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The fractional Lindley distribution is used to model the distribution of perturbations in count data regressions, which allow for dealing with widely dispersed data. It is obtained from the non-fractional Lindley distribution by replacing the support $\mathbb{T} = {\mathbb{R}^ + }$ T = R + by ${\mathbb{T}} = {\mathbb{N}}\backslash \{ 0\} $ T = N ∖ { 0 } and applying time scale theory, whose ambition is to unify the theories of difference equations and differential equations, integral and differential calculus, and the calculus of finite differences. It thus provides a framework for the study of dynamical systems in discrete-continuous time. Delta moments are discrete-time Laplace transforms of the frequency function of the fractional Lindley distribution. The parameter of the fractional Lindley distribution is estimated by least squares, weighted least squares, maximum likelihood, moments, and proportions. The moment estimator always exists, so that delta moments result from the nabla Laplace transform of the frequency function of the fractional Lindley distribution. The maximum likelihood estimates have the least mean-square errors. The proportion method works satisfactorily only when the mode of the distribution is null and the proportion of zeros is high. A simulation allows for quantifying the mean-square errors associated with the estimators. A count regression based on the fractional Lindley distribution with data on the total number of stays after hospital admission among U.S. residents aged 65 and over shows that the Akaike information criteria is significantly lower than with the uniform Poisson and Poisson regressions. [ABSTRACT FROM AUTHOR]

The present work investigates Bloch equations arising in magnetic resonance with Caputo and Caputo Fabrizio derivatives. Banach's fixed point approach is used to construct the existence theory for the model's solution. Also, the stability of the solution is established by Ulam–Hyers conditions. A novel 3-step iterative method is used for the considered model's numerical simulation with Caputo and Caputo Fabrizio derivative. This iterative method is formulated by combining Lagrange's interpolation with the fundamental theorem of integral calculus. The proposed method's error estimate is provided. The simulation results are displayed in tabulated and graphical form for distinct values of fractional order. The results demonstrate how the proposed method is accurate and appropriate for analysing fractional Bloch model. Further, this technique can also approximate the solution of other equations arising in engineering physics and quantum fields. [ABSTRACT FROM AUTHOR]

The given text discusses the use of Riemann approximating sums in calculus courses. It explains how Riemann products can be used to evaluate limits and emphasizes the importance of a specific condition for these products to approach 1 as N approaches infinity. The text also explores the convergence of infinite products and their relationship to infinite series. It provides a heuristic derivation of the limiting values of Riemann products and their connection to Riemann sums. The article concludes by discussing the validity of switching the order of sums and provides a reference for further exploration in real analysis. [Extracted from the article]

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In this study, the analysis focuses on a transient thermoelastic problem in an isotropic homogeneous elastic plate that is exposed to heat loading within the framework of the fractional-order theory. The sectional heat supply is applied on both the front edge and the farthest edge of the rectangular plate. The integral transformation was considered as a means to solve the main governing equations. The Mittag-Leffler function is utilized to express the analytical solution for temperature change, displacement, and stress response. The investigation also encompasses the study of thermoelastic behaviors in a plate featuring a central crack. The stress intensity factors at the fracture tip are determined numerically using the weight function method in this proposed solution. The findings are depicted using numerical computations, considering the material as a media, and visually represented in graphical form. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a version of the Feynman-Kac formula for the tempered fractional general diffusion equation$ \begin{align} \partial^{\beta, \eta}_{t} u(t,x) = \mathfrak{L}u(t,x) +b(t)u(t,x),\; \; x\in\mathcal{X},\; t\geq0, \end{align} $with initial value $ f $ belonging to a Banach space $ (\mathbb{B}, \|\cdot\|) $, where $ \partial^{\beta, \eta}_{t} $ denotes the Caputo tempered fractional derivative with order $ \beta\in(0,1) $ and tempered parameter $ \eta>0 $, $ b(t) $ is a bounded and continuous external potential on $ [0, \infty) $, $ \mathfrak{L} $ is the infinitesimal generator of a general time-homogeneous strong Markov process $ \{X_{t}\}_{t\geq0} $, and $ \mathcal{X} $ denotes a Lusin space that is a topological space being homeomorphic to a Borel subset of a compact metric space. By using the properties of the tempered $ \beta $-stable subordinator $ S_{\beta,\eta}(t) $ and the inverse tempered $ \beta $-stable subordinator $ D_{\beta,\eta}(t) $, and the stochastic calculus for the stochastic integral driven by $ D_{\beta,\eta}(t) $, we show that the Feynman-Kac representation $ u(t,x) $ defined by$ \begin{align} u(t,x) = {\mathbb{E}}^{x}\bigg[f(X_{D_{\beta,\eta}(t)}) e^{\int_{0}^{t}b(r)dD_{\beta,\eta}(r)}\bigg] \end{align} $is the unique mild and weak solutions to the tempered fractional general diffusion equation. From the Feynman-Kac formula, we further show the continuity of the solution with respect to time based on the integral properties of the Mittag-Leffler function and differential formula of covariance for $ D_{\beta,\eta}(t) $. By exploring the scaling property of $ D_{\beta,\eta}(t) $, the explicit order is also presented for the continuity of the solution with respect to tempered parameter $ \eta $. [ABSTRACT FROM AUTHOR]

In this university study, sections of an integral calculus course were randomly assigned to either a control or treatment group for a lesson on volumes of revolution. Both groups were given similar collaborative tasks, but only the students in the treatment group were given access to a set of 3D manipulatives. Pre- and post-assessments were administered to measure student achievement and confidence on the tasks comparing results for the control and treatment groups as well as for the male and female students. No statistically significant differences in student achievement were detected for the control or treatment group or by reported gender on either an immediate posttest or a delayed posttest. There was statistical significance in confidence after engaging in the 3D manipulative tasks favoring the treatment group. However, further inspection by gender revealed that while males in the treatment group were more likely to report higher confidence ratings than males in the control group, the reverse was true for females. [ABSTRACT FROM AUTHOR]

For land rent, it is characteristic that it arises as a consequence of capital investment in the purchase of land, which is not a production investment, because capital is not invested for the reason of organizing agricultural production, the main reason of investing capital is to acquire certain ownership of land areas. In this paper, we will present the possibility of solving the problem of rent calculations using the economic application of the definite integral. First, we will show if the integral calcusus is applied in the rent calculation and then in the domain of its calculation. [ABSTRACT FROM AUTHOR]

Henri Bergson's philosophy is centered on forming a concept of lived time or durée, which he saw as a process of continuous variation and flux. He believed that the study of time should be the foundation of philosophy. By studying time, we find an integration of concrete, infinite, qualitative multiplicity within consciousness that we should use to understand the essence of reality. I show that his insights into the reality of duration come directly from a metaphysical or phenomenological interpretation of integral and differential calculus. Drawing on the recently published lectures from 1902–1905, I show how An Introduction to Metaphysics schematizes the methodology of Matter and Memory and Time and Free Will by means of this mathematical analogy. To Bergson, the concepts of calculus are not mere metaphors; they unleash certain metaphysical implications that problematize the mind's relation to movement, life, consciousness, time, and consequently, reality itself. [ABSTRACT FROM AUTHOR]

We investigated the effects of a major revision of the differential and integral calculus curriculum, the primary goal of which was to improve STEM retention. The revamped curriculum has greater emphasis on the power of computing to help visualize patterns and gain insights to better prepare students for STEM majors, and less emphasis on traditional and theoretical calculus content, such as the limit definition of the derivative. We investigated a comparison between 338 students who had taken the traditional sequence and 328 who had taken the revamped sequence during the Fall 2020 and Spring 2021 semesters. STEM retention, i.e., following through with the initial intent to major in a STEM field, was enhanced by 7% in the revamped group. STEM majors in the traditional group were found to over-perform in their other STEM classes by a 0.18 GPA margin, while non-STEM majors in the revamped group over-performed in their other STEM classes by a 0.17 GPA margin. Both differences are statistically significant. Focus groups were also conducted to gather and synthesize student perceptions. Results may encourage similar innovations to core math curricula in other universities to foster enhanced STEM retention. [ABSTRACT FROM AUTHOR]

This paper revealed new fractional calculus applications of special functions in the geometric function theory. The aim of the study presented here was to introduce and begin the investigations on a new fractional calculus integral operator defined as the fractional integral of order λ for the Bessel function of the first kind. The focus of this research was on obtaining certain geometric properties that give necessary and sufficient univalence conditions for the new fractional calculus operator using the methods associated to differential subordination theory, also referred to as admissible functions theory, developed by Sanford S. Miller and Petru T. Mocanu. The paper discussed, in the proved theorems and corollaries, conditions that the fractional integral of the Bessel function of the first kind must comply in order to be a part of the sets of starlike functions, positive and negative order starlike functions, convex functions, positive and negative order convex functions, and close-to-convex functions, respectively. The geometric properties proved for the fractional integral of the Bessel function of the first kind recommend this function as a useful tool for future developments, both in geometric function theory in general, as well as in differential subordination and superordination theories in particular. [ABSTRACT FROM AUTHOR]

This paper proves an equality for the case of twice-differentiable convex functions involving conformable fractional integrals. Using the established equality, we give new Simpson-type inequalities for the case of twice-differentiable convex functions via conformable fractional integrals. We also consider some special cases which can be deduced from the main results. [ABSTRACT FROM AUTHOR]

This article, titled "Calculation of the Limit of a Special Sequence of Trigonometric Functions," discusses the problem of calculating the exact spectral radius of a special family of functional operators. The authors provide a theorem that solves this problem for rational and simple radical values, but the problem remains open for arbitrary algebraic numbers. The authors also present an elementary proof of a general formula that gives the value of the limit and an estimate of the rate of convergence of the sequence. The article includes theorems, proofs, and auxiliary assertions to support their findings. [Extracted from the article]

In this paper, we study the rate in the Smoluchowski–Kramers approximation for the solution of the following distribution-dependent SDE driven by fractional Brownian motion X t = X 0 + ∫ 0 t b (s , X s , ℒ X s ) d s + ∫ 0 t σ (s , ℒ X s ) B s H , where ℒ X t denotes the law of X t , { B t H , t ∈ [ 0 , T ] } is a d -dimensional fractional Brownian motion with Hurst parameter H ∈ (1 / 2 , 1). Based on the techniques of multiple integrals and Malliavin calculus, we provide an explicit bound on total variation distance for the rate of convergence. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach to the approximate solution of linear differential equations associated with principal fractional trigonometry and the R function. This method proposes a solution that is expressed by adding appropriate fractional linear fundamental functions. Laplace transforms of these functions are irrational. Therefore, we rounded these functions to obtain rational functions in the form of damped cosine, damped sine, cosine, sine and exponential functions. This transformation was achieved by utilizing the concept of fractional commensurate order and, as a result, has direct practical relevance to real-world physics. The precision and effectiveness of the approach are demonstrated through illustrative examples of solving fractional linear systems. [ABSTRACT FROM AUTHOR]

In this paper, the following result is presented:... under specified conditions, the function c that is differentiable at point a is presented, and c' (a) is also calculated. [ABSTRACT FROM AUTHOR]

We investigate the optimal rate of convergence in the multidimensional normal approximation of vector-valued Wiener-Itô integrals whose components all belong to a fixed Wiener chaos with coinciding orders. By combining Malliavin calculus, Stein's method for normal approximation and the method of cumulants, we obtain the optimal rate of convergence with respect to a suitable smooth distance. As applications, we derive the optimal rates of convergence for complex Wiener-Itô integrals, vector-valued Wiener-Itô integrals with kernels of step functions and vector-valued Toeplitz quadratic functionals. [ABSTRACT FROM AUTHOR]

Copyright of Revista de Ingenieria, Matematicas y Ciencias de la Informacion is the property of Corporacion Universitaria Republicana 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.)

This study aims to determine how students' mathematical literacy is in solving math problems seen from their learning independence. The research method used in this research is descriptive qualitative. The subjects in this study were semester III students at STKIP Kusuma Negara Jakarta, with 6 students, with each category of independent learning consisting of two students. This study used researchers as key instruments, tests to measure students' mathematical literacy, interview guidelines, and a questionnaire to measure student learning independence. The results of the study show that: informants with high learning independence tend to be able to achieve all indicators of mathematical literacy. Informants with moderate learning independence tend to be able to achieve most indicators of mathematical literacy. Still, they are wrong in using language and symbolic operations, solving mathematical problems and using mathematical tools. Informants with low learning independence, on the other hand, frequently had difficulty completely interpreting the data. As a result, communication of information and problem-solving become flawed. [ABSTRACT FROM AUTHOR]

We analyze the family of triangles whose sides come from a random subdivision of a given line segment into three segments. The usual geometric measurements on these random triangles (heights, bisectors, medians, angles, area, radii of the incircle, excircles, circumcircle) become random variables for which we determine the distribution function, the probability density, the expectation, the variance and higher order moments. This work can serve as a basis for activities at the college or university level. It is located at the crossroads between probability, geometry, integral calculus, special functions and computer algebra. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some reverses of Callebaut and Hölder inequalities for isotonic functionals via a reverse of Young's inequality we have established recently. Applications for integrals and n-tuples of real numbers are provided as well. [ABSTRACT FROM AUTHOR]

This study evaluated the impact of GeoGebra software in the teaching of differential and integral calculus in higher education, analyzing self-regulation, metacognition, meaningfulness, perception of the environment, symbolic language and reasoning. A quantitative approach and a quasi-experimental design with two independent groups (N=60) were used, collecting data through questionnaires and Likert-type scales, analyzed with non-parametric statistics. The results showed significant improvements in metacognition, symbolic language and perception, enhancing mathematical and spatial thinking. The Kolmogorov-Smirnov test (D=1) indicated a high deviation between groups. The study concludes that GeoGebra is an innovative tool that improves mathematics learning. Future research could explore the use of GeoGebra in various mathematical areas, evaluating its effectiveness along with innovative pedagogical strategies. [ABSTRACT FROM AUTHOR]

This work studies limits of Pfaffian systems, a class of first-order PDEs appearing in the Feynman integral calculus. Such limits appear naturally in the context of scattering amplitudes when there is a separation of scale in a given set of kinematic variables. We model these limits, which are often singular, via restrictions of D -modules. We thereby develop two different restriction algorithms: one based on gauge transformations, and another relying on the Macaulay matrix. These algorithms output Pfaffian systems containing fewer variables and of smaller rank. We show that it is also possible to retain logarithmic corrections in the limiting variable. The algorithms are showcased in many examples involving Feynman integrals and hypergeometric functions coming from GKZ systems. This work serves as a continuation of [1]. [ABSTRACT FROM AUTHOR]

In this paper, we study the functorial descent from self-contragredient cuspidal automorphic representations π of GL7(A) with LS (s; π; ^ ³ / having a pole at s=1 to the split exceptional group G2(A), using Fourier coefficients associated to two nilpotent orbits of E7. We show that one descent module is generic, and under suitable local conditions, it is cuspidal and π is a weak functorial lift of each of its irreducible summands. This establishes the first functorial descent involving the exotic exterior cube L-function. However, we show that the other descent module supports not only the nondegenerate Whittaker–Fourier integral on G2(A) but also every degenerate Whittaker– Fourier integral. Thus it is generic, but not cuspidal. [ABSTRACT FROM AUTHOR]

In this paper, we study the functorial descent from self-contragredient cuspidal automorphic representations π of GL7(A) with LS (s; π; ^ ³ / having a pole at s=1 to the split exceptional group G2(A), using Fourier coefficients associated to two nilpotent orbits of E7. We show that one descent module is generic, and under suitable local conditions, it is cuspidal and π is a weak functorial lift of each of its irreducible summands. This establishes the first functorial descent involving the exotic exterior cube L-function. However, we show that the other descent module supports not only the nondegenerate Whittaker–Fourier integral on G2(A) but also every degenerate Whittaker– Fourier integral. Thus it is generic, but not cuspidal. [ABSTRACT FROM AUTHOR]

Copyright of Revista Foco (Interdisciplinary Studies Journal) is the property of Revista Foco 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.)

The article discusses the challenges of teaching rotational inertia in introductory physics courses and the need for a user-friendly lab to enhance students' understanding of the topic. The traditional rotational inertia lab setup involving pulleys and measurements often confuses students more than it helps. The author proposes a new lab where students use the conservation of energy to calculate the rotational inertia of objects rolling down a ramp, allowing for open-ended exploration and critical thinking. The lab's simplicity and student-centered approach have proven successful in improving students' comprehension of rotation and integral calculus skills. [Extracted from the article]

In the theory of portfolio selection, there are few methods that effectively address the combined challenge of insider information and model uncertainty, despite numerous methods proposed for each individually. This paper studies the problem of the robust optimal investment for an insider under model uncertainty. To address this, we extend the Itô formula for forward integrals by Malliavin calculus, and use it to establish an implicit anticipating stochastic differential game model for the robust optimal investment. Since traditional stochastic control theory proves inadequate for solving anticipating control problems, we introduce a new approach. First, we employ the variational method to convert the original problem into a nonanticipative stochastic differential game problem. Then we use the stochastic maximum principle to derive the Hamiltonian system governing the robust optimal investment. In cases where the insider information filtration is of the initial enlargement type, we derive the closed-form expression for the investment by using the white noise theory when the insider is 'small'. When the insider is 'large', we articulate a quadratic backward stochastic differential equation characterization of the investment. We present the numerical result and conduct an economic analysis of the optimal strategy across various scenarios. [ABSTRACT FROM AUTHOR]

In this study, we delve into the general theory of operator kernel functions (OKFs) in operational calculus (OC). We established the rigorous mapping relation between the kernel function and the corresponding operator through the primary translation operator e − p t , which bears a striking resemblance to the Laplace transform. Our research demonstrates the uniqueness of the kernel function, determined by the rules of operational calculus and its integral representation. This discovery provides a novel perspective on how the operational calculus can be understood and applied, particularly through convolution with kernel functions. We substantiate the accuracy of the proposed method by demonstrating the consistency between the operator solution and the classical solution for the heat conduction problem. Subsequently, on the fractal tree, fractal loop, and fractal ladder structures, we illustrate the application of operational calculus in viscoelastic constitutive and hemodynamics confirming that the method proposed unifies the OKFs in the existing OC theory and can be extended to the operator field. These results underscore the practical significance of our results and open up new possibilities for future research. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive fixed-time fractional integral control for externally disturbed Euler–Lagrange systems. In the first step of the control design, the approach of fractional-order fixed-time integral nonsingular terminal sliding mode control (FoIFxTSM) is introduced. This scheme combines the benefits of fractional calculus with integral sliding mode control, resulting in fast convergence, smooth nonsingular control inputs, and fixed-time stability. By integrating an adaptive scheme, the proposed method is used to control the dynamical system in the presence of uncertainty and external perturbations. The findings of the fixed-time stability using Lyapunov analyses are provided for the closed-loop system. The simulation results are compared with the adaptive fractional-order sliding mode control scheme, and they show the better tracking and convergence performance of the proposed method. [ABSTRACT FROM AUTHOR]

We consider a classical case of integrals containing an irrational integrand in the form of a square root of a quadratic polynomial. It is known that such "irrational integrals" can be expressed in terms of elementary functions by one of three of Euler's substitutions. It is less well known that the Euler substitutions have a geometric interpretation. In the framework of this interpretation, one can see that the number 3 is not the most suitable. We show that it is natural to introduce a fourth Euler substitution. In his original treatise, Leonhard Euler used two substitutions which are sufficient to cover all cases. [ABSTRACT FROM AUTHOR]

Designing and implementing purposefully developed tasks have been linked to students' understanding of mathematical topics. We report on design principles and intentions that guided the development of inquiry-oriented tasks. Through a qualitative analysis of the tasks, we identified seven themes that encapsulated these design intentions: Provide Review; Introduce New Content; Provide Guidance; Prompt Graphing and Visualisation; Prompt Generalisation; Foster Mathematical Creativity; and Prompt Reflection. In the discussion, we align these themes with existing literature and recognise an intersection between designing inquiry-oriented tasks, creativity-fostering tasks and reflective assignments. We additionally provide some recommendations for practitioners and report on students' feedback on these tasks. [ABSTRACT FROM AUTHOR]

This paper explores the realm of fractional integral calculus in connection with the one-dimensional Dunkl operator on the space of tempered functions and Lizorkin type space. The primary objective is to construct fractional integral operators within this framework. By establishing the analogous counterparts of well-known operators, including the Riesz fractional integral, Feller fractional integral, and Riemann–Liouville fractional integral operators, we demonstrate their applicability in this setting. Moreover, we show that familiar properties of fractional integrals can be derived from the obtained results, further reinforcing their significance. This investigation sheds light on the utilization of Dunkl operators in fractional calculus and provides valuable insights into the connections between different types of fractional integrals. The findings presented in this paper contribute to the broader field of fractional calculus and advance our understanding of the study of Dunkl operators in this context. [ABSTRACT FROM AUTHOR]

This work investigates a fractional Susceptible Infected Recovered (SIR) model to study childhood disease. We analyzed the proposed model by applying Caputo, Caputo–Fabrizio, and Atangana–Baleanu fractional derivatives. Here, we use the fractional Adams–Bashforth method to solve the childhood disease model with nonlocal operator. The proposed numerical technique is developed by combining the fundamental theorem of integral calculus with Lagrange's interpolation. This numerical approach is more efficient than the other existing numerical techniques and is easily computed using Matlab as a programming language. The existence and uniqueness of this fractional model are studied with the fixed‐point theorem. These fractional derivatives show different asymptotic behaviors for the distinct values of the fractional order. The numerical results are presented graphically as well as in tabulated form for some value of fractional order. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador 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 Avances de Investigación en Educación Matemática is the property of Sociedad Espanola de Investigacion en Educacion Matematica 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.)

Let EN denote the coarse moduli space of smooth elliptic surfaces over P¹ with fundamental invariant N. We compute the Chow ring A*(EN) for N ≥ 2. For each N ≥ 2, A*(EN) is Gorenstein with socle in codimension 16, which is surprising in light of the fact that the dimension of EN is 10N - 2. As an application, we show that the maximal dimension of a complete subvariety of EN is 16. When N = 2, the corresponding elliptic surfaces are K3 surfaces polarized by a hyperbolic lattice U. We show that the generators for A*(E2) are tautological classes on the moduli space FU of U-polarized K3 surfaces, which provides evidence for a conjecture of Oprea and Pandharipande on the tautological rings of moduli spaces of lattice polarized K3 surfaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study an extended version of bivariant derived algebraic cobordism in which the cycles carry a vector bundle on the source as additional data. We show that, over a field of characteristic 0, this extends the analogous homological theory of Lee and Pandharipande. We then proceed to study in detail the restricted theory where only rank 1 vector bundles are allowed, and employ the obtained structural results to prove a weak version of the projective bundle formula for bivariant cobordism. Since the proof of this theorem works very generally, we introduce the notion of precobordism theories for quasi-projective derived schemes over an arbitrary Noetherian ring of finite Krull dimension as a reasonable class of theories where the proof can be carried out, and prove some of their basic properties. These results can be considered as the first steps towards a Levine-Morel style algebraic cobordism over a base ring that is not a field of characteristic 0. [ABSTRACT FROM AUTHOR]

Are Fourier-Mukai equivalent cubic fourfolds birationally equivalent? We obtain an affirmative answer to this question for very general cubic fourfolds of discriminant 20, where we produce birational maps via the Cremona transformation defined by the Veronese surface. By studying how these maps act on the cubics known to be rational, we surprisingly found new rational examples. [ABSTRACT FROM AUTHOR]

Let Z be a nondegenerate hypersurface in a d-dimensional torus (C*)d defined by a Laurent polynomial f with a d-dimensional Newton polytope P. The subset F(P) ⊂ P consisting of all points in P having integral distance at least 1 to all integral supporting hyperplanes of P is called the Fine interior of P. If F(P) ≠ ∅, we construct a unique projective model Z of Z having at worst canonical singularities and obtain minimal models Z of Z by crepant morphisms b Z → Z. We show that the Kodaira dimension κ = κ(Z) equals min{d - 1, dim F(P)} and the general fibers in the Iitaka fibration of the canonical model Z are nondegenerate (d - 1 - ΰ)-dimensional toric hypersurfaces of Kodaira dimension 0. Using F(P), we obtain a simple combinatorial formula for the intersection number (KZ)d-1. [ABSTRACT FROM AUTHOR]

In this article, authors discussed about image formulas for the some new extended hypergeometric function using elementary properties of the fractional calculus integral operators. Furthermore, using integral transforms some image formulas are also established. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador 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.)

We study the mapping properties of singular integral operators along surfaces of revolutions on product domains. For several classes of surfaces, we prove sharp Lp bounds (1< p< ∞) for these singular integral operators as well as their corresponding maximal operators. By using these Lp bounds and an extrapolation argument we obtain the Lp boundedness of these operators under optimal conditions on the singular kernels. Our results extend and improve several results previously obtained by many authors. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of generalized quasilinear Schrödinger equations which have appeared from plasma physics, as well as high-power ultrashort laser in matter. Combining the variable replacement and the Schauder-Tychonoff fixed point theorem, we establish the nonexistence and existence of positive radial ground state solutions for this problem. [ABSTRACT FROM AUTHOR]

We mainly study the dimension-free Lp-inequality of the Hardy-Littlewood maximal functions with mixed homogeneities M∗G f (x,y) = supt>0 1/|G| |∫G f (x−tu,y−t²v)dudv|, where G is a bounded, closed and symmetric convex subset of Rd+1. When G is in the isotropic position, we prove that there is a constant Cp independent of d such that ||M∗G f||Lp(Rd+1) ≤Cp(L(G))||f|| Lp(Rd+1), for 3/2 < p ≤ ∞, where L(G) is a constant associated with G. [ABSTRACT FROM AUTHOR]