## Advances in Mathematics Research, Volume 1This book presents research from leading scholars throughout the world. Contents: Preface; Reduction Theory of Von Neumann Algebras in Real Case; Some Recent Results and Problems for Set-Valued Mappings; On (p, s)-Regularity of the Inversion Problem for the Sturm-Liouville Equation; Spaces of Functions Holomorphic in Convex Bounded Domains of C and Smooth Up to the Boundary; Weak Bilevel Programming Problems: Existence of Solutions; A Remark about the Shannon's Sampling Theorem; Quantum Integral Equations with Kernels of Quantum White Noise in Space and Time; On the Dependence Structure of a System of Components with a Multivariate Shot-Noise Hazard Rate Process; Global Exponential Stability and Periodic Solutions of Cellular Neural Networks (CNN's) with Delays; Some Remarks on the Charged Top; On a Transport Operator Arising in Growing Cell Populations Spectral Analysis; On Viscoelastic Fluids in Elongation; Fuzzy relational Model for Knowledge Processing and Decision Making; Index |

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### Contents

Reduction Theory of von Neumann Algebras in Real Case | 1 |

Some Recent Results and Problems for SetValued Mappings | 31 |

On p sRegularity of the Inversion Problem for the SturmLiouville Equation | 51 |

Spaces of Functions Holomorphic in Convex Bounded Domains of Cⁿ and Smooth Up to the Boundary | 71 |

Existence of Solutions | 83 |

A Remark about the Shannons Sampling Theorem | 93 |

Quantum Integral Equations with Kernels of Quantum White Noise in Space and Time | 97 |

On the Dependence Structure of a System of Components with a Multivariate ShotNoise Hazard Rate Process | 109 |

New Results Concerning Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks | 135 |

Some Remarks on the Charged Top | 151 |

On a Transport Operator Arising in Growing Cell Populations Spectral Analysis | 159 |

On Viscoelastic Fluids in Elongation | 187 |

Fuzzy Relational Model for Knowledge Processing and Decision Making | 207 |

241 | |

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A G C algebra in H associated Assume assumptions Banach space Borel bar space boundary-regular bounded Caristi selection cellular neural networks compact complete metric space complex components constant control actions converges Corollary DCNNs decision defined Definition denote diagonal operator distribution eigenvalue environment equations estimate exists field of Hilbert finite fixed point theorem fuzzy set Hence Hilbert space implies inequality integral knowledge base knowledge representation leading eigenvalue Lemma lifelengths linear LP(R Lyapunov functional Math Mathematics membership function Moreover multivariate shot-noise process nonempty nonexpansive mappings norm obtain orthant orthant dependent parameters periodic solutions point process Polish space probability measure problem proof of Theorem properties Proposition real Hilbert space real measurable field real VN algebra relation of preference resp respect satisfies sequence set of alternatives set-valued mapping stochastic Theorem 4.1 theory topology values von Neumann algebra weakly