## Advances in Mathematics Research, Volume 4Mathematics has been behind many of humanity's most significant advances in fields as varied as genome sequencing, medical science, space exploration, and computer technology. But those breakthroughs were yesterday. Where will mathematicians lead us tomorrow and can we help shape that destiny? This book assembles carefully selected articles highlighting and explaining cutting-edge research and scholarship in mathematics. Contents: Preface; Solvability of Quasilinear Elliptic Second Order Differential Equations in Rn without Condition at Infinity; Recent Topics on a Class of Nonlinear Integrodifferential Equations of Physical Significance'; Nonparametric Estimation with Censored Observations; Normalisers of Groups Commensurable with PSL2(Z); Spectral Analysis of a Class of Multigroup Neutron Transport Operators in Slab Geometry; Extremum of a Nonlocal Functional Depending on Higher Order Derivatives of the Unknown Function; On Quantum Conditional Probability Spaces; Index. |

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### Contents

1 | |

Recent Topics on a Class of Nonlinear Integrodifferential Evolution Equations of Physical Significance | 19 |

Nonparametric Estimation with Censored Observations | 91 |

Normalisers of Groups Commensurable with PSL2S | 99 |

Spectral Analysis of a Class of Multigroup Neutron Transport Operators in Slab Geometry | 117 |

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action-angle variables Advances in Mathematics Ai(x algebraic amplitude asymptotic Atkin-Lehner involution Banach space Benjamin-Ono bilinear BO equation boundary conditions completeness relation conditional probability constant corresponding dark soliton defined denote density derived discrete spectrum divisor divisor of 24 eigenfunctions eigenvalue problem estimate evolution equations exact divisor exists finite fluid follows G N(m Gabriel Oyibo given Hence inequality initial condition initial value problem inverse scattering iV-soliton solution Jost functions kernel largest divisor lattices Lax pair Lemma linear Math matrix Matsuno modulation equations multigroup multiple neutron transport nonlocal nonlocal NLS equation obtain P-projections periodic wave solution Phys Proof quantum logic satisfied scattering data sequence solitary waves soliton parameters solution of Eq solving spectral square free subgroup subset supergroup Suppose Theorem 2.2 To(N transport operator variables variational zero