## Advances in Mathematics Research, Volume 5Mathematics 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. |

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### Contents

BEST APPROXIMATION IN RANDOM NORMED SPACES | 1 |

THE DESKINS COMPLETIONS AND THETA COMPLETIONS OF A MAXIMAL SUBGROUP | 19 |

Approximation by Matrix Means of WalshFourier Series | 31 |

Irreversibility Factor and Limiting Performance of Financial Systems Thermodynamic Approach | 47 |

Tool for Verification of Hyperbolicity and Structural Stability | 79 |

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adjoint attractor bank best approximation capital cells chain recurrent set classical mechanics cloning template commutator complementary differential composite index consider constant convex convolution core-free corresponding cyclic defined Definition denote diffeomorphism differential equations dynamical system elements equilibrium point exists a maximal exponential finite formula Fourier transform G is solvable Gabriel Oyibo group G Heisenberg group Hence hyperbolic inequality kernel Lemma Math Mathematics maximal completion maximal subgroup minimal normal subgroup Morse spectrum Moyal brackets nilpotent nonlinear normed spaces Nova Science Publishers operator optimal control orbits parameters price estimates problem profit projective bundle Proof Proposition quantisation quantum mechanics random normed spaces recurrent vertices representations ph sequence Serstnev stable stocks of asset structural stability subgroup of G subset supersolvable Sylow 2-subgroup symbolic image Theorem trajectory tumor variable vector wavelet transform weak convergence