# Keyword index P

**p'th power gas****p-adic integers**- 50/2001 - Embeddings of lattices in
**L**^{2}([0,1], Z)

- 50/2001 - Embeddings of lattices in
**p-form gauge fields**- 56/2000 - Hidden symmetries of supersymmetric
*p*-form gauge theories

- 56/2000 - Hidden symmetries of supersymmetric
**p-harmonic**- 120/2006 - C
^{1,α}Regularity for Solutions to the p-Harmonic thin Obstacle Problem.

- 120/2006 - C
**p-harmonic maps**- 29/2002 - Stationary measures and rectifiability

**Painlevé**- 143/2006 - Riccati Chain, Higher Order Painlev\'e Type Equations and Stabilizer Set of Virasoro Orbit

**Painlevé equation**- 54/2007 - On universality of critical behaviour in the focusing nonlinear Schr\"odinger equation, elliptic umbilic catastrophe and the {\it tritronqu\'ee} solution to the Painlev\'e-I equation

**Painleve equation**- 57/2007 - Numerical study of a multiscale expansion of the Korteweg de Vries equation

**Painlev\'e-Gambier**- 41/2009 - On Generalized Sundman Transformation Method, First Integrals and Solutions of Painlev\'e-Gambier Type Equations

**pair-interaction**- 42/2003 - Maximizing Multi-Information

**Palais-Smale condition**- 31/2019 - α-Dirac-harmonic maps from closed surfaces

**panel clustering****panel-clustering****panmixia**- 28/2016 - The Equidistance Index of Population Structure

**parabolic boundary-value problem**- 46/2016 - On the Exit Time and Stochastic Homogenization of Isotropic Diffusions in Large Domains

**parabolic energy monotonicity**- 57/2002 - On moving Ginzburg-Landau filament vortices

**parabolic Green's function**- 3/2013 - Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics --- long version

**parabolic limit**- 34/2003 - Global existence of classical solutions for a hyperbolic chemotaxis model and its parabolic limit

**parabolic monge-ampére equation**- 66/2001 - A note on flows towards reflectors

**Parabolic obstacle problem**- 43/2006 - The Free Boundary Near the Fixed Boundary for the Heat Equation

**parabolic problems**- 80/2011 - Fast solution of multi-dimensional parabolic problems in the TT/QTT-format with initial application to the Fokker-Planck equation

**parabolic systems**- 11/2003 - Parabolic systems with nowhere smooth solutions

**parabolic-elliptic system**- 15/2015 - Blowup and Global Solutions in a Chemotaxis-Growth System

**parabolisch**- 14/2002 (
*Lecture note*) - Partielle Differentialgleichungen aus der Geometrie und Physik I - Parabolische und elliptische Probleme

- 14/2002 (
**parallel**- 115/2005 - Parallel Black Box Domain Decomposition Based -LU Preconditioning

**parallel adaptive grid generation**- 91/2006 - Dual Functions for a Parallel Adaptive Method

**parallel algorithms****parallel computation****parallel computing**- 38/2008 - From mesoscale back to microscale: Reconstruction schemes for coarse-grained stochastic lattice systems

**parallel iterative solvers**- 35/2001 - A parallel algebraic multigrid solver for finite element method based source localization in the human brain

**parallel solvers**- 10/2004 - Fast Parallel Solution of Boundary Integral Equations and Related Problems

**parameter dependent problems**- 68/2012 - Tensor-product approach to global time-space-parametric discretization of chemical master equation

**parametric problems**- 51/2012 - Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients

**Parsimonious Markov models**- 81/2013 - Inhomogeneous Parsimonious Markov Models

**Partial action of a group**- 34/2012 - Induced *-representations and C
^{*}-envelopes of some quantum *-algebras

- 34/2012 - Induced *-representations and C
**partial differential inclusions**- 16/2003 (
*Lecture note*) - Rigidity and Geometry of Microstructures

- 16/2003 (
**partial hyperbolicity**- 93/2005 - Structural stability and hyperbolicity violation in high-dimensional dynamical systems

**partial information lattice**- 72/2017 - Secret Sharing and Shared Information

**partial observability**- 22/2016 - Geometry and Determinism of Optimal Stationary Control in Partially Observable Markov Decision Processes

**partial regularity**- 64/2017 - Partial Regularity for a Nonlinear Sigma Model with Gravitino in Higher Dimensions
- 25/2017 - Regularity of Dirac-harmonic maps with λ−curvature term in higher dimensions
- 95/2002 - Structure of entropy solutions for multi--dimensional scalar conservation laws
- 47/2002 - Structure of entropy solutions: applications to variational problems
- 55/2000 - On the number of singular points of weak solutions to the Navier-Stokes equations

**partial transposition**- 73/2013 - A Note on Resistance of NPT to Mixture of Separable States

**partially deterministic HMM**- 24/2009 - Properties of the Statistical Complexity Functional and Partially Deterministic HMMs

**partition functions**- 45/2010 - Self-consistent-field theory investigation of behavior of hyaluronic acid chains in aqueous salt solution

**path measure****path properties**- 42/1997 - Function spaces as path spaces of Feller processes

**pattern**- 10/2016 - Rattling in spatially discrete diffusion equations with hysteresis

**pattern formation**- 56/2015 - Interpolation inequalities in pattern formation
- 25/2015 - Spatially discrete reaction-diffusion equations with discontinuous hysteresis
- 33/2008 - Clustered chimera states in delay-coupled oscillator systems
- 26/2005 - Making waves: Pattern formation by a cell surface-associated signal
- 98/2004 - Plants and Fibonacci

**Pattern Recognition**- 42/2012 - Adaptive sequential feature selection for pattern classification

**PCG iteration**- 47/2017 - A numerical primer in 2D stochastic homogenization: CLT scaling in the Representative Volume Element

**PDE****pde with stochastic forcing**- 53/2004 - Large-time behavior for viscous and non-viscous Hamilton-Jacobi equations forced by additive noise

**penalty method**- 55/2011 - Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics

**Penrose inequality**- 24/2014 - A Penrose inequality for graphs over Kottler space

**PEPS**- 15/2012 - Changing the topology of Tensor Networks

**Percolation**- 63/2014 - Moment bounds for the corrector in stochastic homogenization of a percolation model

**Percolation problems inspired by epidemic dynamics**- 27/2012 - Immunity space generated by a non trivial genetic-antigenic relation

**Perfect polynomials**- 92/2006 - Gelfand-Ponomarev constructions for quadruples and sextuples, and Herrmann's endomorphisms

**performance**- 65/2008 - Performance of H-LU Preconditioning for Sparse Matrices

**perimeter**- 52/2006 - Convexity of the free boundary for an exterior free boundary problem involving the perimeter

**period mapping**- 90/2014 - Harmonic maps and singularities of period mappings

**Period matrices**- 100/2018 - A numerical transcendental method in algebraic geometry

**periodic and homoclinic motions**- 36/2009 - Periodic and homoclinic travelling waves in infinite lattices

**periodic and homoclinic solutions**- 37/2009 - Subharmonics and homoclinics for a class of Hamiltonian-like equations

**periodic orbits**- 39/2005 - Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous computation of trajectories and Poincaré maps

**Periodic System of Chemical Elements**- 25/2019 - Formal structure of periodic system of elements

**periodic systems**- 12/2017 - Block circulant and Toeplitz structures in the linearized Hartree-Fock equation on finite lattices: tensor approach
- 62/2014 - Tensor Approach to Linearized Hartree-Fock Equation for Lattice-type and Periodic Systems
- 116/2013 - Grid-based lattice summation of electrostatic potentials by low-rank tensor approximation

**Periodic Table**- 25/2019 - Formal structure of periodic system of elements

**periods**- 27/2018 - Computing periods of hypersurfaces

**permanent**- 74/2018 - Circulant matrices and Galois-Togliatti systems

**perpetual motion**- 74/2008 - On Young's Paradox

**Perturbation Theory**- 7/2014 - Perturbative description of the fermionic projector: normalization, causality and Furry's theorem

**Perturbations**- 45/2015 - Rigorous asymptotics of traveling-wave solutions to the thin-film equation and Tanner's law

**Perturbative quantum field theory**- 4/2014 - The scaling and mass expansion

**Peter Weyl theorem**- 72/2007 - Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series

**Peter–Weyl decomposition**- 92/2018 - Associated noncommutative vector bundles over the Vaksman-Soibelman quantum complex projective spaces

**petrov-galerkin formulation**- 117/2005 - Nonconforming box-schemes for elliptic problems on rectangular grids

**phase**- 4/2013 - Synchronization in bipartite networks of oscillators with coupling delays

**phase boundaries**- 35/2006 - Normal modes and nonlinear stability behaviour of dynamic phase boundaries in elastic materials

**phase oscillator**- 24/2010 - Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays

**Phase segregation in disordered materials**- 14/2007 - Sharp-interface limit of a mesoscopic free energy with a random external field

**phase transformation****phase transformations****phase transition**- 113/2013 - Structure properties of evolutionary spatially embedded networks
- 112/2013 - Opinion evolution on a BA scaling network
- 38/2005 - Gamma-convergence of the Allen-Cahn energy with an oscillating forcing term
- 76/2004 - A variational model for dislocations in the line tension limit
- 34/2001 - A Gamma-convergence result for the two-gradient theory of phase transitions
- 27/1998 - Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere

**phase transitions**- 31/2007 - Convergence of phase-field approximations to the Gibbs-Thomson law
- 92/2003 - Γ-limit of a phase-field model of dislocations
- 58/2003 - Multi-information in the thermodynamic limit
- 32/2002 - An example in the gradient theory of phase transitions
- 80/2000 - Numerical analysis of a relaxed variational model of hysteresis in two-phase solids
- 9/1999 - Material instabilities in nematic elastomers

**phase-locked solutions**- 4/2013 - Synchronization in bipartite networks of oscillators with coupling delays

**phrase transitions**- 9/1997 - A nonlocal anisotropic model for phase transitions

Part II: Asymptotic behaviour of rescaled energies

- 9/1997 - A nonlocal anisotropic model for phase transitions
**phylogenetic footprint clusters**- 32/2005 - Detecting Phylogenetic Footprint Clusters by Optimizing Barbeques

**Phylogenetics**- 27/2017 - Phylogenetic complexity of the 3-Kimura model

**Picard groups**- 100/2018 - A numerical transcendental method in algebraic geometry

**Picard--Fuchs equations**- 27/2018 - Computing periods of hypersurfaces

**piecewise affine homeomorphism**- 34/2015 - Residually many BV homeomorphisms map a null set in a set of full measure

**pinning****pinning control**- 40/2007 - Adaptive dynamical networks via neighborhood information: synchronization and pinning control

**pivot strategy**- 29/2010 - Generalized Cross Approximation for 3d-tensors

**plasticity**- 20/2002 - A constitutive model for granular materials with grain crushing

**plate theories**- 15/2009 - Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density

**Plateau**- 16/2006 - On toroidal rotating drops

**plateau problem****plates****plethysm**- 48/2005 - New branching rules induced by plethysm

**plethysm,**- 77/2005 - A Hopf algebraic approach to the theory of group branchings

**pluricomplex green function**- 85/2002 - The Bergman metric and the pluricomplex Green function

**Podles sphere, q-oscillator algebra**- 34/2012 - Induced *-representations and C
^{*}-envelopes of some quantum *-algebras

- 34/2012 - Induced *-representations and C
**Pohozaev identity**- 13/2017 - Energy quantization for a nonlinear sigma model with critical gravitinos

**Pohozaev type constant**- 37/2018 - Asymptotic analysis for Dirac-harmonic maps from degenerating spin surfaces and with bounded index

**pohozaev's identity**- 67/1999 - Blowup in a chemotaxis model without symmetry assumptions

**Poincaré inequality**- 40/2012 - Poincaré and logarithmic Sobolev inequalities by decomposition of the energy landscape

**Poincaré polynomial**- 8/2017 - Discrete Morse-Bott theory for CW complexes

**Poincar\'e inequality**- 44/2011 - Geometric Analysis Aspects of Infinite Semiplanar Graphs with Nonnegative Curvature

**Point interactions**- 107/2006 - A Note on Pseudo-Hermitian Systems with Point Interactions and Quantum Separability

**pointcaré-steklov operators**- 18/2001 - -Matrix approximation for elliptic solution operators in cylindric domains

**Pointwise smoothness**- 53/2009 - On the efficient convolution with the Newton potential

**Poisson bivector**- 141/2006 - Quasi-Hamiltonian Structure and Hojman Construction

**Poisson bracket**- 49/2010 - On almost Poisson commutativity in dimension two

**Poisson equation**- 12/2011 - Low-rank Tensor Structure of Solutions to Elliptic Problems with Jumping Coefficients

**Poisson equation with transition condition**- 53/2006 - About solutions of Poisson's equation with transition condition in non-smooth domains

**Poisson problem**- 101/2018 - Numerical approximation of Poisson problems in long domains

**Poisson structure**- 42/2009 - On Planar and Non-planar Isochronous Systems and Poisson Structures

**Poisson-Boltzmann equation**- 12/2019 - Computing electrostatic potentials using regularization based on the range-separated tensor format

**polar**- 76/2011 - Duality of non-exposed faces

**polarization****policy gradient**- 22/2016 - Geometry and Determinism of Optimal Stationary Control in Partially Observable Markov Decision Processes

**polyconvex**- 68/2003 - On the regularity of critical points of polyconvex functionals

**polyconvex regularization**- 68/2008 - Quasiconvex relaxation of multidimensional control problems with integrands f(t,ξ,v)

**polyconvexity****polycrystal**- 73/2004 - Creep and recrystallization of large polycrystalline masses Part III: Continuum theory of ice sheets
- 72/2004 - Creep and recrystallization of large polycrystalline masses Part II: Constitutive theory for crystalline media with transversely isotropic grains
- 71/2004 - Creep and recrystallization of large polycrystalline masses Part I: General continuum theory

**polyelectrolyte solution**- 45/2010 - Self-consistent-field theory investigation of behavior of hyaluronic acid chains in aqueous salt solution

**polyharmonic eigen value**- 64/2005 - On a polyharmonic eigenvalue problem with indefinite weights.

**polyhedral angles**- 20/1997 - Vertex theorems for capillary drops on support planes

**polyhedral sets**- 16/2011 - On Solution Sets of Information Inequalities

**polyhedral surfaces**- 59/2006 - Genus one polyhedral surfaces, spaces of quadratic differentials on tori and determinants of Laplacians

**Polymer solution**- 49/2014 - On conformational behavior of solvophobic polymer at high pressures

**Polymer solutions**- 36/2014 - A Statistical Theory of co-solvent-induced coil-globule transitions in dilute polymer solution

**polymorphism**- 74/2005 - A mesoscopic model for helical bacterial flagella

**polynomial chaos**- 9/2010 - Tensor-Structured Galerkin Approximation of parametric and stochastic Elliptic PDEs

**polynomial chaos expansion**- 59/2014 - Computation of the Response Surface in the Tensor Train data format

**polynomial function**- 113/2007 - Algebraic, Tropical, and Fuzzy Geometry

**polytope**- 58/2012 - The convex support of the k-star model

**POMDP**- 22/2016 - Geometry and Determinism of Optimal Stationary Control in Partially Observable Markov Decision Processes

**population balance model**- 29/2006 - On the Efficient Evaluation of Coalescence Integrals in Population Balance Models

**population dynamics****population entropy rate**- 66/2016 - From Typical Sequences to Typical Genotypes

**population structure**- 28/2016 - The Equidistance Index of Population Structure

**porous media**- 12/2007 - Error estimates for a mixed finite element discretization of some degenerate parabolic equations

**positive curvature**- 57/1999 - Geometric Diffeomorphism Finiteness in Low Dimensions and Homotopy Group Finiteness

**Positive information decomposition**- 73/2017 - Computing the Unique Information

**positive mass theorem**- 24/2014 - A Penrose inequality for graphs over Kottler space

**positive maximum principle**- 41/1997 - Conservativeness and extensions of Feller semigroups

**positive polynomial**- 75/2018 - Optimal bounds on the positivity of a matrix from a few moments

**positive scalar curvature**- 66/2002 - Singular limit laminations, Morse index, and positive scalar curvature

**positive semidefinite**- 75/2018 - Optimal bounds on the positivity of a matrix from a few moments

**Positive solution**- 16/2008 - Harnack's inequality for some nonlocal equations and application

**post-fertilization traveling waves**- 23/2007 - Spectral stability of post-fertilization traveling waves

**Potential energy**- 23/2009 - The tensor product approximation to single-electron systems

**potential theory**- 63/2006 - Analysis and numerical simulation of magnetic forces between rigid polygonal bodies. Part I: Analysis

**power-law**- 46/2011 - On the Application of the Cross-Correlations in the Chinese Fund Market: Descriptive Properties and Scaling Behaviors

**ppt****PPT state**- 12/2006 - Separability and Entanglement of Identical Bosonic Systems

**pragmatic structuring**- 52/2000 - An information geometric approach to a theory of pragmatic structuring

**precessional switching**- 123/2005 - Multi-scale analysis of magnetization dynamics driven by external fields

**precondition methods**- 10/2017 - Rank structured approximation method for quasi--periodic elliptic problems

**preconditioner****preconditioners**- 55/2010 - Tensor Structured Iterative Solution of Elliptic Problems with Jumping Coefficients
- 37/2010 - Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs
- 9/2010 - Tensor-Structured Galerkin Approximation of parametric and stochastic Elliptic PDEs
- 78/2005 - On the numerical solution of convection-dominated problems using hierarchical matrices

**preconditioning**- 51/2012 - Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients
- 82/2008 - Tensor-structured Preconditioners and Approximate Inverse of Elliptic Operators in ℝ
^{d} - 65/2008 - Performance of H-LU Preconditioning for Sparse Matrices
- 62/2004 - -matrix preconditioners in convection-dominated problems
- 17/2004 - Adaptive Recompression of -Matrices for BEM
- 45/2001 - Boundary concentrated finite element methods

**prediction****prediction process**- 24/2009 - Properties of the Statistical Complexity Functional and Partially Deterministic HMMs

**Predictive Inference**- 26/2012 - A Predictive Approach to Nonparametric Inference for Adaptive Sequential Sampling of Psychophysical Experiments

**Predictive Information**- 60/2013 - Information-driven intrinsic motivation in reinforcement learning

**Prelle-Singer**- 51/2008 - Solutions of some second order ODEs by the extended Prelle-Singer method and symmetrics

**prescribed gauß curvature**- 14/2001 - Hypersurfaces of prescribed Gauss curvature in exterior domains

**pressure**- 92/2001 - On solutions to the Navier-Stokes equations with lower bounds on pressure

**pressure functional**- 71/2007 - C
^{*}-algebraic approach to the Bose-Hubbard model

- 71/2007 - C
**Prevention**- 10/2007 - The probability of HIV infection in a new host and its reduction with microbicides

**Price Formation**- 38/2017 - Bidding with Coordination Risks

**prime ideal**- 113/2007 - Algebraic, Tropical, and Fuzzy Geometry

**principal comodule algebra**- 92/2018 - Associated noncommutative vector bundles over the Vaksman-Soibelman quantum complex projective spaces

**Probabilistic powerdomain**- 30/2018 - Bimonoidal Structure of Probability Monads

**product structures**- 76/2010 - On product structures in Floer homology of cotangent bundles

**Products of orbitals**- 71/2009 - Efficient multi-scale computation of products of orbitals in electronic structure calculations

**projected subtraction approach**- 95/2007 - A highly accurate full subtraction approach for dipole modelling in EEG source analysis using the finite element method

**projection**- 52/2007 - Numerical computation of inner eigenvalues using the Dunford Cauchy integral

**projection theorem**- 75/2011 - Information topologies on non-commutative state spaces

**projective geometry**- 72/2018 - Prym varieties of genus four curves

**projective structure**- 144/2006 - Euler-Poincaré flows on sl
_{n}Opers and Integrability

- 144/2006 - Euler-Poincaré flows on sl
**propagation failure**- 50/2005 - Pinning and De-Pinning Phenomena in Front Propagation in Heterogeneous Media

**Prosopagnosia****proto-organism**- 91/2002 - Proto-Organism Kinetics: Evolutionary Dynamics of Lipid Aggregates with Genes and Metabolism

**proximal point algorithm****Prym varieties**- 72/2018 - Prym varieties of genus four curves

**pseudo-differential operator****pseudo-differential symbols**- 48/2008 - Virasoro Action on Pseudo-differential Symbols and (Noncommutative) Supersymmetric Peakon Type Integrable Systems

**pseudo-holomorphic curves**- 3/2005 - Almost-holomorphic and totally real solenoids in complex surfaces

**pseudodifferential operator**- 109/2006 - The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels

**pseudodifferential symbols**- 88/2007 - Supersymmetric Kuper Camassa-Holm Equation and Geodesic Flow : A Novel Approach

**Pseudopotentials**- 29/2009 - Canonical tensor products as a generalization of Gaussian-type orbitals

**Psychophysics**- 26/2012 - A Predictive Approach to Nonparametric Inference for Adaptive Sequential Sampling of Psychophysical Experiments

**PT-symmetry**- 107/2006 - A Note on Pseudo-Hermitian Systems with Point Interactions and Quantum Separability

**pulsating waves****pure states**- 53/2012 - Improved bounds on negativity of superpositions

**Pythagorean theorem**- 75/2011 - Information topologies on non-commutative state spaces