New Tools in Mathematical Analysis and Applications

- Part I: Complex Geometry.- On the Jacobian Variety of the Accola-Maclachlan Curve of Genus Four.- T-Invariant Points on T-varieties.- Computations on the Hilbert-Mumford Criterion for Grassmanians.- Rational Homotopy and Hodge Theory of Moduli Stacks of Principal G-Bundles.- On Slice Regular Bergman Spaces and Fiber Bundles.- Part II: Complex Variables and Potential Theory.- Inequalities for the Inner Radii of Domains Containing an Arbitrary Ellipse Points and Infinity.- On the Carleman-Bers-Vekua Equation.- On Asymptotics of Ring Q-Homeomorphisms with Respect to p-Modulus near the Origin.- Approximate Solutions of some Problems in Thermoelasticity.- On Local Hölder and Lipschitz Continuities of Solutions to Nonlinear Beltrami Equation.- A Piecewise Continuous Schwarz-Type Boundary-Value Problem in an Angle for Monogenic Functions in a Commutative Biharmonic Algebra.- On Distortion Estimates of Mappings with the Poletsky Condition in Domains with Poincare Inequality.- Part III: Function Spaces and their Applications.- Well-Posedness for a System of Nonlinear Schrödinger Equations with Derivative Nonlinearity via the Energy Method.- Part IV: Harmonic Analysis and Related Topics.- Geometric Herz Spaces and Poisson Kernels in the Upper Half-Space.- Part V: Partial Differential Equations Oncurved Spacetime.- Optimal L8-Decay Rate of Solutions to a Dissipative Nonlinear Schrödinger Equation System.- Global Solutions of the Klein-Gordon Equation under the Quartic Potential in the de Sitter Spacetime.- About Critical Exponents in Semi-Linear de Sitter Models.- Part VI: PDEs in Fluid Mechanics.- A Family of Systems Including the Herschel-Bulkley Fluid Equations.- On the Well-Posedness for the Inviscid Boussinesq Equations in Besov-Herz Spaces.- Blowing up and Dissipation for a Couple of One-Dimensional Non-Local Conservation Laws.- Part VII: Recent Progress in Evolution Equations.- Lp - Lq Estimates for Very Strongly Damped Wave Equations.- Decay Estimates for Space-Time Fractional Equations with Structural Damping and Nonlinear Memory.- Revisit on Global Existence of Solutions for Semilinear Damped Wave Equations in RN with Noncompactly Supported Initial Data.- Part VIII: Stochastic Processes.- Hedging in a Market with Jumps - A FBSDE Approach.- Global Smooth Solutions for the Stochastic Navier-Stokes Equations with Super-Linear Stratonovich Noise in the 3D Torus.- Part IX: Wavelet theory and its Related Topics.- On Characterization of the Gabor Wavelet Transform of Analytic Functionals.- The p-Adic Fourier Transform of the Locally Constant Functions.- Fractional Neural Network Interpolation Operator for Irregular Grid Points.