The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by p...The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by polyominoes. Indeed, if all tilings of a (skewed) quadrant by a tile set can be reduced to a tiling by congruent rectangles (parallelograms), this provides information about tilings of rectangles (parallelograms). We consider a class of tile sets in a square lattice appearing from arbitrary dissections of rectangles in two L-shaped polyominoes and from symmetries of these tiles about the first bisector. Only translations of the tiles are allowed in a tiling. If the sides of the dissected rectangle are coprime, we show the existence of tilings of all (skewed) quadrants that do not follow the rectangular (parallelogram) pattern. If one of the sides of the dissected rectangle is 2 and the other is odd, we also show tilings of rectangles by the tile set that do not follow the rectangular pattern. If one of the sides of the dissected rectangle is 2 and the other side is even, we show a new infinite family of tile sets that follows the rectangular pattern when tiling one of the quadrants. For this type of dis-section, we also show a new infinite family that does not follow the rectangular pattern when tiling rectangles. Finally, we investigate more general dissections of rectangles, with. Here we show infinite families of tile sets that follow the rectangular pattern for a quadrant and infinite families that do not follow the rectangular pattern for any quadrant. We also show, for infinite families of tile sets of this type, tilings of rectangles that do not follow the rectangular pattern.展开更多
BACKGROUND Although en bloc dissection of hepatic hilum lymph nodes has many advantages in radical tumor treatment,the feasibility and safety of this approach for laparo-scopic pancreaticoduodenectomy(LPD)require furt...BACKGROUND Although en bloc dissection of hepatic hilum lymph nodes has many advantages in radical tumor treatment,the feasibility and safety of this approach for laparo-scopic pancreaticoduodenectomy(LPD)require further clinical evaluation and investigation.AIM To explore the application value of the"five steps four quadrants"modularized en bloc dissection technique for accessing hepatic hilum lymph nodes in LPD patients.METHODS A total of 52 patients who underwent LPD via the"five steps four quadrants"modularized en bloc dissection technique for hepatic hilum lymph nodes from April 2021 to July 2023 in our department were analyzed retrospectively.The patients'body mass index(BMI),preoperative laboratory indices,intraoperative variables and postoperative complications were recorded.The relationships between preoperative data and intraoperative lymph node dissection time and blood loss were also analyzed.RESULTS Among the 52 patients,36 were males and 16 were females,and the average age was 62.2±11.0 years.There were 26 patients with pancreatic head cancer,16 patients with periampullary cancer,and 10 patients with distal bile duct cancer.The BMI was 22.3±3.3 kg/m²,and the median total bilirubin(TBIL)concentration was 57.7(16.0-155.7)µmol/L.All patients successfully underwent the"five steps four quadrants"modularized en bloc dissection technique without lymph node clearance-related complications such as postoperative bleeding or lymphatic leakage.Correlation analysis revealed significant associations between preoperative BMI(r=0.3581,P=0.0091),TBIL level(r=0.2988,P=0.0341),prothrombin time(r=0.3018,P=0.0297)and lymph node dissection time.Moreover,dissection time was significantly correlated with intraoperative blood loss(r=0.7744,P<0.0001).Further stratified analysis demonstrated that patients with a preoperative BMI≥21.9 kg/m²and a TIBL concentration≥57.7μmol/L had significantly longer lymph node dissection times(both P<0.05).CONCLUSION The"five steps four quadrants"modularized en bloc dissection technique for accessing the hepatic hilum lymph node is safe and feasible for LPD.This technique is expected to improve the efficiency of hepatic hilum lymph node dissection and shorten the learning curve;thus,it is worthy of further clinical promotion and application.展开更多
Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These ...Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels(N> 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results,which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km^(2), but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer “best identification”results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells.展开更多
A Chebyshev fitting way for a propeller atlas across four quadrants is discussed. As an example, Chebyshev polynomial fitting results and its error analysis are given. Because it’s difficult generally to get a propel...A Chebyshev fitting way for a propeller atlas across four quadrants is discussed. As an example, Chebyshev polynomial fitting results and its error analysis are given. Because it’s difficult generally to get a propeller atlas across four quadrants, a way is used to construct an alternative with higher accuracy based on the properties. As an application example, an alternative for the propeller property of a Deep Submergence Vehicle across four quadrants is given practically and a simulation model of the four quadrants propeller for dynamic condition is set up. The model lays a foundation for DSV full operating-condition movement simulation. A lot of simulation work shows that the results are very close to the practical data and, therefore, are effective.展开更多
As a coprocessor, field-programmable gate array （FPGA） is the hardware computing processor accelerating the computing capacity of coraputers. To efficiently manage the hardware free resources for the placing of task...As a coprocessor, field-programmable gate array （FPGA） is the hardware computing processor accelerating the computing capacity of coraputers. To efficiently manage the hardware free resources for the placing of tasks on FPGA and take full advantage of the partially reconfigurable units, good utilization of chip resources is an important and necessary work. In this paper, a new method is proposed to find the complete set of maximal free resource rectangles based on the cross point of edge lines of running tasks on FPGA area, and the prove process is provided to make sure the correctness of this method.展开更多
We show that the least number of cells (the gap number) one needs to take out from a rectangle with integer sides of length at least 2 in order to be tiled by ribbon right trominoes is less than or equal to 4. If the ...We show that the least number of cells (the gap number) one needs to take out from a rectangle with integer sides of length at least 2 in order to be tiled by ribbon right trominoes is less than or equal to 4. If the sides of the rectangle are of length at least 5, then the gap number is less than or equal to 3. We also show that for the family of rectangles that have nontrivial minimal number of gaps, with probability 1, the only obstructions to tiling appear from coloring invariants. This is in contrast to what happens for simply connected regions. For that class of regions Conway and Lagarias found a tiling invariant that does not follow from coloring.展开更多
When we stare into our complex surroundings, we see objects of different shapes and sizes. However, the shape that is always present, regardless of the complexity of the object, is the circle. The circle is arguably t...When we stare into our complex surroundings, we see objects of different shapes and sizes. However, the shape that is always present, regardless of the complexity of the object, is the circle. The circle is arguably the most fascinating shape in the universe. A circle is defined as the set of all points equidistant from a given point, which, therefore, lies at the center of the circle. One of the various properties of circles is that it has infinite inscribed squares. This is because it is a continuous function, therefore if any point in the circle is transitioned by a specific factor, the other related points in the square would be shifted by the same factor. An ellipse is a similar shape with several inscribed squares. But does any closed curve have an inscribed square? This question was proposed by Otto Toeplitz in 1911 and to this day it is not answered. Another version of this problem is the inscribed rectangle problem which will be discussed in this paper.展开更多
文摘The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by polyominoes. Indeed, if all tilings of a (skewed) quadrant by a tile set can be reduced to a tiling by congruent rectangles (parallelograms), this provides information about tilings of rectangles (parallelograms). We consider a class of tile sets in a square lattice appearing from arbitrary dissections of rectangles in two L-shaped polyominoes and from symmetries of these tiles about the first bisector. Only translations of the tiles are allowed in a tiling. If the sides of the dissected rectangle are coprime, we show the existence of tilings of all (skewed) quadrants that do not follow the rectangular (parallelogram) pattern. If one of the sides of the dissected rectangle is 2 and the other is odd, we also show tilings of rectangles by the tile set that do not follow the rectangular pattern. If one of the sides of the dissected rectangle is 2 and the other side is even, we show a new infinite family of tile sets that follows the rectangular pattern when tiling one of the quadrants. For this type of dis-section, we also show a new infinite family that does not follow the rectangular pattern when tiling rectangles. Finally, we investigate more general dissections of rectangles, with. Here we show infinite families of tile sets that follow the rectangular pattern for a quadrant and infinite families that do not follow the rectangular pattern for any quadrant. We also show, for infinite families of tile sets of this type, tilings of rectangles that do not follow the rectangular pattern.
基金Supported by Health Research Program of Anhui,No.AHWJ2022b032。
文摘BACKGROUND Although en bloc dissection of hepatic hilum lymph nodes has many advantages in radical tumor treatment,the feasibility and safety of this approach for laparo-scopic pancreaticoduodenectomy(LPD)require further clinical evaluation and investigation.AIM To explore the application value of the"five steps four quadrants"modularized en bloc dissection technique for accessing hepatic hilum lymph nodes in LPD patients.METHODS A total of 52 patients who underwent LPD via the"five steps four quadrants"modularized en bloc dissection technique for hepatic hilum lymph nodes from April 2021 to July 2023 in our department were analyzed retrospectively.The patients'body mass index(BMI),preoperative laboratory indices,intraoperative variables and postoperative complications were recorded.The relationships between preoperative data and intraoperative lymph node dissection time and blood loss were also analyzed.RESULTS Among the 52 patients,36 were males and 16 were females,and the average age was 62.2±11.0 years.There were 26 patients with pancreatic head cancer,16 patients with periampullary cancer,and 10 patients with distal bile duct cancer.The BMI was 22.3±3.3 kg/m²,and the median total bilirubin(TBIL)concentration was 57.7(16.0-155.7)µmol/L.All patients successfully underwent the"five steps four quadrants"modularized en bloc dissection technique without lymph node clearance-related complications such as postoperative bleeding or lymphatic leakage.Correlation analysis revealed significant associations between preoperative BMI(r=0.3581,P=0.0091),TBIL level(r=0.2988,P=0.0341),prothrombin time(r=0.3018,P=0.0297)and lymph node dissection time.Moreover,dissection time was significantly correlated with intraoperative blood loss(r=0.7744,P<0.0001).Further stratified analysis demonstrated that patients with a preoperative BMI≥21.9 kg/m²and a TIBL concentration≥57.7μmol/L had significantly longer lymph node dissection times(both P<0.05).CONCLUSION The"five steps four quadrants"modularized en bloc dissection technique for accessing the hepatic hilum lymph node is safe and feasible for LPD.This technique is expected to improve the efficiency of hepatic hilum lymph node dissection and shorten the learning curve;thus,it is worthy of further clinical promotion and application.
基金supported by the National Natural Science Foundation of China (Grant Nos. U20A2097,42075087, 91837310)the National Key Research and Development Program of China (Grant No. 2021YFC3000902)。
文摘Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels(N> 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results,which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km^(2), but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer “best identification”results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells.
文摘A Chebyshev fitting way for a propeller atlas across four quadrants is discussed. As an example, Chebyshev polynomial fitting results and its error analysis are given. Because it’s difficult generally to get a propeller atlas across four quadrants, a way is used to construct an alternative with higher accuracy based on the properties. As an application example, an alternative for the propeller property of a Deep Submergence Vehicle across four quadrants is given practically and a simulation model of the four quadrants propeller for dynamic condition is set up. The model lays a foundation for DSV full operating-condition movement simulation. A lot of simulation work shows that the results are very close to the practical data and, therefore, are effective.
基金Project supported by the Shanghai Leading Academic Discipline Project(Grant No.J50103)the Natural Science Foundation of Jiangxi Province(Grant No.2010GZS0031)the Science Technology Project of Jiangxi Province(Grant No.2010BGB00604)
文摘As a coprocessor, field-programmable gate array （FPGA） is the hardware computing processor accelerating the computing capacity of coraputers. To efficiently manage the hardware free resources for the placing of tasks on FPGA and take full advantage of the partially reconfigurable units, good utilization of chip resources is an important and necessary work. In this paper, a new method is proposed to find the complete set of maximal free resource rectangles based on the cross point of edge lines of running tasks on FPGA area, and the prove process is provided to make sure the correctness of this method.
文摘We show that the least number of cells (the gap number) one needs to take out from a rectangle with integer sides of length at least 2 in order to be tiled by ribbon right trominoes is less than or equal to 4. If the sides of the rectangle are of length at least 5, then the gap number is less than or equal to 3. We also show that for the family of rectangles that have nontrivial minimal number of gaps, with probability 1, the only obstructions to tiling appear from coloring invariants. This is in contrast to what happens for simply connected regions. For that class of regions Conway and Lagarias found a tiling invariant that does not follow from coloring.
文摘When we stare into our complex surroundings, we see objects of different shapes and sizes. However, the shape that is always present, regardless of the complexity of the object, is the circle. The circle is arguably the most fascinating shape in the universe. A circle is defined as the set of all points equidistant from a given point, which, therefore, lies at the center of the circle. One of the various properties of circles is that it has infinite inscribed squares. This is because it is a continuous function, therefore if any point in the circle is transitioned by a specific factor, the other related points in the square would be shifted by the same factor. An ellipse is a similar shape with several inscribed squares. But does any closed curve have an inscribed square? This question was proposed by Otto Toeplitz in 1911 and to this day it is not answered. Another version of this problem is the inscribed rectangle problem which will be discussed in this paper.
