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New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in ℝⁿ
The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable
conformal minimal surfaces in
All our new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice
of a conformal structure. This enables us to obtain significant new applications to the global theory of non-orientable minimal
surfaces. In particular, we construct proper non-orientable conformal minimal surfaces in
eBook
Local dynamics of non-invertible maps near normal surface singularities
We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs
eBook
A Systematic Review Towards Big Data Analytics in Social Media
The recent advancement in internet 2.0 creates a scope to connect people worldwide using society 2.0 and web 2.0 technologies. This new era allows the consumer to directly connect with other individuals, business corporations, and the government. People are open to sharing opinions, views, and ideas on any topic in different formats out loud. This creates the opportunity to make the \"Big Social Data\" handy by implementing machine learning approaches and social data analytics. This study offers an overview of recent works in social media, data science, and machine learning to gain a wide perspective on social media big data analytics. We explain why social media data are significant elements of the improved data-driven decision-making process. We propose and build the \"Sunflower Model of Big Data\" to define big data and bring it up to date with technology by combining 5 V’s and 10 Bigs. We discover the top ten social data analytics to work in the domain of social media platforms. A comprehensive list of relevant statistical/machine learning methods to implement each of these big data analytics is discussed in this work. \"Text Analytics\" is the most used analytics in social data analysis to date. We create a taxonomy on social media analytics to meet the need and provide a clear understanding. Tools, techniques, and supporting data type are also discussed in this research work. As a result, researchers will have an easier time deciding which social data analytics would best suit their needs.
Journal Article
McShane Identities for Higher Teichmüller Theory and the Goncharov–Shen Potential
We derive generalizations of McShane’s identity for higher ranked surface group representations by studying a family of mapping class
group invariant functions introduced by Goncharov and Shen, which generalize the notion of horocycle lengths. In particular, we obtain
McShane-type identities for finite-area cusped convex real projective surfaces by generalizing the Birman–Series geodesic scarcity
theorem. More generally, we establish McShane-type identities for positive surface group representations with loxodromic boundary
monodromy, as well as McShane-type inequalities for general rank positive representations with unipotent boundary monodromy. Our
identities are systematically expressed in terms of projective invariants, and we study these invariants: we establish boundedness and
Fuchsian rigidity results for triple and cross ratios. We apply our identities to derive the simple spectral discreteness of
unipotent-bordered positive representations, collar lemmas, and generalizations of the Thurston metric.
eBook
Sir Cumference and the Viking's map : a math adventure
\"Xaxon Yellowbearyd was the fiercest Viking warrior of his time. Now a map to his hidden treasure lies in the hands of Radius and Per. Together the cousins must decode the strange numbered grid on the map-- and figure out the secret of the Viking's X and Y axes\"--P. [4] of cover
Book
Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory
In this paper, we study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and
operator theory. We first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the
Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. We propose a new notion of tensored-scalar singularity, and
then answer questions on Hankel operators with matrix-valued bounded type symbols. We also examine an interpolation problem related to a
certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejér
Interpolation Problem for matrix rational functions. We then extend the
eBook