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This paper introduces and establishes new Hermite‐Hadamard type inequalities specifically tailored for m$$ m $$‐preinvex functions within the (p,q)$$ \left(p,q\right) $$‐calculus framework. These newly developed inequalities come with accompanying left‐right estimates, which enhance their practical utility. The primary objective of this research is to investigate the properties of (p,q)$$ \left(p,q\right) $$‐differentiable m$$ m $$‐preinvex functions and derive inequalities that extend and generalize existing results in the domain of integral inequalities. The techniques employed in this study hold broader implications, finding relevance in various fields where symmetry is paramount. The findings presented in this paper make a significant contribution to the field of analytic inequalities, offering valuable insights into the behavior and characteristics of m$$ m $$‐preinvex functions. Moreover, the established results demonstrate the wider applicability and generalization of analogous findings from prior literature. The techniques and inequalities introduced herein pave the way for further exploration and research in the realm of integral inequalities. [ABSTRACT FROM AUTHOR]

Introduction: The rate of development and complexity of digital health interventions (DHIs) in recent years has to some extent outpaced the methodological development in economic evaluation and costing. Particularly, the choice of cost components included in intervention or program costs of DHIs have received scant attention. The aim of this study was to build a literature-informed checklist of program cost components of DHIs. The checklist was next tested by applying it to an empirical case, Mamma Mia, a DHI developed to prevent perinatal depression. Method: A scoping review with a structured literature search identified peer-reviewed literature from 2010 to 2022 that offers guidance on program costs of DHIs. Relevant guidance was summarized and extracted elements were organized into categories of main cost components and their associated activities following the standard three-step approach, that is, activities, resource use and unit costs. Results: Of the 3448 records reviewed, 12 studies met the criteria for data extraction. The main cost categories identified were development, research, maintenance, implementation and health personnel involvement (HPI). Costs are largely considered to be context-specific, may decrease as the DHI matures and vary with number of users. The five categories and their associated activities constitute the checklist. This was applied to estimate program costs per user for Mamma Mia Self-Guided and Blended, the latter including additional guidance from public health nurses during standard maternal check-ups. Excluding research, the program cost per mother was more than double for Blended compared with Self-Guided (€140.5 versus €56.6, 2022 Euros) due to increased implementation and HPI costs. Including research increased the program costs to €190.8 and €106.9, respectively. One-way sensitivity analyses showed sensitivity to changes in number of users, lifespan of the app, salaries and license fee. Conclusion: The checklist can help increase transparency of cost calculation and improve future comparison across studies. Plain Language Summary: Estimating program or intervention costs of digital health interventions (DHIs) can be challenging without a checklist. We reviewed scientific literature to identify key cost categories of DHIs: development, research, maintenance, implementation and health personnel involvement. We also summarized relevant information regarding resource use and unit cost for each of the aforementioned categories. Applying this checklist to Mamma Mia, a DHI aimed at preventing perinatal depression, we find that the total cost per user for Mamma Mia Self-Guided is €106.9 and for Mamma Mia Blended is €190.8. Our checklist enhances visibility of DHI cost components and can aid analysts in better estimating costs for economic evaluations. [ABSTRACT FROM AUTHOR]

Inequalities serve as fundamental tools for analyzing various important concepts in stochastic differential problems. In this study, we present results on the existence, uniqueness, and averaging principle for fractional neutral stochastic differential equations. We utilize Jensen, Burkholder–Davis–Gundy, Grönwall–Bellman, Hölder, and Chebyshev–Markov inequalities. We generalize results in two ways: first, by extending the existing result for p = 2 to results in the L p space; second, by incorporating the Caputo–Katugampola fractional derivatives, we extend the results established with Caputo fractional derivatives. Additionally, we provide examples to enhance the understanding of the theoretical results we establish. [ABSTRACT FROM AUTHOR]

In the study of biological systems, nonlinear models are commonly employed, although exact solutions are often unattainable. Therefore, it is imperative to develop techniques that offer approximate solutions. This study utilizes the Elzaki residual power series method (ERPSM) to analyze the fractional nonlinear smoking model concerning the Caputo derivative. The outcomes of the proposed technique exhibit good agreement with the Laplace decomposition method, demonstrating that our technique is an excellent alternative to various series solution methods. Our approach utilizes the simple limit principle at zero, making it the easiest way to extract series solutions, while variational iteration, Adomian decomposition, and homotopy perturbation methods require integration. Moreover, our technique is also superior to the residual method by eliminating the need for derivatives, as fractional integration and differentiation are particularly challenging in fractional contexts. Significantly, our technique is simpler than other series solution techniques by not relying on Adomian's and He's polynomials, thereby offering a more efficient way of solving nonlinear problems. [ABSTRACT FROM AUTHOR]

Piecewise fractional-order differential operators have received more attention in recent years because they can be used to describe various evolutionary dynamical problems to investigate crossover behaviors. In this manuscript, we use the aforementioned operators to investigate a mathematical model of COVID-19. By utilizing fractional calculus, our approach aims to capture the crossover dynamics of disease spread, considering heterogeneity and transitions between epidemic phases. This research seeks to develop a framework using specialized mathematical techniques, such as the Caputo fractional derivative, with the potential to investigate the crossover dynamical behaviors of the considered epidemic model. The anticipated contribution lies in bridging fractional calculus and epidemiology, offering insights for both theoretical advancements and practical public health interventions. In order to improve our understanding of epidemic dynamics and support, we used MATLAB to simulate numerical results for a visual representation of our findings. For this interpretation, we used various fractional-order values. In addition, we also compare our simulated results with some reported results for infected and death classes to demonstrate the efficiency of our numerical method. [ABSTRACT FROM AUTHOR]

In the present research, we consider a biological model of serum hepatitis disease. We carry out a detailed analysis of the mentioned model along with a class with asymptomatic carriers to explore its theoretical and numerical aspects. We initiate the study by using the piecewise fractal–fractional derivative (FFD) by which the crossover effects within the model are examined. We split the time interval into subintervals. In one subinterval, FFD with a power law kernel is taken, while in the second one, FFD with an exponential decay kernel of the proposed model is considered. This model is then studied for its disease-free equilibrium point, existence, and Hyers–Ulam (H-U) stability results. For numerical results of the model and a visual presentation, we apply the Lagrange interpolation method and an extended Adams–Bashforth–Moulton (ABM) method, respectively. [ABSTRACT FROM AUTHOR]

In this research work, we use the concepts of contraction mapping to establish the existence and uniqueness results and also study the averaging principle in L p space by using Jensen's, Grönwall–Bellman's, Hölder's, and Burkholder–Davis–Gundy's inequalities, and the interval translation technique for a class of fractional neutral stochastic differential equations. We establish the results within the framework of the Ψ -Caputo derivative. We generalize the two situations of p = 2 and the Caputo derivative with the findings that we obtain. To help with the understanding of the theoretical results, we provide two applied examples at the end. [ABSTRACT FROM AUTHOR]

We show how phase-sensitive manipulation of a probe field transmission spectrum can be used to find the precise position of an atom. Our method is based on the controlled superposition of two standing wave fields that move in opposite directions. This causes a change in the probe field transmission spectrum. We can control the number and position of localized peaks in the transmission spectrum by changing the relative phase between the two standing waves. We also show that the shift of localized peaks is greatly influenced by the direction of the wave vector in standing wave fields. Our proposed approach provides us with an efficient method of regulating the precise locations of an atom by using phase shift and direction of the wave vector associated with the standing wave fields. This proposal may have potential applications in nano-lithography, advanced laser cooling technology, and quantum information processing. [ABSTRACT FROM AUTHOR]

An interval-valued q-rung orthopair fuzzy set ( I V q r O F S ) is a robust and esteemed model in managing imprecise information, utilizing a controllable parameter q ≥ 1 . Expanding its applicability, we propose a refinement to it, termed the interval-valued p,q-rung orthopair fuzzy set, denoted I V p , q r O F S . This advancement enables the handling of scenarios where varied assessment levels for membership and non-membership grades are necessary, a challenge unaddressed by existing extensions of interval-valued intuitionistic fuzzy sets. We establish the fundamental mathematical operations for the I V p , q r O F S and explore their key properties. To compare interval-valued p,q-rung orthopair fuzzy ( I V p , q r O F ) numbers, a novel score function is put forward and compared to the known I V q r O F S -based score functions to determine its viability. Moreover, we present I V p , q r O F aggregation operators (AOs), accompanied by rigorous proof of their essential characteristics, including boundedness, monotonicity, and symmetry. This study introduces the interaction of I V p , q r O F criteria through the inter-criteria correlation (CRITIC) approach. This method determines criteria weights based on the proposed distance measurements and the score function. The CRITIC method is integrated with the exponential TODIM approach (exp-TODIM), resulting in an innovative decision-making framework that is less susceptible to parameter fluctuations and showcases a high stability. An illustrative example of selecting a suitable supplier is provided to demonstrate the practical application of the developed exp-TODIM approach. Finally, a sensitivity analysis is conducted to exhibit the method's stability, and a comparative analysis is performed to elucidate its strengths and advantages. [ABSTRACT FROM AUTHOR]

The main goals of this paper are to provide an introduction to the idea of interval-valued n -polynomial s -type convex functions and to investigate the algebraic properties of this type of function. This new generalization aims to show the existence of new Hermite–Hadamard inequalities for the recently presented class of interval-valued n -polynomials of s -type convex describing the φ -fractional integral operator. In the classical sense, some special cases are figured out, and the two examples are also given. There are some recently discovered inequalities for interval-valued functions that are regulated by fractional calculus applicable to interval-valued n -polynomial s -type convexity. The results obtained show that future research will be simple to implement, highly efficient, feasible, and extremely precise in its investigation. It could also help solve modeling problems, optimization problems, and fuzzy interval-valued functions that involve both discrete and continuous variables. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a more generalized class of convex stochastic processes and explore some of their algebraic properties. This new class of stochastic processes is called the n -polynomial s -type convex stochastic process. We demonstrate that this new class of stochastic processes leads to the discovery of novel Hermite–Hadamard type inequalities. These inequalities provide upper bounds on the integral of a convex function over an interval in terms of the moments of the stochastic process and the convexity parameter s. To compare the effectiveness of the newly discovered Hermite–Hadamard type inequalities, we also consider other commonly used integral inequalities, such as Hölder, Hölder–Ïşcan, and power-mean, as well as improved power-mean integral inequalities. We show that the Hölder–Ïşcan and improved power-mean integral inequalities provide a better approach for the n -polynomial s -type convex stochastic process than the other integral inequalities. Finally, we provide some applications of the Hermite–Hadamard type inequalities to special means of real numbers. Our findings provide a useful tool for the analysis of stochastic processes in various fields, including finance, economics, and engineering. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of numerical solution and stability of a chemostat model under fractal-fractional order derivative. First, we investigate the positivity and roundedness of the solution of the considered system. Second, we find the existence of a solution of the considered system by employing the Banach and Schauder fixed-point theorems. Furthermore, we obtain a sufficient condition that allows the existence of the stabling of solutions by using the numerical-functional analysis. We find that the proposed system exists as a unique positive solution that obeys the criteria of Ulam–Hyers (U-H) and generalized U-H stability. We also establish a numerical analysis for the proposed system by using a numerical scheme based on the Lagrange interpolation procedure. Finally, we provide two numerical examples to verify the correctness of the theoretical results. We remark that the structure described by the considered model is also sometimes called side capacity or cross-flow model. The structure considered here can be also seen as a limiting case of the pattern chemostats in parallel with diffusion connection. Moreover, the said model forms in natural and engineered systems and can significantly affect the hydrodynamics in porous media. Fractal calculus is an excellent tool to discuss fractal characteristics of porous media and the characteristic method of the porous media. [ABSTRACT FROM AUTHOR]

The concept of linear Diophantine fuzzy set (LDFS) theory with its control parameters is a strong model for machine learning and data-driven multi-criteria decision making (MCDM). The sine-trigonometric function (STF) has two significant features, periodicity and symmetry about the origin that are very useful tools for information analysis. Keeping in view the characteristics of both STF and LDFS theory, this article introduces the sine-trigonometric operations for linear Diophantine fuzzy numbers (LDFNs). These operational laws lay a foundation for developing new linear Diophantine fuzzy sine-trigonometric aggregation operators (LDFSTAOs). The integration of Industry 4.0 technology into healthcare has the potential to revolutionize patient care. One of the most challenging tasks is the selection of efficient suppliers for the healthcare supply chain (HSC). The traditional suppliers are not efficient in accordance with Industry 4.0, with particular uncertainties. A new MCDM framework is presented based on LDFSTAOs to examine the HSC performance in industry 4.0. A credibility test, sensitivity analysis and comparative analysis are performed to express the novelty, reliability, and efficiency of the proposed methodology. [ABSTRACT FROM AUTHOR]

This manuscript is devoted to using Bernoulli polynomials to establish a new spectral method for computing the approximate solutions of initial and boundary value problems of variable-order fractional differential equations. With the help of the aforementioned method, some operational matrices of variable-order integration and differentiation are developed. With the aid of these operational matrices, the considered problems are converted to algebraic-type equations, which can be easily solved using computational software. Various examples are solved by applying the method described above, and their graphical presentation and accuracy performance are provided. [ABSTRACT FROM AUTHOR]

This research work is devoted to undertaking a dynamical system representing SARS-CoV-19 disease under the concept of piecewise fractional-order derivative using the Caputo concept since long-memory and short-memory terms are not well explained by ordinary fractional differential equations. It has been found that for such disruption, piecewise operators of fractional derivatives have been found useful in many cases. Therefore, we study a compartmental model of susceptible and infected individuals under the concept of piecewise derivative. We establish the existence theory of the considered model by using some Banach and Schauder fixed-point theorems. Keeping the importance of stability, a pertinent result related to the said area is also developed. The said concept of stability is based on the concept given by Ulam and Hyers. Further, to derive the numerical results, we use the Euler method to develop a numerical scheme for the considered model. Using real available data, we have presented various graphical presentations of two compartments against different fractional orders and various values of isolation parameters. The crossover behaviors in the dynamics can be clearly observed, which is explained by the piecewise operators, not the usual fractional-order derivative. [ABSTRACT FROM AUTHOR]

The main objective of this study is the use of Taylor’s series method for approximate solution of HIV-1 infection model. This method explores to solve a system of ODE expressed as an infinite series. These series components are easily determined. The presented method’s effectiveness and reliability are shown using a numerical example, and the consequences are evaluated to those acquired from different techniques in the research using tables and graphs. The proposed method has no assumptions about small or large parameters, and the technique’s accuracy increases when the order of approximation is increased. The results reveal that the approximate solution obtained through the use of Taylor's series method is more reliable and accurate. [ABSTRACT FROM AUTHOR]

These days the whole world is facing a serious problem of infectious maladies and how to control the endemic of these diseases. Testing correctly is one of the most important procedures in preventing the spread of infectious diseases, as incorrect testing can turn a susceptible person into an infected person. In this paper, we study the dynamics of imperfect testing and diagnostics of infectious diseases model by replacing the integer order derivative in the sense of fractional order Atangana–Baleanu operator coupled with Caputo operator. This AB-fractional operator is the generalization of classical derivative and gives more data of the factors of the nonlocal dynamical frameworks. Fixed point theorems have been used for the verification of existence results and Picard's stability technique utilized for the stability study of a fractional order imperfect testing infectious disease (ITID) model. Finally, numerical computations are implemented for the fractional order ITID model to illustrate the results graphically. [ABSTRACT FROM AUTHOR]

Four-dimensional continuous chaotic models with Caputo fractional derivative are presented. Fixed point theory is used to investigate the existence and uniqueness of complex systems. The dynamical properties are studied, including the Lyapunov exponent, phase portrait, and time series analysis. The hyperchaotic nature of each system is revealed by the positive exponents. The numerical method is introduced to describe the influence of the order of the Caputo fractional derivative. The phase portraits are presented to investigate the behavior and effect of some key parameters and fractional orders on model dynamics. The systems approach fixed point attractors for fractional-order and increase the visibility of the attractor by decreasing fractional order. This means that a change in fractional order has a significant impact on the dynamics of the models. When the order of the derivative is equal to one, both systems oscillate frequently. However, as the fractional order is reduced, the system oscillations decrease as compared to the integer-order, and the system moves towards its fixed point, reveals the hidden attractors inherent in the system, and enabling it to develop to a stable state more efficiently. [ABSTRACT FROM AUTHOR]

We investigate a general sequential hybrid class of fractional differential equations in the Caputo and Atangana–Baleanu fractional senses of derivatives. We consider the existence and uniqueness of solutions and the Hyers–Ulam (H-U) stability for a general class. We use the Banach and Leray–Schauder alternative theorems for the existence criteria. With the help of nonnegative Green's functions, the fractional-order class is turned into m-equivalent integral forms. As an application of our problem, a fractional-order smoking model in terms of the Atangana–Baleanu derivative is presented as a particular case. [ABSTRACT FROM AUTHOR]

On the grounds of few perceived Gronwall inequalities, we inspect some new relevant nonlinear dynamic inequalities on time scales related to one independent variable. To guarantee the evenness of information division and with the conversation of peculiar cases, it is indicated that these inequalities catch dynamic, delay, Volterra–Fredholm, discrete, fractional, etc. The inequalities suggested right here to other specific bounds on unknown parameters may be handled as powerful equipment for determining the features of various dynamic equations on time scales. It is trusted that this research plan will open new possibilities in in-depth examination of time scale scheme structure of varying nature. [ABSTRACT FROM AUTHOR]

This work is devoted to derive some existence and uniqueness (EU) conditions for the solution to a class of nonlinear delay non-autonomous integro-differential Cauchy evolution problems (CEPs) under Caputo derivative of fractional order. The required results are derived via topological degree method (TDM). TDM is a powerful tool which relaxes strong compact conditions by some weaker ones. Hence, we establish the EU under the situation that the nonlinear function satisfies some appropriate local growth condition as well as of non-compactness measure condition. Furthermore, some results are established for Hyers–Ulam (HU) and generalized HU (GHU) stability. Our results generalize some previous results. At the end, by a pertinent example, the results are verified. [ABSTRACT FROM AUTHOR]

This manuscript investigates fractal-fractional order smoking models with relapse and harmonic mean type incidence rate under the Caputo derivative. We derive the existence and unique results about the solution for the considered model via fixed point theory. For the stability of the considered system, Ulam-Hyers (UH) approach is used. We compute the numerical solution by using fractional Adams-Bashforth method. For the simulation of the model, we consider different values of fractional order δ and fractal dimension θ by using some real values of the parameters. The proposed scheme is used to simulate the available data for some smoking community including potential, light, and quit smokers. Various graphical presentations are given to understand the dynamics of the model at various fractional orders. [ABSTRACT FROM AUTHOR]

We investigate a nonlinear system of pantograph-type fractional differential equations (FDEs) via Caputo-Hadamard derivative (CHD). We establish the conditions for existence theory and Ulam-Hyers-type stability for the underlying boundary value system (BVS) of FDE. We use Krasnoselskii's and Banach's fixed point theorems to obtain the desired results for the existence of solution. Stability is an important aspect from a numerical point of view we investigate here. To justify the main work, relevant examples are provided. [ABSTRACT FROM AUTHOR]

Our manuscript is devoted to investigating a class of impulsive boundary value problems under the concept of the Riemann-Liouville fractional order derivative. The subject problem is of implicit type. We develop some adequate conditions for the existence and puniness of a solution to the proposed problem. For our required results, we utilize the classical fixed point theorems from Banach and Scheafer. It is to be noted that the impulsive boundary value problem under the fractional order derivative of the Riemann-Liouville type has been very rarely considered in literature. Finally, to demonstrate the obtained results, we provide some pertinent examples. [ABSTRACT FROM AUTHOR]

We construct a subclass of Copson's integral inequality in this article. In order to achieve this goal, we attempt to use the Steklov operator for generalizing different inequalities of the Copson type relevant to the situations r > 1 as well as r < 1. We demonstrate the inequalities with the guidance of basic comparison, Holder's inequality, and the integration by parts approach. Moreover, some new variations of Hardy's integral inequality are also presented with the utilization of Steklov operator. We also formulate many remarks and two examples to show the novelty and authenticity of our results. [ABSTRACT FROM AUTHOR]

Discrete fractional calculus (DFC) is suggested to interpret neural schemes with memory impacts. This study seeks to formulate some discrete fractional nonlinear inequalities with ξ ̂ fractional sum operators that are used with some conventional and forthright inequalities. Taking into consideration, we recreate the explicit bounds of Gronwall-type inequalities by observing the principle of DFC for unknown functions here. Such inequalities are of new version relative to the current literature findings so far and can be used as a helpful method to evaluate the numerical solutions of discrete fractional differential equations. We show a few uses of the rewarded inequalities to mirror the advantages of our work. Regarding applications, we can apply the acquainted results to discuss boundedness, uniqueness, and continuous dependency on the initial value problem for the solutions of certain underlying worth problems of fractional difference equations. The leading consequences may be proven by the usage of the analysis process and the methodology of the mean value theorem. These variations can be used as an advantageous device in the subjective examination solutions of discrete fractional difference equations. [ABSTRACT FROM AUTHOR]

This content replicates some discrete nonlinear fractional inequalities by virtue of the fractional sum operator Ψ ¯ on time scales. Through the recognition of the principle of discrete fractional calculus, we are able to recover the precise estimates for unknown functions of inequalities of the Gronwall type. The resultant inequalities are of unique structure comparative with the latest reviewing disclosures and can be described as a complementary tool for numerically testing the solutions of discrete partial differential equations. The foremost consequences are probably confirmed via handling of assessment procedure and technique of mean value speculation. We display few examples of the proposed inequalities to represent the incentives of our effort. [ABSTRACT FROM AUTHOR]

By means of ς fractional sum operator, certain discrete fractional nonlinear inequalities are replicated in this text. Considering the methodology of discrete fractional calculus, we establish estimations of Gronwall type inequalities for unknown functions. These inequalities are of a new form comparative with the current writing discoveries up until this point and can be viewed as a supportive strategy to assess the solutions of discrete partial differential equations numerically. We show a couple of employments of the compensated inequalities to reflect the benefits of our work. The main outcomes might be demonstrated by the use of the examination procedure and the approach of the mean value hypothesis. [ABSTRACT FROM AUTHOR]

The objective of this research is to formulate a specific class of integral inequalities of Gronwall kind concerning retarded term and nonlinear integrals with time scales theory. Our results generate several new inequalities that reflect continuous and discrete form, as well as giving the unknown function an upper bound estimate. The effectiveness of such inequalities arises from the belief that it is widely relevant in unique circumstances where there is no valid utilization of various available inequalities. Applications are additionally represented to display the legitimacy of built-up hypotheses. [ABSTRACT FROM AUTHOR]

The objective of this research is to formulate a specific class of integral inequalities of Gronwall kind concerning retarded term and nonlinear integrals with time scales theory. Our results generate several new inequalities that reflect continuous and discrete form, as well as giving the unknown function an upper bound estimate. The effectiveness of such inequalities arises from the belief that it is widely relevant in unique circumstances where there is no valid utilization of various available inequalities. Applications are additionally represented to display the legitimacy of built-up hypotheses. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to set up some new estimates of a specific class of dynamic integral inequalities (DII) which are partially linear on a time scale T with two independent variables. These, from the one hand, sum up and, on the other hand, offer a helpful method for both the qualitative and quantitative study of dynamic equations on time scales. Some applications are taken into consideration to show the validity of the fundamental results. [ABSTRACT FROM AUTHOR]

In this paper, we build up some generalizations of nonlinear integral inequalities and recreate the results of some Pachpatte's inequalities on time scales. We not just settle new estimated bounds of a particular class of nonlinear retarded dynamic inequalities, but additionally determine and unify continuous analogs alongside a subjective time scale T . We demonstrate applications of the treated inequalities to reflect the benefits of our work. The key effects will be proven by using the analysis procedure and the standard time-scale comparison theorem technique. [ABSTRACT FROM AUTHOR]

By the utilization of diamond-α derivatives, certain new generalizations of Ou-Iang type of dynamic integral inequalities of one independent variable on time scales are examined. The resulting inequalities are significant in the study of various fields of dynamic equations. A few mathematical applications are also presented. [ABSTRACT FROM AUTHOR]

This paper investigates some system of integral inequalities of one independent variable on time scales. The conclusion can be obtained by using Hadamard-type fractional differential equations and Greene's method which bring together and expand some integral inequalities on time scales. The established inequalities give explicit bounds on unknown functions which can be utilized as a key in examining the properties of certain classes of partial dynamic equations and difference equations on time scales. As an application, a system of fractional differential equations is considered to explain the value of our results. [ABSTRACT FROM AUTHOR]

The aim of the study is to investigate the biochemical composition of grapeseed oil and cake from an unexplored Indian grape‐juice cultivar, Manjari Medika (MM). The composition of oil and residual seed cake is evaluated using various chromatographic and spectroscopic techniques. The findings demonstrate that the vitamin E content of MM‐seed oil (1.15–1.35 g kg−1) is distinctively higher than the Codex standard, suggesting its superior quality as an edible oil. The predominant triacylglycerols include trilinolein (LLL, 43%), dilinoleoyl‐stearylglycerol (LSL, 19%), and dilinoleoyl‐palmitoylglycerol (LLP, 11%), which are earlier recognized as natural antioxidants. The seed‐cake is rich in polyphenols including acylated anthocyanins (e.g., pelargonidin‐3‐O‐coumaroyl glucoside) and certain other flavonoids (e.g., catechin). The profile of phytonutrients in MM seed‐oil and cake is significantly superior to its seeded female parent and two other widely cultivated wine‐grape varieties. In brief, the studied by‐products of this new grape‐juice cultivar can be an important source of high‐value ingredients for use in food supplements, nutraceuticals, and functional foods. Practical applications: This study reports the phytochemical profile of the seed‐oil and seed cake derived from a newly developed grape variety, Manjari Medika. High contents of selective antioxidants: lipids, vitamin E, and phenols in the seed‐oil and cake with health benefits suggest their potential for use in nutraceutical and functional foods. These byproducts can be utilised as ingredients of functional foods and nutraceuticals (e.g., grape seed oil capsule) and also as raw materials in food supply chains (e.g., for production of grape cookies or cake). MM can also be utilized as a colorant in the food industry. [ABSTRACT FROM AUTHOR]

Several inequalities were proved in 2018 by Boudeliou, in 2015 by Abdeldain and El-Deeb and in 1998 by Pachpatte. It is our aim in this paper to generalize these inequalities to time scales. Beside that, we also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as special cases. Furthermore, we study the boundedness of some problems by applying our results. [ABSTRACT FROM AUTHOR]

Background: False detection of pesticides in agricultural produce may raise serious questions regarding both consumer safety and trade. High levels of delta-hexachlorocyclohexane (δ-HCH; 11.7-22.3 mg/kg) were detected in some tobacco samples in a retention time-based GC analysis. Hence, the selection of an appropriate analytical method is an uncompromisable necessity. Objectives: This research work aimed to elucidate false detection of pesticides along with identification of coeluting tobacco matrix compounds to understand the dynamics of false detection with an increase in the number of analyzed pesticides and to screen suitable analytical methods. Methods: Initially, retention time-based GC analysis was performed for monitoring of 10 pesticide residues in tobacco leaf matrix, followed by GC-MS/selected-ion monitoring (SIM) analysis. Then, the total number of pesticides to be analyzed was increased to 47, and residue analysis was performed by involving GC-MS/SIM and multidimensional (MD) GC-MS. Results: A false-positive detection of δ-HCH due to a coeluting tobacco aroma compound, neophytadiene, during residue analysis of 10 pesticides in tobacco (Nicotiana tabacum L.) leaf was observed. This problem was resolved by employing the unique quantifier and qualifier ions in SIM mode. However, with 47 pesticides, neophytadiene completely masked the signal of δ-HCH, which resulted in an impure spectrum of δ-HCH (<30% similarity match) even after application of selective quantifier and qualifier ions. Finally, MDGC-MS analysis could resolve it by chromatographic separation of the said analyte from the coeluting matrix compound. Conclusions: The findings of this work offer the potential to minimize false reporting of target pesticides to comply with consumer safety and trade standards. Highlights: The study identifies various tobacco matrix compounds coeluting with pesticides during multiresidue analysis. Neophytadiene, a tobacco aroma compound, resulted in false-positive detection of δ-HCH. The MDGC-MS could be effectively used as a confirmatory analysis tool for reliable detection of pesticide residue in tobacco leaf matrix. [ABSTRACT FROM AUTHOR]

We investigate a certain class of nonlinear Gronwall–Bellman–Pachpatte type of integral inequalities involving retarded term and nonlinear integrals. Our results derive some new inequalities as well as give an upper bound estimation of the unknown function. The significance of these inequalities originate from the truth that it is far applicable in specific situations in which different available inequalities do not apply legitimately. Our consequences additionally can be used as powerful tools in the analysis of certain classes of differential equations, integral equations, and evolution equations. An example is also illustrated to show the validity of our established theorems. [ABSTRACT FROM AUTHOR]

A greedy algorithm in combination with radial basis functions partition of unity collocation (GRBF‐PUC) scheme is used as a locally meshless method for American option pricing. The radial basis function partition of unity method (RBF‐PUM) is a localization technique. Because of having interpolation matrices with large condition numbers, global approximants and some local ones suffer from instability. To overcome this, a greedy algorithm is added to RBF‐PUM. The greedy algorithm furnishes a subset of best nodes among the points X. Such nodes are then used as points of trial in a locally supported RBF approximant for each partition. Using of greedy selected points leads to decreasing the condition number of interpolation matrices and reducing the burdensome in pricing American options. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate and extend some Pachpatte type dynamic inequalities on time scales in three independent variables which provide explicit bounds on unknown functions and their derivatives. Some applications are also discussed here in order to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate and extend some Pachpatte type dynamic inequalities on time scales in three independent variables which provide explicit bounds on unknown functions and their derivatives. Some applications are also discussed here in order to illustrate the usefulness of our results. [ABSTRACT FROM AUTHOR]

Highlights • Comprehensive multiresidue analysis of pesticides in grapevine leaf matrix. • The scope of the method also covers plant growth regulators. • A high throughput QuEChERS-based workflow is optimized for sample preparation. • The GC–MS/MS and LC–MS/MS method performance are demonstrated at ≥0.01 mg/kg. • The method performance complied with the SANTE/11813/2017 guidelines and EU-MRLs. Abstract Grape leaf, which is known for its nutritional and medicinal properties, is finding increased applications for cuisine and remedial purposes. This article reports a comprehensive analytical method for the identification and quantification of a broad range of pesticides and plant growth regulators (PGRs) in the grape leaf matrix. The sample preparation method for pesticides involved an optimized QuEChERS-based extraction protocol, with subsequent clean-up by the dispersive solid phase extraction (dSPE) using a mixture of sorbents (25 mg PSA + 5 mg GCB + 150 mg MgSO 4). The PGRs were extracted with methanol. The performance of the method was investigated and validated for a mixture of 363 pesticides (148 in GC–MS/MS and 203 in LC–MS/MS) and 12 PGRs (LC–MS/MS) in compliance with the analytical quality control criteria of the SANTE/11813/2017 guidelines. The matrix effects were comparatively higher against grape berries. The findings indicated satisfactory recoveries at 10 ng/g and higher levels with precision RSDs less than 20%. This method has potential applications in commercial residue testing laboratories and also for the regulatory compliance check purposes for its lower LOQs compared to the corresponding EU-MRLs. [ABSTRACT FROM AUTHOR]

Tuber crops substantially contribute to the food security in the developing countries. Often, their cultivation involves unregulated applications of pesticides, leading to MRL non-compliances. Despite their rising currency in international trade, there exist scarcely any methods for pesticide residue analysis in these matrices. Therefore, we developed a multi-residue method for simultaneous analysis of a diverse range of pesticides in tuber crops, based on pressurized liquid extraction by ethyl acetate, followed by selective identification and quantification of the residues using GC–MS selected reaction monitoring. The method was evaluated for 150 pesticides. Results showed that their limits of quantification were 0.1–10 ng/g, with recoveries of 70–120%. When compared to the conventional analytical techniques, such as QuEChERS and buffered ethyl acetate extraction, this method provided superior performance in terms of precision, and recovery of the spiked and incurred residues with similar productivity. The method holds promise for commercial and regulatory residue analysis. [ABSTRACT FROM AUTHOR]

A novel screening and quantitation method is reported for non-target multiresidue analysis of pesticides using ultra-HPLC-quadrupole-Orbitrap mass spectrometry in spice matrices, including black pepper, cardamom, chili, coriander, cumin, and turmeric. The method involved sequential full-scan (resolution = 70,000), and variable data independent acquisition (vDIA) with nine consecutive fragmentation events (resolution = 17,500). Samples were extracted by the QuEChERS method. The introduction of an SPE-based clean-up step through hydrophilic-lipophilic-balance (HLB) cartridges proved advantageous in minimizing the false negatives. For coriander, cumin, chili, and cardamom, the screening detection limit was largely at 2 ng/g, while it was 5 ng/g for black pepper, and turmeric. When the method was quantitatively validated for 199 pesticides, the limit of quantification (LOQ) was mostly at 10 ng/g (excluding black pepper, and turmeric with LOQ = 20 ng/g) with recoveries within 70–120%, and precision-RSDs <20%. Furthermore, the method allowed the identification of suspected non-target analytes through retrospective search of the accurate mass of the compound-specific precursor and product ions. Compared to LC–MS/MS, the quantitative performance of this Orbitrap-MS method had agreements in residue values between 78–100%. [ABSTRACT FROM AUTHOR]

The goal of this paper is to achieve some new results related to integrodifferential inequalities of one independent variable which can be applied as a study of qualitative and quantitative properties of solutions of some nonlinear integral equations. [ABSTRACT FROM AUTHOR]

TGFβ1 is the most pleiotropic of all known cytokines and thus, to avoid uncontrolled TGFβ-activated processes, its activity is tightly regulated. Studies in fibrosis have led to the discovery that αv integrins are the major regulators of the local activation of latent TGFβ in our tissues. Since all cells can express one or more types of αv integrins, this raises the possibility that, in the complex milieu of a developing cancer, multiple cell types including both cancer cells and stromal cells activate TGFβ. In normal tissues, TGFβ1 is a tumour suppressor through its ability to suppress epithelial cell division, whereas in cancer, in which tumour cells develop genetic escape mechanisms to become resistant to TGFβ growth suppression, TGFβ signalling creates a tumour-permissive environment by activating fibroblast-to-myofibroblast transition, by promoting angiogenesis, by suppressing immune cell populations and by promoting the secretion of both matrix proteins and proteases. In addition, TGFβ drives epithelial-to-mesenchymal transition (EMT) increasing the potential for metastasis. Since αv integrins activate TGFβ, they almost certainly drive TGFβ-dependent cancer progression. In this review, we discuss the data that are helping to develop this hypothesis and describe the evidence that αv integrins regulate the TGFβ promotion of cancer. [ABSTRACT FROM AUTHOR]

Public exposure to pesticide residues through the main/side-stream smoke of tobacco ( Nicotiana tabacum L.) is an international concern. This article reports optimization and validation of large-scale multiresidue analysis methods involving low pressure and traditional gas chromatography tandem mass spectrometry in compliance with the guidance residue levels (GRLs) of Cooperative Centre for Scientific Research Relative to Tobacco (CORESTA). Analysis by low pressure GC–MS/MS offered three times rapid turn around time over the traditional GC–MS/MS with limits of quantifications (LOQs) less than 2 μg/L for all the 259 test compounds and the recoveries in the range of 70–118% (±20%) at 10 and 20 μg/kg levels of fortification. [ABSTRACT FROM AUTHOR]

Endophytes have been isolated from a large diversity of plants and have been shown to enhance the remediation efficiency of plants, but little information is available on the influence of endophytic bacteria on phytoremediation of widespread environmental contaminants such as polycyclic aromatic hydrocarbons (PAHs). In this study we selected a naturally occurring endophyte for its combined ability to colonize plant roots and degrade phenanthrene in vitro. Inoculation of two different willow clones and a grass with Pseudomonas putida PD1 was found to promote root and shoot growth and protect the plants against the phytotoxic effects of phenanthrene. There was an additional 25-40% removal of phenanthrene from soil by the willow and grasses, respectively inoculated with PD1 when compared to the uninoculated controls. Fluorescent microscopy using fluorescent protein tagging of PD1 confirmed the presence of bacteria inside the root tissue. Inoculation of willows with PD1 consistently improved the growth and health when grown in hydroponic systems with high concentrations of phenanthrene. To our knowledge this is the first time that the inoculation of willow plants has been shown to improve the degradation of PAHs and improve the health of the host plants, demonstrating potential wide benefit to the field of natural endophyte-assisted phytoremediation. [ABSTRACT FROM AUTHOR]

In this work, we introduce new definitions of left and right-sides generalized conformable K -fractional derivatives and integrals. We also prove new identities associated with the left and right-sides of the Hermite-Hadamard-Fejér type inequality for ϕ -preinvex functions. Moreover, we use these new identities to prove some bounds for the Hermite-Hadamard-Fejér type inequality for generalized conformable K -fractional integrals regarding ϕ -preinvex functions. Finally, we also present some applications of the generalized definitions for higher moments of continuous random variables, special means, and solutions of the homogeneous linear Cauchy-Euler and homogeneous linear K -fractional differential equations to show our new approach. [ABSTRACT FROM AUTHOR]