage time. Antioxidants compatible with biodiesel are being used to address its drawbacks. Utilizing antioxidants effectively improves the quality of biodiesel. Enhancing the quality of biodiesel for use as a clean energy source benefits both the global economy and ecology. Therefore, we believe that our work will contribute to the advancement of the worldwide industry. The study used blends consisting of 20% biodiesel and 80% diesel fuel. Isatin-thiosemicarbazones were tested as additives in blends at a concentration of 3000 parts per million (ppm) using an oxifast device. Comparing them to the chemical antioxidant Trolox. FT-IR, DSC, and TGA were used to characterize these samples. DSC measured sample crystallization temperatures (Tc). Samples with antioxidants showed decreased values compared to the non-antioxidant diesel sample D100. Several DSC tests were conducted to determine the antioxidant strengths of various samples. The results showed that the FT-IR spectrum's antioxidant effect regions grow clearer with antioxidants. The extra antioxidant is effective. Biodiesel's oxidative stability improves with isatin-thiosemicarbazones at varying concentrations. The kinetics of thermal decomposition of isatin-thiosemicarbazones under non-isothermal conditions have been determined using the Kissinger, Ozawa, and Boswell techniques. The activation energies of compounds 1 and 2 were calculated 137–147 kJ mol^-1 and 173–183 kJ mol^-1, respectively.

Glycerol conversion to valuable biomolecules has been a research avenue that has attracted a significant interest in recent years due to its increasing over production, with possibilities for chemical transformation for eco-friendly processes and distinct compounds with biological activities. Also, in the current climate change in which a major emphasis is being placed on the design of green processes, solvents are key factors from both an economic and environmental point of view. In this context, due to its abundance and low-price, glycerol represents an innovative solvent coming from biomass and produce in high amount. On the other hand, Epichlorydrin, Glycidol and Solketal have become useful intermediates in chemical transformations when using glycerol as a raw material. This review focuses on glycerol as a green solvent in the synthesis of complex molecules, Epichlorydrin, Glycidol, Solketal and Tosyl solketal as an efficient recycling process for glycerol, as well as building blocks in the synthesis of glycerol derivatives, which are undeniable new source of potentials drugs.

Resistance to the existing drugs and increasing numbers of diseases result in identifying new drug candidates with new forms of activity. Marine sources of alkylglycerols such as the liver oil Shark (SLO) mixture of certain species or rat fish (elasmobranch fishes) contain high levels of these compounds as a mixture of few species varying by length and unsaturation or saturation of the alkyl chain. They have multiple biological activities such as hematopoiesis stimulation, lowering radiotherapy-induced injuries, reducing tumor growth and improving vaccination efficiency. The synthesis of two Alkylglycerols (AKGs) containing at least one alkyne moiety in the alkyl chain has been reported. In this work, we describe the synthesis of others unknown AKGs based alkyne 1-O-(hexadec-11’-ynyl)-sn-glycerol 4 and 1-O-(octadec-9’-ynyl)-sn-glycerol 5 as analogues of bioactive ether lipids found in the SLO mixture.

In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterra integral equations of the second kind and a fractional differential equation. For a particular solution of the proposed problem, its visualization is carried out for various values of the order of the fractional derivative. It is shown that the order of the derivative affects the intensity of the diffusion process (subdiffusion), as well as the shape of the wave front.

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

Cordycepin has good antitumor activity, but its clinical application is limited due to the easy deamination of N6 in structure. In this study, a large lipopolysis group was introduced at the cordycepin N6 to improve the problem, Cordycepin derivatives(3a-4c) were synthesized, and biological evaluation of compounds were studied. In the study, the vitro antitumor activity of the compounds against MCF7 cells, HepG2 cells and SGC-7901 cells was evaluated by MTT assay. In the results, compound 4a showed the most obvious inhibitory effect on MCF7 cells with IC50 value of 27.566±0.52 μM, which was much lower than cordycepin. Compound 4a showed high selectivity between MCF7 and normal MCF-10A cells. Further biological evaluation showed that compound 4a promoted apoptosis and blocked the cell cycle in G0/G1 phase. Then, Western Blot was used to detect related apoptotic proteins. It was found that Compound 4a could down-regulate the expression of Bcl-2 protein and up-regulate the expression of p53, Bax, Caspase-3, and Caspase-9 proteins. The mitochondrial membrane potential decreased continuously and the positive expression rate decreased. It was speculated that compound 4a induced the apoptosis of MCF7 cells through the mitochondrial pathway.

The tetracyclic pyrido[4,3-b]carbazole olivacine and four of its oxygenated derivatives have been synthesized by a late-stage palladium-catalyzed Heck-type cyclization of the pyrrole ring as key step. In a test for inhibition of the growth of Mycobacterium tuberculosis 9-methoxyolivacine showed the most significant inhibiting activity against Mycobacterium tuberculosis with an MIC₉₀ value of 1.5 μM.

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 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.

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.

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

Neural Fractional Differential Equations (Neural FDE) represent a neural network architecture specifically designed to fit the solution of a fractional differential equation to given data. This architecture combines an analytical component, represented by a fractional derivative, with a neural network component, forming an initial value problem. During the learning process, both the order of the derivative and the parameters of the neural network must be optimised. In this work, we investigate the non-uniqueness of the optimal order of the derivative and its interaction with the neural network component. Based on our findings, we perform a numerical analysis to examine how different initialisations and values of the order of the derivative (in the optimisation process) impact its final optimal value. Results show that the neural network on the right-hand side of the Neural FDE struggles to adjust its parameters to fit the FDE to the data dynamics for any given order of the fractional derivative. Consequently, Neural FDEs do not require a unique α value, instead, they can use a wide range of α values to fit data. This flexibility is beneficial when fitting to given data is required, and the underlying physics is not known.

The results of the most recent investigation of triterpenoid-based antiviral agents effective namely in the HIV-1 and HSV-1 treatment were reviewed and summarized. Several key historical achievements are included to stress consequences and continuity in this research. Most of the agents studied belong into a series of compound derived from betulin or betulinic acid, and their synthetic derivative called bevirimat. A termination of clinical trials of bevirimat in the Phase IIb initiated a search for more successful compounds partly derived from bevirimat or designed independently of bevirimat structure. Surprisingly, a majority of bevirimat mimics are derivatives of betulinic acid, while other plant triterpenoids, such as ursolic acid, oleanolic acid, glycyrrhetinic acid or other miscellaneous triterpenoids, are relatively rarely involved in a search for novel antiviral agent. Therefore, this review article is divided into three parts based on the leading triterpenoid core structure.

Monoterpenes as natural products are the subject of increased attention in the search for new pharmacological agents because of their numerous biological activities including antifungal, antibacterial, antioxidant, anticancer, antispasmodic, hypotensive, vasodilating effects, etc. In vitro and in vivo studies reveal their antidepressant, anxiolytic, and memory-enhancing in experimental dementia and Parkinson’s disease effects. Chemical modification of natural substances by conjugation with various synthetic components is a modern method of obtaining new biologically active compounds. The discovery of new potential drugs among monoterpene derivatives is a progressive direction in experimental pharmacology and a promising approach to the therapy of various pathologies. Biologically active substances such as monoterpenes borneol, camphor, geraniol, pinene, and thymol, were used to synthesize compounds with different properties, including analgesic, anti-inflammatory, anticonvulsant, anti-depressant, anti-Alzheimer’s, anti-parkinsonian, antiviral and antibacterial (anti-tuberculosis). Myrtenal is a perspective monoterpenoid with therapeutic potential in various fields of medicine. Its chemical modifications often lead to new or more pronounced biological effects. As an example, conjugation of myrtenal with the known pharmacophore adamantane allows one to enhance some of its key properties. Myrtenal-adamantane derivatives exhibited a variety of beneficial properties – antimicrobial, antifungal, antiviral, anticancer, anxiolytic, and neuroprotective, which are worth examining in more detail and at length.