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1. 发明申请

US20110082895A1 EXPLOITATION OF TOPOLOGICAL CATEGORIZATION OF CHAOTIC AND FRACTAL FUNCTIONS INCLUDING FIELD LINE CALCULATIONS 有权
标题翻译：使用包括现场线计算在内的混沌和分离函数的拓扑分类
公开(公告)号：US20110082895A1
公开(公告)日：2011-04-07
申请号：US12877922
申请日：2010-09-08
申请人： Michael T. Everest
发明人： Michael T. Everest
IPC分类号： G06F17/10
CPC分类号： G06F7/4806
摘要： A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations
摘要翻译：基于包容性间隔的拓扑分类方法提供了一种在复杂和更高维度中分析离散动态系统的逃生拓扑的一般方法，包括计算复杂和超复合的潜力以及复杂迭代的场线

2. 发明授权

US08332446B1 Setup of precise polynomial evaluation by utilizing a compressed root product form 有权
标题翻译：通过使用压缩的根产品形式设置精确的多项式评估
公开(公告)号：US08332446B1
公开(公告)日：2012-12-11
申请号：US12271663
申请日：2008-11-14
申请人： Michael T. Everest
发明人： Michael T. Everest
IPC分类号： G06F7/38
CPC分类号： G06F7/544 , G06F7/483
摘要： Based on the root-product polynomial form, this method compresses essential information of a polynomial by transforming polynomials into a form which eliminates cancellation error, when evaluating polynomials, of one unknown, for real, complex, and quaternion, which are implemented with floating point numbers. Additional filtering methods simplify evaluation, including the elimination of extremely small and large root factors, which can cause out-of-range errors. The usual setup problem for root-product forms, that of needing potentially unlimited root precision and floating point range, is largely eliminated for real polynomials, and greatly mitigated for complex and quaternion, and other hypercomplex polynomials.
摘要翻译：基于根产品多项式形式，该方法通过将多项式变换为消除抵消误差的形式，在评估多项式时，通过浮点实现的一个未知数，实数，复数和四元数，来压缩多项式的基本信息数字。额外的过滤方法简化了评估，包括消除极小和大的根系因素，这可能导致超出范围的误差。根本产品形式的常见设置问题，需要潜在的无限根精度和浮点范围的设置问题，在实际多项式中大部分被消除，并且对于复数和四元数以及其他超复杂多项式而言大大减轻。

3. 发明申请

US20140289294A1 COMPLETE MAPPING OF FRACTAL POTENTIAL AND FIELD LINES 审中-公开
标题翻译：分段电位和场线的完整映射
公开(公告)号：US20140289294A1
公开(公告)日：2014-09-25
申请号：US14300169
申请日：2014-06-09
申请人： Michael T. Everest
发明人： Michael T. Everest
IPC分类号： G06F7/48
CPC分类号： G06F7/4806 , G06F17/14 , G06T11/001
摘要： Faster methods for topological categorization and field line calculations are developed by using decomposition regions together with the self-winding techniques first developed in a prior patent application. A point iteration technique provides direct calculation of low order digits of winding counts without use of complex intervals. Easy to calculate derivatives define decomposition interval boundaries which substitute for methods using the slower complex interval processing of the prior patent. Methods common to this and the prior patent are developed for visualizing conformal mappings of iterated functions.
摘要翻译：通过使用分解区域和先前专利申请中首先开发的自动上链技术，开发更快的拓扑分类和现场线计算方法。点迭代技术可直接计算绕组计数的低位数，而不需要复杂的间隔。易于计算的导数定义了使用先前专利的较慢复杂间隔处理替代方法的分解间隔边界。开发了用于可视化迭代函数的保形映射的这个和现有专利的共同方法。

4. 发明授权

US08095583B1 Chaotic and fractal field line calculations using decomposition and self winding 有权
$Chaotic and fractal field line calculations using decomposition and self winding$
标题翻译：混沌和分形场线计算使用分解和自动上链
公开(公告)号：US08095583B1
公开(公告)日：2012-01-10
申请号：US11757858
申请日：2007-06-04
申请人： Michael T. Everest
发明人： Michael T. Everest
IPC分类号： G06F15/00 , G09G5/00
CPC分类号： G06F7/4806 , G06F17/14 , G06T11/001
摘要： Faster methods for topological categorization and field line calculations are developed by using decomposition regions together with the self-winding techniques first developed in a prior patent application. A point iteration technique provides direct calculation of low order digits of winding counts without use of complex intervals. Easy to calculate derivatives define decomposition interval boundaries which substitute for methods using the slower complex interval processing of the prior patent. Methods common to this and the prior patent are developed for visualizing conformal mappings of iterated functions.
摘要翻译：通过使用分解区域和先前专利申请中首先开发的自动上链技术，开发更快的拓扑分类和现场线计算方法。点迭代技术可直接计算绕组计数的低位数，而不需要复杂的间隔。易于计算的导数定义了使用先前专利的较慢复杂间隔处理替代方法的分解间隔边界。开发了用于可视化迭代函数的保形映射的这个和现有专利的共同方法。

5. 发明申请

US20110082894A1 EXPLOITATION OF TOPOLOGICAL CATEGORIZATION OF CHAOTIC AND FRACTAL FUNCTIONS, INCLUDING FIELD LINE CALCULATIONS 有权
标题翻译：使用混沌和分割函数的拓扑分类，包括现场线性计算
公开(公告)号：US20110082894A1
公开(公告)日：2011-04-07
申请号：US12877908
申请日：2010-09-08
申请人： Michael T. Everest
发明人： Michael T. Everest
IPC分类号： G06F17/14
CPC分类号： G06F7/4806
摘要： A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations.
摘要翻译：基于包容性间隔的拓扑分类方法提供了一种在复杂和更高维度中分析离散动态系统的逃生拓扑的一般方法，包括计算复杂和超复合的潜力以及复杂迭代的场线。

6. 发明授权

US07801939B1 Complex and hypercomplex inclusive interval expression evaluations with stable numeric evaluations and precision efficacy testing 有权
标题翻译：复杂和超复杂包容性间期表达式评估与稳定的数值评估和精确功效测试
公开(公告)号：US07801939B1
公开(公告)日：2010-09-21
申请号：US11336166
申请日：2006-01-19
申请人： Michael T. Everest
发明人： Michael T. Everest
IPC分类号： G06F7/38
CPC分类号： G06F7/49989
摘要： Improvements to optimal interval operators are developed for interval expression evaluation using arithmetic and real power operators applied to complex and hypercomplex number systems. A method for determining efficacy of numeric precision, incorporating minor changes to interval operators, provides detection of insufficient numeric evaluation precision.
摘要翻译：对于使用应用于复杂和超复合数量系统的算术和实数算子的间隔表达式评估，开发了对最优区间算子的改进。用于确定数值精度效能的方法，对间隔算子进行微小修改，提供了对数值评估精度不足的检测。

7. 发明授权

US08468190B2 Complex and hypercomplex inclusive interval expression evaluations with stable numeric evaluations and precision efficacy testing 有权
标题翻译：复杂和超复杂包容性间期表达式评估与稳定的数值评估和精确功效测试
公开(公告)号：US08468190B2
公开(公告)日：2013-06-18
申请号：US12877895
申请日：2010-09-08
申请人： Michael T. Everest
发明人： Michael T. Everest
IPC分类号： G06F7/38
CPC分类号： G06F7/49989
摘要： Improvements to optimal interval operators are developed for interval expression evaluation using arithmetic and real power operators applied to complex and hypercomplex number systems. A method for determining efficacy of numeric precision, incorporating minor changes to interval operators, provides detection of insufficient numeric evaluation precision.
摘要翻译：对于使用应用于复杂和超复合数量系统的算术和实数算子的间隔表达式评估，开发了对最优区间算子的改进。用于确定数值精度效能的方法，对间隔算子进行微小修改，提供了对数值评估精度不足的检测。

8. 发明授权

US08402076B2 Exploitation of topological categorization of chaotic and fractal functions, including field line calculations 有权
$Exploitation of topological categorization of chaotic and fractal functions, including field line calculations$
标题翻译：利用混沌和分形函数的拓扑分类，包括场线计算
公开(公告)号：US08402076B2
公开(公告)日：2013-03-19
申请号：US12877908
申请日：2010-09-08
申请人： Michael T. Everest
发明人： Michael T. Everest
IPC分类号： G06F7/00 , G06F7/38
CPC分类号： G06F7/4806
摘要： A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations.
摘要翻译：基于包容性间隔的拓扑分类方法提供了一种在复杂和更高维度中分析离散动态系统的逃生拓扑的一般方法，包括计算复杂和超复合的潜力以及复杂迭代的场线。

9. 发明申请

US20100332572A1 EXPLOITATION OF TOPOLOGICAL CATEGORIZATION OF CHAOTIC AND FRACTAL FUNCTIONS, INCLUDING FIELD LINE CALCULATIONS 有权
标题翻译：使用混沌和分割函数的拓扑分类，包括现场线性计算
公开(公告)号：US20100332572A1
公开(公告)日：2010-12-30
申请号：US12877949
申请日：2010-09-08
申请人： Michael T. Everest
发明人： Michael T. Everest
IPC分类号： G06F7/38
CPC分类号： G06F7/4806
摘要： A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations
摘要翻译：基于包容性间隔的拓扑分类方法提供了一种在复杂和更高维度中分析离散动态系统的逃生拓扑的一般方法，包括计算复杂和超复合的潜力以及复杂迭代的场线

10. 发明授权

US07805481B1 Exploitation of topological categorization of chaotic and fractal functions, including field line calculations 有权
$Exploitation of topological categorization of chaotic and fractal functions, including field line calculations$
标题翻译：利用混沌和分形函数的拓扑分类，包括场线计算
公开(公告)号：US07805481B1
公开(公告)日：2010-09-28
申请号：US11336187
申请日：2006-01-19
申请人： Michael T. Everest
发明人： Michael T. Everest
IPC分类号： G06F7/38
CPC分类号： G06F7/4806
摘要： A topological categorization method, based on inclusive intervals, provides a general method of analyzing escape topologies for discrete dynamic systems, in complex and higher dimensions, including the calculation of both potential for complex and hypercomplex and field lines for complex iterations.
摘要翻译：基于包容性间隔的拓扑分类方法提供了一种在复杂和更高维度中分析离散动态系统的逃生拓扑的一般方法，包括计算复杂和超复合的潜力以及复杂迭代的场线。

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