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This study investigates weakly singular nonlinear functional Volterra integral equations (WSNFVIEs) of Urysohn type involving Riemann–Liouville operator. By imposing specific smoothness conditions on the involved functions, we establish both the existence and uniqueness of the solution using a fixed point approach. Subsequently, we employ discretization methods such as the trapezoidal and Euler methods to approximate the solution, resulting in a system of nonlinear algebraic equations. To ascertain the convergence order of the Euler method (first order) and the trapezoidal method (second order), we utilize the Grönwall inequality and its discrete counterpart. Additionally, we introduce a novel Grönwall inequality to establish the convergence of the trapezoidal method. Thoroughly we examine the Hyers–Ulam–Rassias and Hyers–Ulam stability of the integral equations within the specified domain. Finally, the efficacy of the proposed methods is validated through numerical examples accompanied by comparative analyses. [ABSTRACT FROM AUTHOR]

In this paper, we prove the controllability of mild solutions of neutral functional evolution equations with state-dependent delay and nonlocal conditions. We establish the non local controllability of mild solutions under certain conditions by combining Avramescu's nonlinear alternative for the sum of compact and contraction operators in Fréchet spaces with semigroup theory. [ABSTRACT FROM AUTHOR]

In the present work a class of p-Laplacian fractional hybrid-Sturm-Liouville-Langevin integro-differential equations with functional boundary value conditions involving Caputo-Hadamard fractional derivative is studied. Using the hybrid fixed point theorem for three operators by Dhage, the existence result is obtained. Finally, an example is given to illustrate the main result. [ABSTRACT FROM AUTHOR]

In this work, to show the existence and uniqueness solution of functional integrodifferential equation with nonlocal condition and finite delay function. This article contains continuously dependence of integral solution and existence of strict solution established by using integrated resolvent operator theory with support of Lipschitz continuous. In this article the operator (T (t)) t ⩾ 0 is assumed the locally Lipschitz continuous integrated resolvent operator and proved the existence of strict solution on reflexive and general Banach spaces. Finally an example is given related to this work. [ABSTRACT FROM AUTHOR]

This paper introduces a new concept of Caputo type interval-valued fractional conformable calculus. Based on this, some theorems and properties related to fractional conformable calculus are presented. As an application, this paper attempts to investigate an initial value problem of functional integro-differential equations with Caputo type interval-valued fractional conformable derivatives. We not only prove the existence of at least one solution, the extremal solutions and the unique solution of the above problem, but also establish some monotone iterative sequences converging to the extremal solutions. More meaningful and important, some comparison principles and generalized Gronwall inequality related to the proposed problem are also proved. Two examples are presented to illustrate the main results. We firmly believe that the concept of interval-valued fractional conformable calculus, new comparison principles and generalized Gronwall inequality introduced here can be conveniently applied to qualitative analysis of a variety of new interval-valued fractional conformable biological models, economic models, etc., which will better describe and explain various complex phenomena derived from the real world. [ABSTRACT FROM AUTHOR]

[Display omitted] • Columbic repulsion and ionic strength affects the rate of free radical reactions. • This relationship can be effectively modelled using the Debye-Smoluchowski equation. • The effect is modest when both species carry a single negative charge. The rate constant for the reaction of CO 3 ∙ - with anionic species could be influenced by Columbic forces and ionic strength of the cellular environment. We investigated the reaction of CO 3 ∙ - with urate, ascorbate and caffeate at the M06-2X/6–311 + G(d,p) level in an aqueous environment. The thermal rate constant was adjusted using the Debye-Smoluchowski and Brønsted-Bjerrum equations. Electrostatic interactions moderately reduced the rate constant for single electron transfer from urate and caffeate to CO 3 ∙ - , but were negligible for the reaction with ascorbate. However, when we took into account the primary kinetic salt effect, the Debye-Smoluchowski rate constants were increased to values close to those predicted without inclusion of the Debye factor. Columbic repulsion and ionic strength have a modest impact on the rate constant for reactions involving an ionic radical. However, if the reactions involved ions of opposite charge, the influence of the Debye function would become more significant. [ABSTRACT FROM AUTHOR]

If a colleague of mine, whose opinion I respect, disagrees with me about some claim, this might give me pause regarding my position on the matter. The Equal Weight view proposes that in such cases of peer disagreement I ought to give my colleague's opinion as much weight as my own, and decrease my certainty in the disputed claim. One prominent criticism of the Equal Weight view is that treating higher-order (indirect) evidence in this way invariably swamps first-order (direct) evidence. While the opinions of our peers matter in our deliberations, the Equal Weight view counter-intuitively requires that evidence of mere disagreement is more important than standard kinds of evidence. I offer a proposal for how we should idealize epistemic agents that identifies the variable feature of disagreements that accounts for the shifting significance of direct and indirect evidence in different disagreement contexts. Specifically, by idealizing epistemic agents as deriving functions that characterize the non-subjective relationship between a body of evidence and the reasonableness of believing the various propositions supported by that evidence, we can accommodate the intuition to compromise that motivates the Equal Weight view, without accepting the counter-intuitive results. [ABSTRACT FROM AUTHOR]

Using the techniques of Darbo's fixed-point theorem associated with measures of noncompactness, we investigate the existence results for functional stochastic integral equations in Banach Algebra, which are useful in many real-life problems, such as applied mathematics, physics, and economics problems. Our existence results treat numerous existence results achieved by different authors as special cases. An example is also provided to show the effectiveness of our main results. [ABSTRACT FROM AUTHOR]

In this article, we look at some of the less explored aspects of the gamma function. We provide a new proof of Euler's reflection formula and discuss its significance in the theory of special functions. We also discuss the solution of Landau to a problem posed by Legendre, concerning the determination of values of the gamma function using functional identities. In 1848, Oscar Schlömilch gave an interesting additive analogue of the duplication formula. We prove a generalized version of this formula using the theory of hypergeometric functions. [ABSTRACT FROM AUTHOR]

In this work, the existence of Hilfer fractional integro-differential equations with nonlocal conditions are discussed. To obtain such result, we use M o ¨ nch fixed point theorem and the techniques of noncompactness. An application is presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

Copyright of Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales is the property of Academia Colombiana de Ciencias Exactas, Fisicas y Naturales and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Transactions of Beijing Institute of Technology is the property of Beijing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of MAT-KOL (Banja Luka), Matematicki Kolokvijum is the property of Scientific Society of Mathematicians Banja Luka and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract We propose an Evolutionary Strategy-based One Class Constraint Synthesis (ESOCCS), a novel method for computer-assisted synthesis of constraints for Mathematical Programming models. ESOCCS synthesizes constraints of Linear Programming and Non-Linear Programming types using solely examples of feasible states of the modeled entity. This is a crucial feature from the viewpoint of modeling real-world business processes from data, as acquisition of examples of feasible states is straightforward for a normally operating process, while infeasible states corresponding to errors and faults are avoided in practice and thus uncommon. ESOCCS is verified on a suite of synthetic benchmarks having known model representations and synthesizes models with noticeable fidelity to the known representations in terms of syntax and semantics. We employ ESOCCS and an off-the-shelf solver in a fully automated setup for modeling and optimization of a real-world business process of rice production. The resulting optimal parameters of production are validated in the context of three exemplary rice farms. Likely increase in profit thanks to applying those parameters is concluded. Highlights • We synthesize Mathematical Programming models from one-class training examples. • We use Expectation Maximization, Evolutionary Strategy and Linear Programming. • The synthesized models are assessed using synthetic benchmark problems. • We automate workflow of modeling and optimization of a business process. • We optimize rice production process. [ABSTRACT FROM AUTHOR]

It is proved in this paper that any preassigned system of five and more than five finite quantity squares with total area 1 may be packed in parallel into a rectangle whose area is at least S d =(2 + 3 1/2 )/3. [ABSTRACT FROM AUTHOR]

Many university degree programs (including chemical engineering ones) require final year students and Masters’ students to do an extended research project under the supervision of an academic staff member. However, obtaining a satisfying allocation for both students and supervisors is often a challenging task, especially when the amount of available supervisors is particularly tight and their popularities are highly diverse. In this article we propose a novel method based on a ranked list of supervisors and categories provided by each student, where a category corresponds to a general research area, incorporating this information into the allocation process. A student’s satisfaction may therefore correspond to getting a project either with a highly ranked supervisor and/or in a highly ranked category. With this information, we propose here a systematic approach that relies on a novel mixed-integer linear programming (MILP) model based on a flexible definition of students’ satisfaction. Our MILP overcomes the limitations of manual allocation approaches, which when applied to large cohorts are highly time consuming and may produce suboptimal solutions leading to poor satisfaction levels. This MILP has been applied successfully in the School of Chemical Engineering and Analytical Science of The University of Manchester with increased levels of student satisfaction. [ABSTRACT FROM AUTHOR]

In this paper, the single-machine scheduling problem with convex multiresource dependent processing times, subject to meeting job deadlines, is considered. The objective is to minimize the total cost, including the resource allocation costs and the fixed costs. We assume that the actual processing time of each job (task) is a function of the amount of resources allocated. Therefore, the decision variables of the model are: (1) resources allocated to the jobs; (2) total consumed resources; (3) processing times of the jobs; (4) start/completion times of the jobs. We reformulate and solve the problem using a posynomial geometric programming model. In the proposed exact solution method based on the geometric programming, the original problem of any size is reduced to a two-variable unconstrainted optimization problem, which can be easily solved by a simple grid search. [ABSTRACT FROM AUTHOR]

Image deconvolution is an ill-posed problem that requires a regularization term to solve. The most common forms of image priors used as the regularization term in image deconvolution tend to produce smoothed (slightly blurry) images, hence don’t well reconstruct image details. In this paper, a new image prior is introduced. This prior is used as a regularization term to model the non-blind image deconvolution problem. The complete regularization term consists of two parts: one that penalizes non-sparsity of the gradient, and the other that penalizes the blurriness in the image. The resulting regularization term favors sharp images over blurry ones. It means that the minimum of this term corresponds to the true sharp solution. The minimization problem is non-convex and we propose a scheme based on half-quadratic regularization. We demonstrate the efficiency of the proposed method by performing several quantitative and qualitative comparisons with the existing non-blind image deconvolution methods for deblurring artificial and real blurred images. The experimental results show that the proposed method tends to well reconstruct image details whilst suppresses noise. In addition, the reconstructed images have a higher PSNR and a lower blurriness value compared to those in the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we used the three-dimensional triangular functions (3D-TFs) for the numerical solution of three-dimensional nonlinear mixed Volterra–Fredholm integral equations. First, 3D-TFs and their properties are described. Then the properties of 3D-TFs together with their operational matrix are used to reduce the problem to a nonlinear system of algebraic equations. Furthermore, existence and uniqueness of the solution of three-dimensional nonlinear mixed Volterra–Fredholm integral equations are proved. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique. Also, some interesting comparisons between proposed method, block-pulse functions (BPFs) method and modified block-pulse functions (MBPFs) method are presented. [ABSTRACT FROM AUTHOR]

The article shows the possibility of using mathematical programming methods to obtain optimal solutions of building structures. As an optimization algorithm used the method optimization, based on the property of monotonicity used dependencies. Emphasizes the usefulness of mathematical modeling methods in providing integrated security construction projects and reduce the risk of the onset of failure. [ABSTRACT FROM AUTHOR]

Let f and g be real-valued continuous injections defined on a non-empty real interval I , and let ( X , ℒ , λ ) and ( Y , ℳ , μ ) be probability spaces in each of which there is at least one measurable set whose measure is strictly between 0 and 1. We say that ( f , g ) is a ( λ , μ ) -switch if, for every ℒ ⊗ ℳ -measurable function h : X × Y → R for which h [ X × Y ] is contained in a compact subset of I , it holds f − 1 ( ∫ X f ( g − 1 ( ∫ Y g ∘ h d μ ) ) d λ ) = g − 1 ( ∫ Y g ( f − 1 ( ∫ X f ∘ h d λ ) ) d μ ) , where f − 1 is the inverse of the corestriction of f to f [ I ] , and similarly for g − 1 . We prove that this notion is well-defined, by establishing that the above functional equation is well-posed (the equation can be interpreted as a permutation of generalized means and raised as a problem in the theory of decision making under uncertainty), and show that ( f , g ) is a ( λ , μ ) -switch if and only if f = a g + b for some a , b ∈ R , a ≠ 0 . [ABSTRACT FROM AUTHOR]

In this paper we extend the nonlinear PI method within an integrator backstepping framework. The main idea of our approach is a novel selection of the virtual control laws through suitable nonlinear integral equations. Using the proposed methodology a new robust regulation control scheme is developed for time-varying strict feedback nonlinear systems with unknown control directions. A simulation study demonstrates the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

Fast and accurate simulation of responses of logging-while-drilling (LWD) electromagnetic (EM) tools in complex 2D and 3D formations is very important for reconstruction of the resistivity distribution in proactive geosteering. Currently, real-time interpretation is based on the 1D parametric inversion. Advances in fast simulation beyond the 1D model would open a way for real-time 2D inversion. We developed, implemented numerically, and tested an efficient method for simulation of LWD EM tools in complex 2D formations with an arbitrary 3D position of the tool. The method is based on the boundary integral equations for the tangential components of the field and the Fourier transform, which reduces the problem to a series of 1D integral equations. Computations are carried out simultaneously for the whole set of measurement points with the same matrix, which provides a short computation time per point. We verified the method by comparing our results with those obtained by the well-known explicit 1D method and by commercial software in the 2D case. Numerical results justified that the method is accurate and time efficient. Also, as an example, we simulated the signals of real propagation and azimuthal resistivity tools for a complex 2D formation model with fault. The software based on our method can be useful in planning geosteering jobs in complex formations. [ABSTRACT FROM AUTHOR]

In this paper, the authors established the general solution and generalized Ulam - Hyers stability of the simple additive-quadratic and simple cubicquartic functional equations f(2x) = 3f(x) + f(- x), g(2x) = 12g(x) + 4g(- x), via Banach space using direct and fixed point method. [ABSTRACT FROM AUTHOR]

The main object of research in this article is a study of the continuous solutions set structure of difference-functional equations of the form x (qt) = a(t)x(t) + b(t) x(t + 1) + f (t) , where a (t) , b(t) , f (t) — some real functions and q — real constant. Using methods of the theory of differential and difference equations a question of continuous solutions existence of linear difference-functional equations with constant coefficients was investigated and a building method for them was proposed. In particular for homogeneous equations, a continuous bounded solutions family that depends on an arbitrary continuous 1-periodic function with 0 < q < 1, a > 1 and 0 < a < 1, q > 1 , t — positive was built. Furthermore, if 0 < q < 1, a > 0 , then continuous solutions existence for heterogeneous equations with an arbitrary real value t is proved and continuous bounded solutions family of a heterogeneous equation with an arbitrary nonnegative t are built. [ABSTRACT FROM AUTHOR]

The computational feasibility of many systems with large degrees of freedom such as chemically reacting systems hinges on the reduction of the set to a manageable size with a minimal loss of relevant information. Several sophisticated reduction techniques based on different rationales have been proposed; however, there is no consensus on the best approach or method. While the search for simple but accurate schemes continues, the classical quasi-steady state assumption (QSSA), despite serious shortcomings, remains popular due to its conceptual and computational simplicity. Invoking the similarity between a reduced invariant manifold and a streamline in fluid flow, we develop an advanced QSSA procedure which yields the accuracy of more complex reduction schemes. This flow-physics inspired approach also serves to reconcile the classical QSSA approach with recent methods such as functional equation truncation (FET) and intrinsic low dimensional manifold (ILDM) approaches. [ABSTRACT FROM AUTHOR]

This study examined the development of skills to report with different levels of exactness. A total of 62 first-grade children and 58 fourth-grade children were asked about numbers and lengths (numeral tasks) and colors and positions of objects (nominal tasks) with instructions suggesting different levels of exactness, "roughly" or "exactly". In Study 1, the instructions were given as a between-subjects factor. The results showed that when the "roughly" instruction was given, participants gave approximate answers more frequently than when the "exactly" instruction was given especially in the numeral tasks, and older children did so more frequently than younger children. In Study 2, the instructions were given as a within-subjects factor: a half of participants were given "roughly" and then "exactly" instructions, and the others were given the instructions in the opposite order. The results showed that younger children could change the levels of answers depending on instruction in the numeral tasks but not in the nominal tasks, whereas older children could do so in both tasks. The results suggest that the skills for reporting with different levels of exactness are related not only to cognitive development, but also to the linguistic context, such as the tasks and instructions. [ABSTRACT FROM AUTHOR]

Abstract: Skin marker motion analyses are the most widespread techniques to study human movements. Nevertheless, trajectories obtained through such methods are biased because of soft tissue artifacts and lead, consequently, to false collisions and dislocations when bone motion is under investigation. It's an open challenge to enhance kinematics curves particularly for the knee joint involved in the mechanics of gait. The kinematics of flexion/extension of the knee is classically modeled by a rotation around a fixed axis. However, the trend of current biomechanical studies is to improve this modeling by introducing a morphological knowledge such as ligament constraints. In this paper, we propose to highlight the morpho-functionnal link on this joint thanks to two contributions. The first one consists in proposing a method capable of extracting a kinematics of flexion/extension of the knee from a unique CT scan. This method is based on the determination of a mobile axis capable of keeping the information of rolling/sliding. The second one consists in a qualitative and quantitative temporal analysis of the position of the bones during the movement. We compare the results of the two kinematics (static and mobile axis) using original figures of articular coherence and an associated index. [Copyright &y& Elsevier]

In this paper, by using the fixed point method, we investigate the orthogonal stability of orthogonally Jensen additive functional equation, the orthogonally cubic functional equation and the orthogonally quartic functional equation in non-Archimedean normed spaces. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduced the Leibniz type additive-quadratic functional equation of the form f(x - t) + f(y - t) + f(z - t) = 3f(x + y +z/3 - t) + f(2x - y -z/3) + f(-x + 2y - z/3) + f(-x -y + 2z/3) and obtained its general solution and generalized Ulam - Hyers stability of Leibniz AQ - mixed type functional equation in quasi-beta normed space using direct and fixed point methods. [ABSTRACT FROM AUTHOR]

Using the fixed point method, we prove the Hyers-Ulam stability of an orthogonally additive-quadratic functional equation in non-Archimedean normed spaces. [ABSTRACT FROM AUTHOR]

In this paper the Adomian Decomposition Method (ADM) is employed in order to solve linear and nonlinear functional equations and the results are then compared with those produced by Homotopy Perturbation Method (HPM) through a system of Lotka Voltera type of PDEs. The result produced by HPM are promising and ADM appears as a special case of HPM for Lotka Voltera type of PDEs. [ABSTRACT FROM AUTHOR]

Inspired by some relevant recent results of A. E. Abbas we determine utility functions invariant with respect to some classes of transformations. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of the present paper is to investigate two functional inequalities with the unknown mapping acting on an ordered ring. Our investigations are motivated by the notion of averaging operators and by some earlier studies of related functional equations. [Copyright &y& Elsevier]

Abstract: The purpose of the paper is to deal with functions on an Abelian group which satisfy the following composite functional equation: for almost all pairs . The concept of “almost all pairs” is defined in an abstract manner. Our main result states that, under some technical assumptions, every such a function behaves in some sense similar to a function which satisfy the above equation for all pairs . [Copyright &y& Elsevier]

Abstract: In this paper the plane elasticity problem of two bonded dissimilar functionally graded strips containing an interface crack is studied. The governing equation in terms of Airy stress function is formulated and exact solutions are obtained for several special variations of material properties in Fourier transformation domain. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Numerical results show that fracture toughness of materials can be greatly improved by graded variation of elastic modulus and the influence of the specific form of elastic modulus on the fracture behavior of FGM is limited. [Copyright &y& Elsevier]