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Residues
Suppose f(z) has an isolated singularity at z0. Then it has a Laurent series expansion around z0, that converges on the region 0 < |z — z0|< R, for...
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Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism
We consider small perturbations of a conformal iterated function system produced by either adding or removing some generators with small derivative...
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Long Time Asymptotics Behavior of the Focusing Nonlinear Kundu-Eckhaus Equation
The authors study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus (KE for short) equation and construct the long time asymptotic...
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Multi-Factor Polynomial Diffusion Models and Inter-Temporal Futures Dynamics
In stochastic multi-factor commodity models, it is often the case that futures prices are explained by two latent state variables which represent the...
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Pseudo-Rate Matrices, Beyond Dayhoff’s Model
One of the fundamental techniques of biology is sequence alignment, namely transforming one sequence into another with minimal change. Sequence...
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Quantum Field Theory on the Example of the Simplest Cubic Model
The paper is devoted to the description of the basic tools of quantum field theory on the example of the simplest cubic model. We introduce such...
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Lightweight and Homomorphic Security Protocols for IoT
The rise in usage of IoT devices for data collection in various fields has been astronomical in recent times. There has been an increased requirement...
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Gevrey Asymptotics
As said at the beginning of Chap. 3 , Poincaré asymptotics is not sufficient to study the summability...
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Asymptotic Behavior of Point Processes of Exceeding the High Levels of Gaussian Stationary Sequence
AbstractThe paper studies the asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond a level tending to infinity...
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Prediction of Social Status on Depression by Using Logistic Regression
This chapter analyzes the effects of age and an individual’s social economic degree on depression using binomial logistic regression. The farmers and...
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Numerical Analysis of the Blow-Up of One-Dimensional Polymer Fluid Flow with a Front
AbstractOne-dimensional flows of an incompressible viscoelastic polymer fluid that are qualitatively similar to the solutions of Burgers’ equation...
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The Discrete Logarithm Problem Over Prime Fields: The Safe Prime Case. The Smart Attack, Non-Canonical Lifts and Logarithmic Derivatives
We connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.
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Rigid Analytic p-Adic Simpson Correspondence for Line Bundles
The p -adic Simpson correspondence due to Faltings (Adv Math 198(2):847–862, 2005) is a p -adic analogue of non-abelian Hodge theory. The following is...
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On Expansions and Nodes for Sparse Grid Collocation of Lognormal Elliptic PDEs
This work is a follow-up to our previous contribution (“Convergence of sparse collocation for functions of countably many Gaussian random variables...
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A historical perspective on Schützenberger-Pinsker inequalities (extended version)
This paper presents a tutorial overview of so-called Pinsker inequalities which establish a precise relationship between information and statistics,...
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Derivations and Special Functions Over Fields
Derivations play an integral role in the calculus and analysis; however, they have an algebraic exposition too. This algebraic notion has now become...
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Approximation of Mathieu Functions by Parabolic Cylinder Functions
AbstractThe Mathieu equation with complex coefficients of a special form is considered. Simple nonuniform asymptotics of its solutions in terms of...