This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”....This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others.展开更多
The test of Prentice [1] is a non-parametric statistical test for the two-way analysis of variance using ranks. The null distribution of this test typically is approximated using the Chi-square distribution. However, ...The test of Prentice [1] is a non-parametric statistical test for the two-way analysis of variance using ranks. The null distribution of this test typically is approximated using the Chi-square distribution. However, the exact null distribution deviates from the Chi-square approximation in certain cases commonly found in applications of the test, motivating adjustments to the distribution. This manuscript presents adjustments to this null distribution correcting for continuity, multivariate skewness, and multivariate kurtosis. The effects of alternative scoring methods as non-polynomial functions of rank sums are also presented as a broader application of the approximation.展开更多
In this paper we prove in a new way, the well known result, that Fermat’s equation a<sup>4</sup> + b<sup>4</sup> = c<sup>4</sup>, is not solvable in ℕ , when abc≠0 . To show this ...In this paper we prove in a new way, the well known result, that Fermat’s equation a<sup>4</sup> + b<sup>4</sup> = c<sup>4</sup>, is not solvable in ℕ , when abc≠0 . To show this result, it suffices to prove that: ( F 0 ): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is not solvable in ℕ , (where a 1 , b 1 , c 1 ∈2ℕ+1 , pairwise primes, with necessarly 2≤s∈ℕ ). The key idea of our proof is to show that if (F<sub>0</sub>) holds, then there exist α 2 , β 2 , γ 2 ∈2ℕ+1 , such that ( F 1 ): α 2 4 + ( 2 s−1 β 2 ) 4 = γ 2 4 , holds too. From where, one conclude that it is not possible, because if we choose the quantity 2 ≤ s, as minimal in value among all the solutions of ( F 0 ) , then ( α 2 ,2 s−1 β 2 , γ 2 ) is also a solution of Fermat’s type, but with 2≤s−1<s , witch is absurd. To reach such a result, we suppose first that (F<sub>0</sub>) is solvable in ( a 1 ,2 s b 1 , c 1 ) , s ≥ 2 like above;afterwards, proceeding with “Pythagorician divisors”, we creat the notions of “Fermat’s b-absolute divisors”: ( d b , d ′ b ) which it uses hereafter. Then to conclude our proof, we establish the following main theorem: there is an equivalence between (i) and (ii): (i) (F<sub>0</sub>): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is solvable in ℕ , with 2≤s∈ℕ , ( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs. (ii) ∃( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs, for wich: ∃( b ′ 2 , b 2 , b ″ 2 )∈ ( 2ℕ+1 ) 3 coprime in pairs, and 2≤s∈ℕ , checking b 1 = b ′ 2 b 2 b ″ 2 , and such that for notations: S=s−λ( s−1 ) , with λ∈{ 0,1 } defined by c 1 − a 1 2 ≡λ( mod2 ) , d b =gcd( 2 s b 1 , c 1 − a 1 )= 2 S b 2 and d ′ b = 2 s−S b ′ 2 = 2 s B 2 d b , where ( 2 s B 2 ) 2 =gcd( b 1 2 , c 1 2 − a 1 2 ) , the following system is checked: { c 1 − a 1 = d b 4 2 2+λ = 2 2−λ ( 2 S−1 b 2 ) 4 c 1 + a 1 = 2 1+λ d ′ b 4 = 2 1+λ ( 2 s−S b ′ 2 ) 4 c 1 2 + a 1 2 =2 b ″ 2 4;and this system implies: ( b 1−λ,2 4 ) 2 + ( 2 4s−3 b λ,2 4 ) 2 = ( b ″ 2 2 ) 2;where: ( b 1−λ,2 , b λ,2 , b ″ 2 )={ ( b ′ 2 , b 2 , b ″ 2 ) if λ=0 ( b 2 , b ′ 2 , b ″ 2 ) if λ=1;From where, it is quite easy to conclude, following the method explained above, and which thus closes, part I, of this article. .展开更多
In this research, we study the relationship between mental workload and facial temperature of aircraft participants during a simulated takeoff flight. We conducted experiments to comprehend the correlation between wor...In this research, we study the relationship between mental workload and facial temperature of aircraft participants during a simulated takeoff flight. We conducted experiments to comprehend the correlation between work and facial temperature within the flight simulator. The experiment involved a group of 10 participants who played the role of pilots in a simulated A-320 flight. Six different flying scenarios were designed to simulate normal and emergency situations on airplane takeoff that would occur in different levels of mental workload for the participants. The measurements were workload assessment, face temperatures, and heart rate monitoring. Throughout the experiments, we collected a total of 120 instances of takeoffs, together with over 10 hours of time-series data including heart rate, workload, and face thermal images and temperatures. Comparative analysis of EEG data and thermal image types, revealed intriguing findings. The results indicate a notable inverse relationship between workload and facial muscle temperatures, as well as facial landmark points. The results of this study contribute to a deeper understanding of the physiological effects of workload, as well as practical implications for aviation safety and performance.展开更多
In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, t...In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.展开更多
Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of ...Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.展开更多
The semantic segmentation of very high spatial resolution remote sensing images is difficult due to the complexity of interpreting the interactions between the objects in the scene. Indeed, effective segmentation requ...The semantic segmentation of very high spatial resolution remote sensing images is difficult due to the complexity of interpreting the interactions between the objects in the scene. Indeed, effective segmentation requires considering spatial local context and long-term dependencies. To address this problem, the proposed approach is inspired by the MAC-UNet network which is an extension of U-Net, densely connected combined with channel attention. The advantages of this solution are as follows: 4) The new model introduces a new attention called propagate attention to build an attention-based encoder. 2) The fusion of multi-scale information is achieved by a weighted linear combination of the attentions whose coefficients are learned during the training phase. 3) Introducing in the decoder, the Spatial-Channel-Global-Local block which is an attention layer that uniquely combines channel attention and spatial attention locally and globally. The performances of the model are evaluated on 2 datasets WHDLD and DLRSD and show results of mean intersection over union (mIoU) index in progress between 1.54% and 10.47% for DLRSD and between 1.04% and 4.37% for WHDLD compared with the most efficient algorithms with attention mechanisms like MAU-Net and transformers like TMNet.展开更多
The global bifurcation and chaos are investigated in this paper for a van der Pol-Duffing-Mathieu system with a single-well potential oscillator by means of nonlinear dynamics. The autonomous system corresponding to t...The global bifurcation and chaos are investigated in this paper for a van der Pol-Duffing-Mathieu system with a single-well potential oscillator by means of nonlinear dynamics. The autonomous system corresponding to the system under discussion is analytically studied to draw all global bifurcation diagrams in every parameter space. These diagrams are called basic bifurcation ones. Then fixing parameter in every space and taking the parametrically excited amplitude as a bifurcation parameter, we can observe how to evolve from a basic bifurcation diagram to a chaos pattern in terms of numerical methods. The results are sufficient to show that the system has distinct dynamic behavior. Finally, the properties of the basins of attraction are observed and the appearance of fractal basin boundaries heralding the onset of a loss of structural integrity is noted in order to consider how to control the extent and the rate of the erosion in the next paper.展开更多
In this paper, we develop a mathematical model of the COVID-19 pandemic in Burkina Faso. We use real data from Burkina Faso National Health Commission against COVID-19 to predict the dynamic of the disease and also th...In this paper, we develop a mathematical model of the COVID-19 pandemic in Burkina Faso. We use real data from Burkina Faso National Health Commission against COVID-19 to predict the dynamic of the disease and also the cumulative number of reported cases. We use public policies in model in order to reduce the contact rate, this allows to show how the reduction of the daily report of infectious cases goes, so we would like to draw the attention of decision makers for a rapid treatment of reported cases.展开更多
This study sought to determine the best method to quantify training based on heart rate data. It proposes a modification of Banister’s original performance model to improve the accuracy of predicted performance. The ...This study sought to determine the best method to quantify training based on heart rate data. It proposes a modification of Banister’s original performance model to improve the accuracy of predicted performance. The new formulation introduces a variable that accounts for changes in the subject’s initial performance as a result of the quantity of training. The two systems models were applied to a well-trained female monofin swimmer over a 24-week training period. Each model comprised a set of parameters unique to the individual and was estimated by fitting model-predicted performance to measured performance. We used the Alienor method associated to Optimization-Preserving Operators to identify these parameters. The quantification method based on training intensity zones gave a better estimation of predicted performance in both models. Using the new model in sports in which performance is generally predicted (running, swimming) will help us to define its real interest.展开更多
Math Works近日推出Robotics System Toolbox（机器人系统工具箱），这个新产品是Release 2015a的组成部分。、通过即用型算法和用于开发自动移动机器人应用程序的硬件连接性，Robotics System Toolbox提供了常用的机器人算法，以及MAT...Math Works近日推出Robotics System Toolbox（机器人系统工具箱），这个新产品是Release 2015a的组成部分。、通过即用型算法和用于开发自动移动机器人应用程序的硬件连接性，Robotics System Toolbox提供了常用的机器人算法，以及MATLAB和Simulink与机器人操作系统（ROS）之间的接口和集成。现在，机器人研究人员和工程师们可以在单个统一的设计环境中开发机器人算法，在支持ROS的机器人和机器人仿真器（如Gazebo和V—REP）上测试和部署机器人算法。它通过减少从MATLAB程序转换到ROS程序所需的手动修改时间，留出了更多的时间来测试和调试算法。展开更多
Two versions of a mathematical model are proposed for the process underlying the choice of settlement sites of past, present and future populations along the world coastline. The model is primarily based on the geomet...Two versions of a mathematical model are proposed for the process underlying the choice of settlement sites of past, present and future populations along the world coastline. The model is primarily based on the geometry of coastline at the scale of the map representing the region under study. It can be used to determine sites of human occupation for archaeological interest, as well as to plan future movements of present coastal populations due to the current sea level rise. Two examples related to history are presented: the first applies to the coastal peopling of the Mediterranean region, and the second to the settlement of Acadians in North-East of the Canadian province of New Brunswick in the second half of the 18th century.展开更多
文摘This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others.
文摘The test of Prentice [1] is a non-parametric statistical test for the two-way analysis of variance using ranks. The null distribution of this test typically is approximated using the Chi-square distribution. However, the exact null distribution deviates from the Chi-square approximation in certain cases commonly found in applications of the test, motivating adjustments to the distribution. This manuscript presents adjustments to this null distribution correcting for continuity, multivariate skewness, and multivariate kurtosis. The effects of alternative scoring methods as non-polynomial functions of rank sums are also presented as a broader application of the approximation.
文摘In this paper we prove in a new way, the well known result, that Fermat’s equation a<sup>4</sup> + b<sup>4</sup> = c<sup>4</sup>, is not solvable in ℕ , when abc≠0 . To show this result, it suffices to prove that: ( F 0 ): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is not solvable in ℕ , (where a 1 , b 1 , c 1 ∈2ℕ+1 , pairwise primes, with necessarly 2≤s∈ℕ ). The key idea of our proof is to show that if (F<sub>0</sub>) holds, then there exist α 2 , β 2 , γ 2 ∈2ℕ+1 , such that ( F 1 ): α 2 4 + ( 2 s−1 β 2 ) 4 = γ 2 4 , holds too. From where, one conclude that it is not possible, because if we choose the quantity 2 ≤ s, as minimal in value among all the solutions of ( F 0 ) , then ( α 2 ,2 s−1 β 2 , γ 2 ) is also a solution of Fermat’s type, but with 2≤s−1<s , witch is absurd. To reach such a result, we suppose first that (F<sub>0</sub>) is solvable in ( a 1 ,2 s b 1 , c 1 ) , s ≥ 2 like above;afterwards, proceeding with “Pythagorician divisors”, we creat the notions of “Fermat’s b-absolute divisors”: ( d b , d ′ b ) which it uses hereafter. Then to conclude our proof, we establish the following main theorem: there is an equivalence between (i) and (ii): (i) (F<sub>0</sub>): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is solvable in ℕ , with 2≤s∈ℕ , ( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs. (ii) ∃( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs, for wich: ∃( b ′ 2 , b 2 , b ″ 2 )∈ ( 2ℕ+1 ) 3 coprime in pairs, and 2≤s∈ℕ , checking b 1 = b ′ 2 b 2 b ″ 2 , and such that for notations: S=s−λ( s−1 ) , with λ∈{ 0,1 } defined by c 1 − a 1 2 ≡λ( mod2 ) , d b =gcd( 2 s b 1 , c 1 − a 1 )= 2 S b 2 and d ′ b = 2 s−S b ′ 2 = 2 s B 2 d b , where ( 2 s B 2 ) 2 =gcd( b 1 2 , c 1 2 − a 1 2 ) , the following system is checked: { c 1 − a 1 = d b 4 2 2+λ = 2 2−λ ( 2 S−1 b 2 ) 4 c 1 + a 1 = 2 1+λ d ′ b 4 = 2 1+λ ( 2 s−S b ′ 2 ) 4 c 1 2 + a 1 2 =2 b ″ 2 4;and this system implies: ( b 1−λ,2 4 ) 2 + ( 2 4s−3 b λ,2 4 ) 2 = ( b ″ 2 2 ) 2;where: ( b 1−λ,2 , b λ,2 , b ″ 2 )={ ( b ′ 2 , b 2 , b ″ 2 ) if λ=0 ( b 2 , b ′ 2 , b ″ 2 ) if λ=1;From where, it is quite easy to conclude, following the method explained above, and which thus closes, part I, of this article. .
文摘In this research, we study the relationship between mental workload and facial temperature of aircraft participants during a simulated takeoff flight. We conducted experiments to comprehend the correlation between work and facial temperature within the flight simulator. The experiment involved a group of 10 participants who played the role of pilots in a simulated A-320 flight. Six different flying scenarios were designed to simulate normal and emergency situations on airplane takeoff that would occur in different levels of mental workload for the participants. The measurements were workload assessment, face temperatures, and heart rate monitoring. Throughout the experiments, we collected a total of 120 instances of takeoffs, together with over 10 hours of time-series data including heart rate, workload, and face thermal images and temperatures. Comparative analysis of EEG data and thermal image types, revealed intriguing findings. The results indicate a notable inverse relationship between workload and facial muscle temperatures, as well as facial landmark points. The results of this study contribute to a deeper understanding of the physiological effects of workload, as well as practical implications for aviation safety and performance.
文摘In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.
文摘Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.
文摘The semantic segmentation of very high spatial resolution remote sensing images is difficult due to the complexity of interpreting the interactions between the objects in the scene. Indeed, effective segmentation requires considering spatial local context and long-term dependencies. To address this problem, the proposed approach is inspired by the MAC-UNet network which is an extension of U-Net, densely connected combined with channel attention. The advantages of this solution are as follows: 4) The new model introduces a new attention called propagate attention to build an attention-based encoder. 2) The fusion of multi-scale information is achieved by a weighted linear combination of the attentions whose coefficients are learned during the training phase. 3) Introducing in the decoder, the Spatial-Channel-Global-Local block which is an attention layer that uniquely combines channel attention and spatial attention locally and globally. The performances of the model are evaluated on 2 datasets WHDLD and DLRSD and show results of mean intersection over union (mIoU) index in progress between 1.54% and 10.47% for DLRSD and between 1.04% and 4.37% for WHDLD compared with the most efficient algorithms with attention mechanisms like MAU-Net and transformers like TMNet.
基金The subject is supported by NNSF and PSF of China
文摘The global bifurcation and chaos are investigated in this paper for a van der Pol-Duffing-Mathieu system with a single-well potential oscillator by means of nonlinear dynamics. The autonomous system corresponding to the system under discussion is analytically studied to draw all global bifurcation diagrams in every parameter space. These diagrams are called basic bifurcation ones. Then fixing parameter in every space and taking the parametrically excited amplitude as a bifurcation parameter, we can observe how to evolve from a basic bifurcation diagram to a chaos pattern in terms of numerical methods. The results are sufficient to show that the system has distinct dynamic behavior. Finally, the properties of the basins of attraction are observed and the appearance of fractal basin boundaries heralding the onset of a loss of structural integrity is noted in order to consider how to control the extent and the rate of the erosion in the next paper.
文摘In this paper, we develop a mathematical model of the COVID-19 pandemic in Burkina Faso. We use real data from Burkina Faso National Health Commission against COVID-19 to predict the dynamic of the disease and also the cumulative number of reported cases. We use public policies in model in order to reduce the contact rate, this allows to show how the reduction of the daily report of infectious cases goes, so we would like to draw the attention of decision makers for a rapid treatment of reported cases.
文摘This study sought to determine the best method to quantify training based on heart rate data. It proposes a modification of Banister’s original performance model to improve the accuracy of predicted performance. The new formulation introduces a variable that accounts for changes in the subject’s initial performance as a result of the quantity of training. The two systems models were applied to a well-trained female monofin swimmer over a 24-week training period. Each model comprised a set of parameters unique to the individual and was estimated by fitting model-predicted performance to measured performance. We used the Alienor method associated to Optimization-Preserving Operators to identify these parameters. The quantification method based on training intensity zones gave a better estimation of predicted performance in both models. Using the new model in sports in which performance is generally predicted (running, swimming) will help us to define its real interest.
文摘Math Works近日推出Robotics System Toolbox（机器人系统工具箱），这个新产品是Release 2015a的组成部分。、通过即用型算法和用于开发自动移动机器人应用程序的硬件连接性，Robotics System Toolbox提供了常用的机器人算法，以及MATLAB和Simulink与机器人操作系统（ROS）之间的接口和集成。现在，机器人研究人员和工程师们可以在单个统一的设计环境中开发机器人算法，在支持ROS的机器人和机器人仿真器（如Gazebo和V—REP）上测试和部署机器人算法。它通过减少从MATLAB程序转换到ROS程序所需的手动修改时间，留出了更多的时间来测试和调试算法。
文摘Two versions of a mathematical model are proposed for the process underlying the choice of settlement sites of past, present and future populations along the world coastline. The model is primarily based on the geometry of coastline at the scale of the map representing the region under study. It can be used to determine sites of human occupation for archaeological interest, as well as to plan future movements of present coastal populations due to the current sea level rise. Two examples related to history are presented: the first applies to the coastal peopling of the Mediterranean region, and the second to the settlement of Acadians in North-East of the Canadian province of New Brunswick in the second half of the 18th century.
