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Fractional calculus is not a new topic, in reality it has almost the same history as that of classical calculus. In this paper, new approaches are developed to solve a class of nonlinear fractional differential initial value problems with fractional derivative defined in Caputo sense. Two numerical methods have been presented, Fractional Adams-Bashforth-Moulton Method (FABMM) and Fractional Differential Transformation Method (FDTM) compared with Adomian Decomposition Method (ADM), used for very specific type of problems. The methods are used on two different nonlinear fractional differential equations of the form, with and without exact solution for the same initial condition. We present new results that deal with the Adomian Decomposition Method (ADM), suitable to handle fractional calculus applications. The results are obtained with comparisons made between FDTM, FABMM and the exact solutions at each integration point, given, both graphically and tabularly, for different fractional orders, constant step-size and small time interval. Our work, with using symbolic software packages as Wolfram Mathematica 12.1, can be considered as an alternative to existing techniques, and will have wide applications in science and engineering fields. y(0)=0. We present new results that deal with the Adomian Decomposition Method (ADM), suitable to handle fractional calculus applications. The results are obtained with comparisons made between FDTM, FABMM and the exact solutions at each integration point, given, both graphically and tabularly, for different fractional orders from 0 to 1, constant step-size h=0.01 and small time interval. Our work, with using symbolic software packages as Wolfram Mathematica, can be considered as an alternative to existing techniques, and will have wide applications in science and engineering fields. [ABSTRACT FROM AUTHOR]

In this paper we present a new numerical method for solving fractional differential equations (FDEs) based on Genocchi polynomials operational matrix through collocation method. The operational matrix of fractional integration in Riemann-Liouville sense is derived. The upper bound for the error of the operational matrix of fractional integration is also shown. The properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. Illustrative examples are finally given to show the simplicity, accuracy and applicability of the method. [ABSTRACT FROM AUTHOR]

This paper focuses on some 3-Engel groups. Suppose x and y are elements of a group G. The commutativity degree of a group is the probability that two elements in the group commute and is denoted by P(G). Meanwhile, the nth commutativity degree of a group G is the probability that for any pairs of x and y in G, xn and y commute. In this paper, the nth commutativity degree of some 3-Engel groups is determined. [ABSTRACT FROM AUTHOR]

This paper examines optimal predation by a predator preying upon two types of prey, modes and mimics. Models are unpalatable prey and mimics are palatable prey resembling the models so as to derive some protection from predation. This biological phenomenon is known in Ecology as Batesian mimicry. An optimal control problem in continuous time is formulated with the sole objective to maximize the net energetic benefit to the predator from predation in the presence of evolving prey populations. The constrained optimal control is bang-bang with the scalar control taken as the probability of attacking prey. Conditions for the existence of singular controls are obtained. [ABSTRACT FROM AUTHOR]

In a recent paper [A reducibility of the Kampé de Fériet function, Advances in Comput. Math. and its Applications, Vol. 1, No. 1, pp. 76-79 (2012)], the author has evaluated one very interesting reduction formula. In this paper, two new reduction formulas of Kampe de Feriet function have been evaluated by using Gauss's second summation theorem on the sum of a 3F2. The results established in this paper are simple, interesting, easily established and may be useful. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce new classes of functions called totally-continuous functions and its variants totally semi-continuous functions and semi totally-continuous functions in double fuzzy topological spaces. Their characterizations, examples and relationship with other notions of continuous functions in this space are provided. [ABSTRACT FROM AUTHOR]

This paper discusses the stability of the Modified Craig-Sneyd scheme when applied to two-dimensional convection-diffusion equations with mixed derivatives. A preliminary result is summarized that specially considers the size of the mixed derivative coefficients, which is very useful in practice. [ABSTRACT FROM AUTHOR]

New software package for fuzzy calculus is presented in this paper. Most important feature of this package is solving fuzzy linear systems of equations and inequalities in fuzzy algebras. Together with this, some other functionality is implemented. An example is also given. [ABSTRACT FROM AUTHOR]

Main purpose of this paper is to construct higher-order w-q-Genocchi numbers and polynomials by using p-adic q-deformed fermionic integral on Zp. We derive some interesting identities related to higher-order w-q-Genocchi numbers and polynomials. We also construct Hurwitz type multiple w-Genocchi zeta function which interpolates these polynomials at negative integers. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to the function evaluation using tables. The proposal argues for the use of a more complete primitive, namely a weighted sum, which converts the calculation of the function values into a recursive operation defined by a two input table. The weighted sum can be tuned for different values of the weighting parameters which hold the features of the particular evaluated function. The implementation can be achieved with a very simple circuit. The computational throughput is related to both the table size and the number of parallelization levels. Tn what concerns to the calculation error, two main trends can be considered if round-off is performed or not. It seems that the calculation carried out by means of a table-based recursive method provides efficient designs that can be tailored to the application requirements. Our method outlines advantages when compared with other well-known proposals because it provides memory and hardware resource saving as well as a good trade-off between speed and error. [ABSTRACT FROM AUTHOR]

The mathematical formulation of Quantum Mechanics in terms of complex Hilbert space is derived for finite dimensions, starting from a general definition of physical experiment and from five simple Postulates concerning experimental accessibility and simplicity. For the infinite dimensional case, on the other hand, a C*-algebra representation of physical transformations is derived, starting from just four of the five Postulates via a Gelfand-Naimark-Segal (GNS) construction. The present paper simplifies and sharpens the previous derivation in Ref. [1]. The main ingredient of the axiomatization is the postulated existence of faithful states that allows one to calibrate the experimental apparatus. Such notion is at the basis of the operational definitions of the scalar product and of the transposed of a physical transformation. What is new in the present paper with respect to Ref. [1], is the operational deduction of an involution corresponding to the complex-conjugation for effects, whose extension to transformations allows to define the adjoint of a transformation when the extension is composition-preserving. The existence of such composition-preserving extension among possible extensions is analyzed. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Studies of differences in educational test scores typically employ differences in means as their outcome. This paper argues that mean differences, though helpful and informative, fail to provide a satisfactory framework through which to view differences in educational test scores, and proposes that our understanding of many differences in educational test scores would be enhanced by comparisons of who ends up in the top and bottom tails of the distribution. I suggest that ordinary least squares regression, a measure based on mean comparisons, does not sufficiently describe gender differences in mathematics achievement, and that important insights are gained by using logistic regression to observe the composition of the tails of the distribution. [ABSTRACT FROM AUTHOR]

The relation between the Ahlfors map and Szegö kernel S (z, a) is classical. The Szegö kernel is a solution of a Fredholm integral equation of the second kind with the Kerzman-Stein kernel. The exact zeros of the Ahlfors map are known for a particular family of doubly connected regions and a particular triply connected region. This paper presents a numerical method for computing the zeros of the Ahlfors map of any bounded multiply connected regions with smooth boundaries. The method depends on the values of S (z(t), a), S'(z(t), a) and θ'(t), where θ(t) is the boundary correspondence function of Ahlfors map. A formula is derived for computing S'(z(t), a). An integral equation for θ'(t) is used for finding the zeros of Ahlfors map. The numerical examples presented here demonstrate the method. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of composition of two arbitrary rotations in SO(3,ℝ) given in their vector-parameter form. The cases when one or two half-turns are involved in the composition or the resulting rotation is a half turn receive also rigorous treatment. Technically, this is done by lifting the problem to the covering group SU(2). Systematization of the results is made and relying on them, some applications are discussed. A convenient and economic computational method for composing rotations in vector-parameter form is proposed. It is such that the composition of two arbitrary (including half-turns) rotations can be done with at most 12 multiplications. Finally, we present an explicit variant of the construction behind Cartan's theorem in the case of SO(3,ℝ). [ABSTRACT FROM AUTHOR]

In this paper we define the notation of mapping on intuitionistic fuzzy soft classes and we have studied some properties of intuitionistic fuzzy soft images and inverse images. Finally we give examples and counterexamples for these concepts. [ABSTRACT FROM AUTHOR]

This paper discusses an integral solution (a, b, c) of the Diophantine equations x3n+y3n = 2z2n for n ≥ 2 and it is found that the integral solution of these equation are of the form a = b = t2, c = t3 for any integers t. [ABSTRACT FROM AUTHOR]

This paper deals with the enumeration of the different classes of 2-element fuzzy hypergroups and with the construction of some classes of 2-element mimic fuzzy hypergroups. It also introduces the notion of the pseudo-mimic fuzzy hypergroup. [ABSTRACT FROM AUTHOR]

The aim of this paper is to derive relations between Eulerian polynomials and Array Polynomials. We also give some identities related to the Array type polynomials Bell type numbers. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of pre-contrast functions and studies their geometric properties. A contrast function is an asymmetric squared distance like function. A pre-contrast function corresponds to the differential of a contrast function, however, it is not integrable in general. While a contrast function induces a statistical manifold, a pre-contrast function induces a statistical manifold admitting torsion. As an application of pre-contrast functions, geometry of non-conservative estimating functions in statistics is also studied. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to construct partial twisted zeta-type function, which interpolates q-generalized Frobenius-Euler numbers and twisted q-generalized Frobenius-Euler numbers. We give some applications related to this function. [ABSTRACT FROM AUTHOR]

In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose to embed the deformation field in a weighted minimal surface problem. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. Minimizing this weighted Polyakov energy drives the deformation field toward a minimal surface, while being attracted by the solution of the registration problem. Our geometric framework involves two important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including non-flat and multiscale images. Secondly, to the best of our knowledge, this method is the first re-parametrization invariant registration method introduced in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of generalized fuzzy subalgebras and generalized fuzzy ideals of Boolean algebras are introduced, A necessary and sufficient condition for a fuzzy subset of Boolean algebra to be a generalized fuzzy subalgebra (ideal) is stated, and images and inverse-images of generalized fuzzy subalgebra (ideal) under Boolean algebra homomorphism are studied. [ABSTRACT FROM AUTHOR]

In this paper we summarize the results of our investigation of the moving localized structures in lattice like systems. Dynamics of discrete localized modes in cubic, cubic-quintic, saturable photorefractive lattice and in the Bose-Einstein condensate modelled by the nonpolynomial Schrödinger equation are considered in the framework of the Peierls-Nabarro barrier. Two approaches are numerically tested: free-energy approach and mapping analysis. We show that only the last one is appropriate. [ABSTRACT FROM AUTHOR]

This short paper is concerned with a new algorithm for collision and distance calculation between CSG octrees, a generalization of an octree model created from a Constructive Solid Geometry (CSG) object. The data structure uses interval arithmetic and allows us to extend the tests for classifying points in space as inside, on the boundary, or outside a CSG object to entire sections of the space at once. Tree nodes with additional information about relevant parts of the CSG object are introduced in order to reduce the depth of the required subdivision. The new data structure reduces the input complexity and enables us to reconstruct the CSG object. We present an efficient algorithm for computing the distance between CSG objects encoded by the new data structure. The distance algorithm is based on a distance algorithm for classical octrees but, additionally, it utilizes an elaborated sort sequence and differentiated handling of pairs of octree nodes to enhance its efficiency. Experimental results indicate that, in comparison to common octrees, the new representation has advantages in the field of proximity query. [ABSTRACT FROM AUTHOR]

Gantmacher and Krein from their investigations on oscillations of mechanical systems, defined an important class of matrices, called oscillatory matrices. An n×n totally nonnegative matrix A is called oscillatory if some positive integral power of it is totally positive. Besides this, we note that some of properties of the oscillatory matrix studied by Ando can be extended to rectangular matrices. We note that Fallat in [4] analyzes a classical criterion obtained by Gantmacher and Krein for determining when a totally nonnegative matrix is oscillatory and he shows a new proof of this criterion by using bidiagonal factorizations of invertible totally nonnegative matrices and using the associated weighted planar network. In this paper, we extend the oscillatory matrices to rectangular matrices and we obtain a characterization of this class of matrices by incorporating bidiagonal factorizations. On the other hand, the totally nonnegative matrices in double echelon form, introduced by Crans, Fallat and Johnson, are examples of rectangular oscillatory matrices. [ABSTRACT FROM AUTHOR]

In this paper dedicated to the memory of Walter Philipp, we formalize the rules of classical→ quantum correspondence and perform a rigorous mathematical analysis of the assumptions in Bell’s NO-GO arguments. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Numbers, variables, and equations are used differently in a physics class than in a pure mathematics class. In physics, these symbols not only obey formal mathematical rules but also carry physical ideas and relations. This paper focuses on modeling how this combination of physical and mathematical knowledge is constructed. The cognitive blending framework highlights both the different ways this combination can occur and the emergence of new insights and meaning that follows such a combination. After an introduction to the blending framework itself, several examples from undergraduate physics students’ work are analyzed. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Students' solutions to the "student-professor problem" have provided a source for investigating students' algebraic mental models. This paper seeks to expand on previous investigations by approaching "student-professor type" situations from a new perspective. It uses ideas of equality and covariation while analyzing students' successful strategies to suggest new pedagogical strategies for helping students develop algebraic reasoning. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]

In this paper, we define the concepts of rough statistical convergence and rough statistical Cauchy of a double sequence. Then we obtain a rough statistically Cauchy criterion for the real double sequences. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of TL-subalgebras, TLideals and TL-implicative ideals of BCK-algebra are introduced, A necessary and sufficient condition for a Lsubset of BCK-algebra to be a L-subalgebra (ideal, implicative ideal) is stated, and images and inverse-images of TL-subalgebra under BCK-algebra homomorphism are studied. Also, several characterizations of TL-ideals (implicative ideals) are given. Where T is an arbitrary infinitely -distributive t-norm on a given complete Brouwerian lattice L. [ABSTRACT FROM AUTHOR]

This article reports on the solutions of the time-fractional diffusion equation. It discusses the numerical analysis of the time-fractional diffusion equation by using the time fractional derivative in the Caputo sense of order. It provides the equation for the Wright function with the series that appears within the solution of the time-fractional diffusion equation.

We determine symmetry reductions of a Generalized Dullin-Gottwald-Holm equation. We obtain the subclasses of these general equations which are quasi self-adjoint and weak self-adjoint. [ABSTRACT FROM AUTHOR]

A rather general method is presented of how to derive the exact distribution of a function of a random vector if the vector does not satisfy standard model assumptions. [ABSTRACT FROM AUTHOR]

The paper presents the theoretical basis of the relationship between the parameter of the flow of irregular failures with working time ?(l), and the relationship between the number of converted unit repairs during one unit of working time S(L). These relations will serve for the determination of the optimal repairing interval for the means of transportation with regard the unexpected failures and the costs for repair of their components. [ABSTRACT FROM AUTHOR]

In this contribution the eigenfrequencies of a multi-body-system of MIKOTA-type are investigated. Based on the properties of the mass and stiffness matrices of the chain structured mass-spring vibration system an algebraic proof for the conjecture of MIKOTA is given. [ABSTRACT FROM AUTHOR]

Taking its historical point of departure in Heisenberg’s work, this article offers a view of quantum mechanics as, arguably, the first truly experimental and truly mathematical physical theory, that is, a theory concerned with experimenting with nature and mathematics alike. It is truly experimental because it is not, as in classical physics, merely the independent behavior of the system considered, in other words, what happens in any event, that we track, but what kind of experiments we perform that defines what happens. By the same token, the theory is also truly mathematical because, at least in the interpretation adopted here, its mathematical formalism does not stand in the service of a mathematical description of (quantum) physical processes in space and time in the way the formalism of classical physics does, but is only used to predict the outcomes of relevant experiments. It also follows that quantum theories experiment more freely with mathematics itself, since we invent predictive mathematical schemes, rather than proceed by refining mathematically our phenomenal representations of nature, which process constrains us in classical mechanics. [ABSTRACT FROM AUTHOR]

The fluctuationlessness approximation gives powerful and easily utilizable solutions for a lot of applications of numerical analysis. For example, it helps us to create univariate numerical integration schemes which converge very rapidly. On the other hand, the space extension approaches aim to convert equations into some other structures which can be handled more easily. It is possible to apply this approach to the solutions obtained with fluctuationlessness approximation in order to improve the quality of approximation. [ABSTRACT FROM AUTHOR]

The aim of this study is to document the behaviors of first semester engineering students at the beginning of the calculus course. Students were asked to identify, interpret and represent graphically the changes in one variable with respect to changes in another variable in different settings [ABSTRACT FROM AUTHOR]

This study has as its main purpose the analysis of student responses to questions related to their understanding of the meaning and representation of straight-line solutions of systems of differential equations. The theoretical framework used in the design of instruments and for the analysis of students’ responses is Action-Process-Object-Schema (APOS) theory, in particular, the notions of triad and double triad. [ABSTRACT FROM AUTHOR]

Numerical techniques (windowed Fourier transforms and wavelets) are developed for carrying out a local mode analysis k(x) of ICRF field solutions. It is shown that simultaneous resolution of long- and short-wavelength waves in typical rf mode conversion scenarios requires the use of a modified wavelet transform. The ability to get quantitative information by this technique is assessed and visualization techniques for wave polarization information are illustrated. © 2003 American Institute of Physics [ABSTRACT FROM AUTHOR]

This paper examines cognitive structures activated as learners re-present verbal problem statements as algebraic experiences. Symbolization is viewed as a dynamic interaction among three knowledge structures. Capacity to write equations is related to the congruence among these structures. Participants' responses are analyzed to uncover the nature of the activated knowledge. The results provide insight into learners' cognitive structures and activity. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]