Conventional soil maps contain valuable knowledge on soil–environment relationships.Such knowledge can be extracted for use when updating conventional soil maps with improved environmental data.Existing methods take ...Conventional soil maps contain valuable knowledge on soil–environment relationships.Such knowledge can be extracted for use when updating conventional soil maps with improved environmental data.Existing methods take all polygons of the same map unit on a map as a whole to extract the soil–environment relationship.Such approach ignores the difference in the environmental conditions represented by individual soil polygons of the same map unit.This paper proposes a method of mining soil–environment relationships from individual soil polygons to update conventional soil maps.The proposed method consists of three major steps.Firstly,the soil–environment relationships represented by each individual polygon on a conventional soil map are extracted in the form of frequency distribution curves for the involved environmental covariates.Secondly,for each environmental covariate,these frequency distribution curves from individual polygons of the same soil map unit are synthesized to form the overall soil–environment relationship for that soil map unit across the mapped area.And lastly,the extracted soil–environment relationships are applied to updating the conventional soil map with new,improved environmental data by adopting a soil land inference model(SoLIM)framework.This study applied the proposed method to updating a conventional soil map of the Raffelson watershed in La Crosse County,Wisconsin,United States.The result from the proposed method was compared with that from the previous method of taking all polygons within the same soil map unit on a map as a whole.Evaluation results with independent soil samples showed that the proposed method exhibited better performance and produced higher accuracy.展开更多
Two new recognition methods for the spatial planar POlygon using perspective invariants are presented. The corss-ratio (R c) of a vetex and the co-base area rotio (RA) of a edge in a spatial planar polygon are propose...Two new recognition methods for the spatial planar POlygon using perspective invariants are presented. The corss-ratio (R c) of a vetex and the co-base area rotio (RA) of a edge in a spatial planar polygon are proposed and used as the invariant primitive of the recognition eigenvector. The second distance error decision rule (SD EDR) estimating the relative error of RA is introduced also too. The mthods could recognize a spatial planar polygon with an arbitrary orientation through only a single perspective view. Experimental examples are gievn.展开更多
The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of...The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of such polygons. As special cases of our investigations, we settle two conjectures involving arithmetic polygons.展开更多
When am I ever going to use this?GEOGRAPHY The size and shape of each state in the United States is different.Analyze the shapes of the states in both groups at the right.1.Find the difference between the shapes of th...When am I ever going to use this?GEOGRAPHY The size and shape of each state in the United States is different.Analyze the shapes of the states in both groups at the right.1.Find the difference between the shapes of the states in Group 1and the shapes of the states in Group 2.2.Why do most states have boundaries that are not straight line segments?The states listed in Group 1 above are examples of polygons.A polygon is a simple,closed figure formed by three or more straight lines.A simple figure does not have lines that cross each other.You have drawn a closed figure when your pencil ends up where it started.展开更多
Wheel polygonal wear can immensely worsen wheel/rail interactions and vibration performances of the train and track,and ultimately,lead to the shortening of service life of railway components.At present,wheel/rail med...Wheel polygonal wear can immensely worsen wheel/rail interactions and vibration performances of the train and track,and ultimately,lead to the shortening of service life of railway components.At present,wheel/rail medium-or high-frequency frictional interactions are perceived as an essential reason of the high-order polygonal wear of railway wheels,which are potentially resulted by the flexible deformations of the train/track system or other external excitations.In this work,the effect of wheel/rail flexibility on polygonal wear evolution of heavy-haul locomotive wheels is explored with aid of the long-term wheel polygonal wear evolution simulations,in which different flexible modeling of the heavy-haul wheel/rail coupled system is implemented.Further,the mitigation measures for the polygonal wear of heavy-haul locomotive wheels are discussed.The results point out that the evolution of polygonal wear of heavy-haul locomotive wheels can be veritably simulated with consideration of the flexible effect of both wheelset and rails.Execution of mixed-line operation of heavy-haul trains and application of multicut wheel re-profiling can effectively reduce the development of wheel polygonal wear.This research can provide a deep-going understanding of polygonal wear evolution mechanism of heavy-haul locomotive wheels and its mitigation measures.展开更多
An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible numbe...An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12,f(12) = 12.展开更多
We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of free...We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy.Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem,we propose a novel Galerkin boundary element method,with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon.Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.展开更多
After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organiz...After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.展开更多
The problem of initial collision between convex polygons is studied in detail, and a fast algorithm for finding the embedded depth is obtained, by which the fast approximate algorithm for solving packing problems of c...The problem of initial collision between convex polygons is studied in detail, and a fast algorithm for finding the embedded depth is obtained, by which the fast approximate algorithm for solving packing problems of convex polygons in plane is constructed.展开更多
Polygonal faults(PFs)generally have a classic polygonal geometry in map view.However,under the influence of tectonic faults,diapirs,channels,and slopes,the classic polygonal geometry of PFs is not preserved,demonstrat...Polygonal faults(PFs)generally have a classic polygonal geometry in map view.However,under the influence of tectonic faults,diapirs,channels,and slopes,the classic polygonal geometry of PFs is not preserved,demonstrating differences(different characters)in map-view 3D seismic data covering an area of 334km^(2) of the Changchang(CC)sag,are used to document the mapview and cross-sectional characteristics of PFs.These data also help investigate the irregularly polygonal geometries of PFs due to the presence of influence factors,such as transtensional faults,submarine fans,channels,diapirs/gas chimneys,and the basal slope within the lower-middle Miocene strata.Results show that various irregularly polygonal geometries of PFs can be classified into enechelon and arcuate PFs,channel-segmenting and-bounding PFs,radial PFs,and rectangular PFs in map-view.En-echelon and arcuate PFs are induced by transtensional faults and exhibit a unique‘flower’structure in NE-and SE-trending cross-sections in the NW area of the study area.This finding is documented for the first time.Channel-segmenting PFs occur in the(northwest)low-amplitude muddy channel and are inhibited in the(southeast)high-amplitude sandy channel in the SW area.Radial PFs are radially aligned around a gas chimney/diapir containing some high-amplitude anomalies(HAAs)in the middle area.The presence of intrusive sandstones with HAAs along the periphery of the diapirs restricts the occurrence of PFs.Two high-amplitude submarine fans act as a mechanical barrier to the propagation of PFs.Meanwhile,the(moderate)slope in the NE area induces rectangular PFs.Additionally,the geneses of the PFs in the current study are comprehensively discussed.This study adds to our understanding of the differences between PFs with irregularly polygonal geometries.展开更多
Deep-water coarse-grained channels are embedded within a polygonal fault tier,and the polygonal faults(PFs)present non-polygonal geometries rather than classic polygonal geometry in plan view.However,PFs present diffe...Deep-water coarse-grained channels are embedded within a polygonal fault tier,and the polygonal faults(PFs)present non-polygonal geometries rather than classic polygonal geometry in plan view.However,PFs present differences when they encounter deep-water(coarse-grained vs.fine-grained)channels with different lithology,which has not been further studied to date.Three-dimensional(3D)seismic data and a drilling well from Beijiao sag of Qiongdongnanbasin,South China Sea were utilized to document the plan view and cross-sectional properties of the PFs and their differences and genetic mechanism were investigated.Results show that,first,PFs can be divided morphologically into channel-segmenting PFs and channel-bounding PFs in plan view.The former virtually cuts or segments the axes of channels in highand low-amplitudes,and the latter nearly parallels the boundaries of the channels.Both are approximately perpendicular to each other.Secondly,channel-bounding PFs that related to low-amplitude channels are much longer than those of high-amplitude ones;channel-segmenting PFs related to low-amplitude channels are slightly longer than the counterparts related to high-amplitude channels.Lastly,the magnitudes(e.g.,heights)of the PFs are proportional to the scales(e.g.,widths and heights)of low-amplitude channels,whereas the magnitudes of the PFs are inversely proportional to the scales of high amplitude channels.Coarse-grained(high amplitude)channels act as a mechanical barrier to the propagation of PFs,whereas fine-grained(low-amplitude)channels are beneficial to the propagation and nucleation of PFs.Additionally,the genetic mechanism of PFs is discussed and reckoned as combined geneses of gravitational spreading and overpressure hydrofracture.The differences of the PFs can be used to reasonably differentiate coarse-grained channels from fine-grained channels.This study provides new insights into understanding the different geometries of the PFs related to coarse-grained and fine-grained channels and their genetic mechanism.展开更多
Waterside creatures or aquatic organisms use a fin or web to generate a thrust force. These fins or webs have a non-convex section, referred to as a non-convex shape. We investigate the drag force acting on ...Waterside creatures or aquatic organisms use a fin or web to generate a thrust force. These fins or webs have a non-convex section, referred to as a non-convex shape. We investigate the drag force acting on a non-convex plate during unsteady motion. We perform the experiment in a water tank during free fall. We fabricate the non-convex plate by cutting isosceles triangles from the side of a convex hexagonal plate. The base angle of the triangle is between 0° to 45°. The base angle is 0 indicates the convex hexagonal thin plate. We estimate the drag coefficient with the force balance acting on the model based on the image analysis technique. The results indicate that increasing the base angle by more than 30° increased the drag coefficient. The drag coefficient during unsteady motion changed with the growth of the vortex behind the model. The vortex has small vortices in the shear layer, which is related to the Kelvin-Helmholtz instabilities.展开更多
The article is devoted to the problem of forecasting strong earthquakes by the geomagnetic method. The geomagnetic method is widely used on this problem in seismically active regions of the world as one of the promisi...The article is devoted to the problem of forecasting strong earthquakes by the geomagnetic method. The geomagnetic method is widely used on this problem in seismically active regions of the world as one of the promising, informative and operational geophysical methods. The results of long-term geomagnetic studies on the problem of forecasting strong earthquakes in Uzbekistan are presented. Geomagnetic studies were carried out on the territories of the Tashkent, Ferghana, and Kyzylkum geodynamic polygons in the epicentral zones of strong earthquakes that occurred. Long-term, medium- and short-term precursors of earthquakes have been identified. Anomalous changes in the geomagnetic field associated with the decline in aftershock activity were also revealed. The dependence between the duration of the manifestation of long-term magnetic precursors and the magnitude of earthquakes is determined. Absolute proton magnetometers MMP-1, MV-01 (Russia), and G-856 (USA) were used to measure the geomagnetic field.展开更多
The anterior system of the polygon of Willis plays an anastomotic role between the carotid territories and communicates with the posterior system. It ensures adequate cerebral blood flow in the event of internal occlu...The anterior system of the polygon of Willis plays an anastomotic role between the carotid territories and communicates with the posterior system. It ensures adequate cerebral blood flow in the event of internal occlusion. Its ability to redistribute blood flow depends on its morphology, the presence and size of the vessels that constitute it and their variants, knowledge of which is essential. The morphology of the carotid system is not constant and a number of variants are well recognized with greater hemodynamic importance. In this context, we undertook this work which aims to seek the anatomical variants of the anterior part of the PW;to determine the diameters of the vessels of the latter and to correlate these results with epidemiological data. We carried out a retrospective, descriptive and analytical study over a period of 4 months at Fann University Hospital, targeting patients who had undergone brain MRI with a 3D TOF sequence whatever the indication. Patients with lesions of cerebrovascular pathologies such as ischemia, hemorrhage, aneurysm, arteriovenous malformations or presenting a limited analysis examination due to the presence of kinetic or other artifact, were not included. Demographic data and anatomical variants were studied as well as the measurements of any continuous arterial segment greater than 0.8 mm in diameter. Those less than 0.8 mm in diameter were considered hypoplastic. The C3 segment of the internal carotid arteries, the A1 segment of the anterior cerebral arteries, the anterior communicating artery, constituted our main measurement sites. The sex ratio was 1.06, the mean age of the patients was 43 years ± 17.9 with extremes of 11 and 85 years. The anterior configuration of the polygon was complete in 57.5% representing 50% of men and 65.5% of women, in 56% of subjects under 40 years old and 58% in subjects over 40 years old. We noted a predominance of type a in 47% of patients followed by type g found in 35% of patients. The morphology of the anterior system of the Willis polygon is a function of its variants, some of which have greater hemodynamic importance than others. Its knowledge is essential for the management of cerebrovascular diseases.展开更多
基金supported by the National Natural Science Foundation of China (41431177 and 41422109)the Innovation Project of State Key Laboratory of Resources and Environmental Information System of China (O88RA20CYA)the Outstanding Innovation Team in Colleges and Universities in Jiangsu Province, China
文摘Conventional soil maps contain valuable knowledge on soil–environment relationships.Such knowledge can be extracted for use when updating conventional soil maps with improved environmental data.Existing methods take all polygons of the same map unit on a map as a whole to extract the soil–environment relationship.Such approach ignores the difference in the environmental conditions represented by individual soil polygons of the same map unit.This paper proposes a method of mining soil–environment relationships from individual soil polygons to update conventional soil maps.The proposed method consists of three major steps.Firstly,the soil–environment relationships represented by each individual polygon on a conventional soil map are extracted in the form of frequency distribution curves for the involved environmental covariates.Secondly,for each environmental covariate,these frequency distribution curves from individual polygons of the same soil map unit are synthesized to form the overall soil–environment relationship for that soil map unit across the mapped area.And lastly,the extracted soil–environment relationships are applied to updating the conventional soil map with new,improved environmental data by adopting a soil land inference model(SoLIM)framework.This study applied the proposed method to updating a conventional soil map of the Raffelson watershed in La Crosse County,Wisconsin,United States.The result from the proposed method was compared with that from the previous method of taking all polygons within the same soil map unit on a map as a whole.Evaluation results with independent soil samples showed that the proposed method exhibited better performance and produced higher accuracy.
文摘Two new recognition methods for the spatial planar POlygon using perspective invariants are presented. The corss-ratio (R c) of a vetex and the co-base area rotio (RA) of a edge in a spatial planar polygon are proposed and used as the invariant primitive of the recognition eigenvector. The second distance error decision rule (SD EDR) estimating the relative error of RA is introduced also too. The mthods could recognize a spatial planar polygon with an arbitrary orientation through only a single perspective view. Experimental examples are gievn.
文摘The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of such polygons. As special cases of our investigations, we settle two conjectures involving arithmetic polygons.
文摘When am I ever going to use this?GEOGRAPHY The size and shape of each state in the United States is different.Analyze the shapes of the states in both groups at the right.1.Find the difference between the shapes of the states in Group 1and the shapes of the states in Group 2.2.Why do most states have boundaries that are not straight line segments?The states listed in Group 1 above are examples of polygons.A polygon is a simple,closed figure formed by three or more straight lines.A simple figure does not have lines that cross each other.You have drawn a closed figure when your pencil ends up where it started.
基金Supported by National Natural Science Foundation of China(Grant Nos.U2268210,52302474,52072249).
文摘Wheel polygonal wear can immensely worsen wheel/rail interactions and vibration performances of the train and track,and ultimately,lead to the shortening of service life of railway components.At present,wheel/rail medium-or high-frequency frictional interactions are perceived as an essential reason of the high-order polygonal wear of railway wheels,which are potentially resulted by the flexible deformations of the train/track system or other external excitations.In this work,the effect of wheel/rail flexibility on polygonal wear evolution of heavy-haul locomotive wheels is explored with aid of the long-term wheel polygonal wear evolution simulations,in which different flexible modeling of the heavy-haul wheel/rail coupled system is implemented.Further,the mitigation measures for the polygonal wear of heavy-haul locomotive wheels are discussed.The results point out that the evolution of polygonal wear of heavy-haul locomotive wheels can be veritably simulated with consideration of the flexible effect of both wheelset and rails.Execution of mixed-line operation of heavy-haul trains and application of multicut wheel re-profiling can effectively reduce the development of wheel polygonal wear.This research can provide a deep-going understanding of polygonal wear evolution mechanism of heavy-haul locomotive wheels and its mitigation measures.
基金Supported by National Natural Science Foundation of China(Grant No.12271139)。
文摘An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12,f(12) = 12.
文摘We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions.Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy.Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem,we propose a novel Galerkin boundary element method,with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon.Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.
文摘After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.
文摘The problem of initial collision between convex polygons is studied in detail, and a fast algorithm for finding the embedded depth is obtained, by which the fast approximate algorithm for solving packing problems of convex polygons in plane is constructed.
基金supported by the Key Laboratory of Marine Mineral Resources,Ministry of Land and Resources of China(No.KLMMR-2018-B-07)the National Basic Research Program of China(No.2011ZX05025-006-02)the National Natural Science Foundation of China(No.41672206)。
文摘Polygonal faults(PFs)generally have a classic polygonal geometry in map view.However,under the influence of tectonic faults,diapirs,channels,and slopes,the classic polygonal geometry of PFs is not preserved,demonstrating differences(different characters)in map-view 3D seismic data covering an area of 334km^(2) of the Changchang(CC)sag,are used to document the mapview and cross-sectional characteristics of PFs.These data also help investigate the irregularly polygonal geometries of PFs due to the presence of influence factors,such as transtensional faults,submarine fans,channels,diapirs/gas chimneys,and the basal slope within the lower-middle Miocene strata.Results show that various irregularly polygonal geometries of PFs can be classified into enechelon and arcuate PFs,channel-segmenting and-bounding PFs,radial PFs,and rectangular PFs in map-view.En-echelon and arcuate PFs are induced by transtensional faults and exhibit a unique‘flower’structure in NE-and SE-trending cross-sections in the NW area of the study area.This finding is documented for the first time.Channel-segmenting PFs occur in the(northwest)low-amplitude muddy channel and are inhibited in the(southeast)high-amplitude sandy channel in the SW area.Radial PFs are radially aligned around a gas chimney/diapir containing some high-amplitude anomalies(HAAs)in the middle area.The presence of intrusive sandstones with HAAs along the periphery of the diapirs restricts the occurrence of PFs.Two high-amplitude submarine fans act as a mechanical barrier to the propagation of PFs.Meanwhile,the(moderate)slope in the NE area induces rectangular PFs.Additionally,the geneses of the PFs in the current study are comprehensively discussed.This study adds to our understanding of the differences between PFs with irregularly polygonal geometries.
基金Supported by the Key Laboratory of Marine Mineral ResourcesMinistry of Land and Resources of China(No.KLMMR-2018-B-07)+1 种基金the National Basic Research Program of China(No.2011ZX05025-006-02)the National Natural Science Foundation of China(No.41672206)。
文摘Deep-water coarse-grained channels are embedded within a polygonal fault tier,and the polygonal faults(PFs)present non-polygonal geometries rather than classic polygonal geometry in plan view.However,PFs present differences when they encounter deep-water(coarse-grained vs.fine-grained)channels with different lithology,which has not been further studied to date.Three-dimensional(3D)seismic data and a drilling well from Beijiao sag of Qiongdongnanbasin,South China Sea were utilized to document the plan view and cross-sectional properties of the PFs and their differences and genetic mechanism were investigated.Results show that,first,PFs can be divided morphologically into channel-segmenting PFs and channel-bounding PFs in plan view.The former virtually cuts or segments the axes of channels in highand low-amplitudes,and the latter nearly parallels the boundaries of the channels.Both are approximately perpendicular to each other.Secondly,channel-bounding PFs that related to low-amplitude channels are much longer than those of high-amplitude ones;channel-segmenting PFs related to low-amplitude channels are slightly longer than the counterparts related to high-amplitude channels.Lastly,the magnitudes(e.g.,heights)of the PFs are proportional to the scales(e.g.,widths and heights)of low-amplitude channels,whereas the magnitudes of the PFs are inversely proportional to the scales of high amplitude channels.Coarse-grained(high amplitude)channels act as a mechanical barrier to the propagation of PFs,whereas fine-grained(low-amplitude)channels are beneficial to the propagation and nucleation of PFs.Additionally,the genetic mechanism of PFs is discussed and reckoned as combined geneses of gravitational spreading and overpressure hydrofracture.The differences of the PFs can be used to reasonably differentiate coarse-grained channels from fine-grained channels.This study provides new insights into understanding the different geometries of the PFs related to coarse-grained and fine-grained channels and their genetic mechanism.
文摘Waterside creatures or aquatic organisms use a fin or web to generate a thrust force. These fins or webs have a non-convex section, referred to as a non-convex shape. We investigate the drag force acting on a non-convex plate during unsteady motion. We perform the experiment in a water tank during free fall. We fabricate the non-convex plate by cutting isosceles triangles from the side of a convex hexagonal plate. The base angle of the triangle is between 0° to 45°. The base angle is 0 indicates the convex hexagonal thin plate. We estimate the drag coefficient with the force balance acting on the model based on the image analysis technique. The results indicate that increasing the base angle by more than 30° increased the drag coefficient. The drag coefficient during unsteady motion changed with the growth of the vortex behind the model. The vortex has small vortices in the shear layer, which is related to the Kelvin-Helmholtz instabilities.
文摘The article is devoted to the problem of forecasting strong earthquakes by the geomagnetic method. The geomagnetic method is widely used on this problem in seismically active regions of the world as one of the promising, informative and operational geophysical methods. The results of long-term geomagnetic studies on the problem of forecasting strong earthquakes in Uzbekistan are presented. Geomagnetic studies were carried out on the territories of the Tashkent, Ferghana, and Kyzylkum geodynamic polygons in the epicentral zones of strong earthquakes that occurred. Long-term, medium- and short-term precursors of earthquakes have been identified. Anomalous changes in the geomagnetic field associated with the decline in aftershock activity were also revealed. The dependence between the duration of the manifestation of long-term magnetic precursors and the magnitude of earthquakes is determined. Absolute proton magnetometers MMP-1, MV-01 (Russia), and G-856 (USA) were used to measure the geomagnetic field.
文摘The anterior system of the polygon of Willis plays an anastomotic role between the carotid territories and communicates with the posterior system. It ensures adequate cerebral blood flow in the event of internal occlusion. Its ability to redistribute blood flow depends on its morphology, the presence and size of the vessels that constitute it and their variants, knowledge of which is essential. The morphology of the carotid system is not constant and a number of variants are well recognized with greater hemodynamic importance. In this context, we undertook this work which aims to seek the anatomical variants of the anterior part of the PW;to determine the diameters of the vessels of the latter and to correlate these results with epidemiological data. We carried out a retrospective, descriptive and analytical study over a period of 4 months at Fann University Hospital, targeting patients who had undergone brain MRI with a 3D TOF sequence whatever the indication. Patients with lesions of cerebrovascular pathologies such as ischemia, hemorrhage, aneurysm, arteriovenous malformations or presenting a limited analysis examination due to the presence of kinetic or other artifact, were not included. Demographic data and anatomical variants were studied as well as the measurements of any continuous arterial segment greater than 0.8 mm in diameter. Those less than 0.8 mm in diameter were considered hypoplastic. The C3 segment of the internal carotid arteries, the A1 segment of the anterior cerebral arteries, the anterior communicating artery, constituted our main measurement sites. The sex ratio was 1.06, the mean age of the patients was 43 years ± 17.9 with extremes of 11 and 85 years. The anterior configuration of the polygon was complete in 57.5% representing 50% of men and 65.5% of women, in 56% of subjects under 40 years old and 58% in subjects over 40 years old. We noted a predominance of type a in 47% of patients followed by type g found in 35% of patients. The morphology of the anterior system of the Willis polygon is a function of its variants, some of which have greater hemodynamic importance than others. Its knowledge is essential for the management of cerebrovascular diseases.
