77 research outputs found

    Mapping properties for conic regions associated with wright functions

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    In this paper, we are mainly interested to find sufficient conditions for the convolution operator Y(lambda,mu)f(z) = zW(lambda,mu)(z) * f(z) belonging to the classes UCV (k, alpha), S-p (k, alpha), S*(sigma) and C-sigma

    Geometrical Theory of Analytic Functions

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    The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria

    Normalizability, integrability and monodromy maps of singularities in three-dimensional vector fields

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    In this thesis we consider three-dimensional dynamical systems in the neighbourhood of a singular point with rank-one and rank-two resonant eigenvalues. We first introduce and generalize here a new technique extending previous work which was described by Aziz an Christopher (2012), where a second first integral of a 3D system can be found if the system has a Darboux-analytic first integral and an inverse Jacobi multiplier. We use this new technique to find two independent first integrals one of which contains logarithmic terms, allowing for non-zero resonant terms in the formal normal form of vector field. We also consider sufficient conditions for the existence of one analytic first integral for three dimensional vector fields around a singularity. Starting from the generalized Lotka-Volterra system with rank-one resonant eigenvalues, using the normal form method, we find an inverse Jacobi multiplier of the system under suitable conditions. Moreover, these conditions are sufficient conditions for the existence of one analytic first integral of the system. We apply this to demonstrate the sufficiency of the conditions in Aziz and Christopher (2014). In the case of two-dimensional systems, Christopher et al (2003) addressed the question of orbital normalizability, integrability, normalizability and linearizability of a complex differential system in the neighbourhood at a critical point. We here address the question of normalizability, orbital normalizability, and integrability of three-dimensional systems in the neighbourhood at the origin for rank-one resonance system. We consider the case when the eigenvalues of three-dimensional systems have rank-one resonance satisfying the condition the sum of eigenvalues is equal to zero a typical example, and we use a further change of coordinates to bring the formal normal form for three-dimensional systems into a reduced normal form which contains a finite number of resonant monomials. By using this technique, we can find two independent first integrals formally. The first one of these first integrals is of Darboux-analytic type, and other first integral contains logarithmic terms corresponding to non-zero resonant monomials of the original system. We introduce the monodromy map in three-dimensional vector fields by using these two independent first integrals to study a relationship between normalizability and integrability of systems. In the case of rank-one resonant eigenvalues, we get a monodromy map which is in normal form, and then in the same way as the case of vector fields, we use a further change of coordinates to reduce this map into a reduced map which contains only a finite number of resonant monomials. This thesis also examines briefly the case of rank-two resonant eigenvalues of three-dimensional systems. The normal form in this case contains an infinite number of resonant monomials, we were not able to find a reduced normal form with a finite number of resonant monomials. This situation is therefore much more complex than the rank-one case. Thus, we simplify the investigation by truncating the 3D system to a 3D homogeneous cubic system as a first step to understanding the general case. Even though we can find two independent first integrals, the second one involves the hypergeometric function, leading to some interesting topics for further investigation.Kurdistan Regional Government-Ira

    Total Empiricism: Learning from Data

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    Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems in the analysis and interpretation of the results. Instead of trying to fix the model or "correct" the data, we here describe a totally empirical statistical approach that does not rely on ad hoc distributional assumptions in order to overcome many problems in contemporary statistics. Starting from elementary combinatorics, we motivate an information-guided formalism to quantify knowledge extracted from the given data. Subsequently, we derive model-agnostic methods to identify patterns that are solely evidenced by the data based on our prior knowledge. The data-centric character of empiricism allows for its universal applicability, particularly as sample size grows larger. In this comprehensive framework, we re-interpret and extend model distributions, scores and statistical tests used in different schools of statistics.Comment: Keywords: effective description, large-N, operator formalism, statistical testing, inference, information divergenc

    Acta Scientiarum Mathematicarum : Tomus 56. Fasc. 3-4.

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    NUC BMAS Sciences (Draft)

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    Number Theory, Analysis and Geometry: In Memory of Serge Lang

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    Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas, namely number theory, analysis and geometry, representing Lang’s own breadth of interests. A special introduction by John Tate includes a brief and engaging account of Serge Lang’s life
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