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
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
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
The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method...The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.展开更多
The effect of rectangle wave pulse current on solidification structure of ZA27 alloy was studied. The restdts show that the wave pattern relies on the frequency range of harmonic wave and the energy of pulse current w...The effect of rectangle wave pulse current on solidification structure of ZA27 alloy was studied. The restdts show that the wave pattern relies on the frequency range of harmonic wave and the energy of pulse current within the frequency range of pulse current. Imposed pulse current could induce the solidification system to oscillate. The frequency range and the relevant energy distribution of pulse current exert an influence on the amount of atoms involved for forming critical nucleus, the surface states of dusters in melt, the oscillating state of melt on the surface of dusters, the active energy of atom diffusion , the frequnce response of the resonance of bulk melt and the absorbability of the solidification system to the external work. Rectangle wave pulse current involves rich harmonic waves ; the amplitudes of high order of harmonic waves are higher and reduce slowly, so it has a better effect on inoculation and modification.展开更多
In many engineering applications, it is necessary to calculate the min-area encasing box of a circumscription. In this paper, an algorithm for generating the min-area rectangle encasing box, based on revolving angle, ...In many engineering applications, it is necessary to calculate the min-area encasing box of a circumscription. In this paper, an algorithm for generating the min-area rectangle encasing box, based on revolving angle, is investigated and hence put forward. The algorithm computes the areas of the outer rectangular bounds of a closed contour in different revolving angles θ by dispersing approach where 0< θ < π/2 because of the axial symmetry. It is very simple, straight forward and highly efficient. The complexity of its computing time reaches O(n·k ). Practical applications suggest its usefulness and efficiency.展开更多
Helicopters are widely used in maritime Search and Rescue(SAR) missions. To ensure the success of SAR missions, search areas need to be carefully planned. With the development of computer technology and weather foreca...Helicopters are widely used in maritime Search and Rescue(SAR) missions. To ensure the success of SAR missions, search areas need to be carefully planned. With the development of computer technology and weather forecast technology, the survivors’ drift trajectories can be predicted more precisely, which strongly supports the planning of search areas for the rescue helicopter. However, the methods used to determine the search area based on the predicted drift trajectories are mainly derived from the continuous expansion of the area with the highest Probability of Containment(POC), which may lead to local optimal solutions and a decrease in the Probability of Success(POS), especially when there are several subareas with a high POC. To address this problem, this paper proposes a method based on a Minimum Bounding Rectangle and Kmeans clustering(MBRK). A silhouette coefficient is adopted to analyze the distribution of the survivors’ probable locations, which are divided into multiple clusters with K-means clustering. Then,probability maps are generated based on the minimum bounding rectangle of each cluster. By adding or subtracting one row or column of cells or shifting the planned search area, 12 search methods are used to generate the optimal search area starting from the cell with the highest POC in each probability map. Taking a real case as an example, the simulation experiment results show that the POS values obtained by the MBRK method are higher than those obtained by other methods,which proves that the MBRK method can effectively support the planning of search areas and that K-means clustering improves the POS of search plans.展开更多
In this paper, the principle of multi-point forming (MPF) technique is presented. One of the most serious defects, wrinkling, during the multi-point forming process of a shallow rectangle cup is discussed by means of ...In this paper, the principle of multi-point forming (MPF) technique is presented. One of the most serious defects, wrinkling, during the multi-point forming process of a shallow rectangle cup is discussed by means of numerical simulation on the shallow rectangle cup forming process. The effects of thickness, material of sheet metal and the pressure of the blank holder are investigated. Based on the simulation results, the reasons and control methods of wrinkling are pointed out. Moreover, the experiment on the multi-point die forming of the shallow rectangle cup by the MPF machine is done to validate the efficiency of the numerical simulation, and the result proves that the application of an elastic cushion in the forming can restrain wrinkling efficiently.展开更多
In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singula...In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.展开更多
The analytic representation of the transient radiation for an aperture excited by a rectangle pulse is obtained. It shows that the field duration and amplitude depend on the observation distance, the elevation angle, ...The analytic representation of the transient radiation for an aperture excited by a rectangle pulse is obtained. It shows that the field duration and amplitude depend on the observation distance, the elevation angle, the pulse width of the rectangle pulse and the aperture size.展开更多
The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied ...The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied only on a simple domain composed of rectangles or parallelograms whose sides are parallel to two different straight lines. We propose a new triangular Hermite element with 13 degrees of freedom. It is used in combination with the Bogner-Fox-Schmit element near the boundary of an arbitrary polygonal domain and provides continuous differentiability of an approximate solution in the whole domain up to the boundary.展开更多
The statistical dynamics of partially incoherent ultrafast lasers are complex and chaotic,which is significant for fundamental research and practical applications.We experimentally and theoretically reveal the statist...The statistical dynamics of partially incoherent ultrafast lasers are complex and chaotic,which is significant for fundamental research and practical applications.We experimentally and theoretically reveal the statistical dynamics of the spectral evolutions and correlations in an incoherent noise-like rectangle pulse laser(NLRPL).Based on statistical histogram analysis,the probability distribution asymmetry of the spectral intensity fluctuation is decayed with the wavelength far away from the spectral peak due to the detection noise.The full-spectral correlation values indicate that the spectral similarity between two round trips is exponentially weakened as the round-trip offset increases.By studying the correlation map of spectral components,we find that the area of the high-correlation region is relevant to the pump power,which is reduced by increasing the pump power.The mutual information of the spectra demonstrates that two spectral components with symmetry about the spectral peak have a statistical dependence.Experimental observations and statistical properties can coincide well with theoretical numerical simulations.We reveal the pump-dependent spectral correlation of the NLRPL and provide multiple statistical methods for the characterizations of chaotic dynamics in incoherent light sources.展开更多
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.
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The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.
基金Funded by the Natural Science Foundation of Gansu Province(No.ZS021-A25-027-C)
文摘The effect of rectangle wave pulse current on solidification structure of ZA27 alloy was studied. The restdts show that the wave pattern relies on the frequency range of harmonic wave and the energy of pulse current within the frequency range of pulse current. Imposed pulse current could induce the solidification system to oscillate. The frequency range and the relevant energy distribution of pulse current exert an influence on the amount of atoms involved for forming critical nucleus, the surface states of dusters in melt, the oscillating state of melt on the surface of dusters, the active energy of atom diffusion , the frequnce response of the resonance of bulk melt and the absorbability of the solidification system to the external work. Rectangle wave pulse current involves rich harmonic waves ; the amplitudes of high order of harmonic waves are higher and reduce slowly, so it has a better effect on inoculation and modification.
文摘In many engineering applications, it is necessary to calculate the min-area encasing box of a circumscription. In this paper, an algorithm for generating the min-area rectangle encasing box, based on revolving angle, is investigated and hence put forward. The algorithm computes the areas of the outer rectangular bounds of a closed contour in different revolving angles θ by dispersing approach where 0< θ < π/2 because of the axial symmetry. It is very simple, straight forward and highly efficient. The complexity of its computing time reaches O(n·k ). Practical applications suggest its usefulness and efficiency.
文摘Helicopters are widely used in maritime Search and Rescue(SAR) missions. To ensure the success of SAR missions, search areas need to be carefully planned. With the development of computer technology and weather forecast technology, the survivors’ drift trajectories can be predicted more precisely, which strongly supports the planning of search areas for the rescue helicopter. However, the methods used to determine the search area based on the predicted drift trajectories are mainly derived from the continuous expansion of the area with the highest Probability of Containment(POC), which may lead to local optimal solutions and a decrease in the Probability of Success(POS), especially when there are several subareas with a high POC. To address this problem, this paper proposes a method based on a Minimum Bounding Rectangle and Kmeans clustering(MBRK). A silhouette coefficient is adopted to analyze the distribution of the survivors’ probable locations, which are divided into multiple clusters with K-means clustering. Then,probability maps are generated based on the minimum bounding rectangle of each cluster. By adding or subtracting one row or column of cells or shifting the planned search area, 12 search methods are used to generate the optimal search area starting from the cell with the highest POC in each probability map. Taking a real case as an example, the simulation experiment results show that the POS values obtained by the MBRK method are higher than those obtained by other methods,which proves that the MBRK method can effectively support the planning of search areas and that K-means clustering improves the POS of search plans.
文摘In this paper, the principle of multi-point forming (MPF) technique is presented. One of the most serious defects, wrinkling, during the multi-point forming process of a shallow rectangle cup is discussed by means of numerical simulation on the shallow rectangle cup forming process. The effects of thickness, material of sheet metal and the pressure of the blank holder are investigated. Based on the simulation results, the reasons and control methods of wrinkling are pointed out. Moreover, the experiment on the multi-point die forming of the shallow rectangle cup by the MPF machine is done to validate the efficiency of the numerical simulation, and the result proves that the application of an elastic cushion in the forming can restrain wrinkling efficiently.
基金The work of Jin Li was supported by National Natural Science Foundation of China(Grant No.11471195)China Postdoctoral Science Foundation(Grant No.2015T80703)+1 种基金Shan-dong Provincial Natural Science Foundation of China(Grant No.ZR2016JL006)Na-tional Natural Science Foundation of China(Grant No.11771398).
文摘In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.
文摘The analytic representation of the transient radiation for an aperture excited by a rectangle pulse is obtained. It shows that the field duration and amplitude depend on the observation distance, the elevation angle, the pulse width of the rectangle pulse and the aperture size.
文摘The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied only on a simple domain composed of rectangles or parallelograms whose sides are parallel to two different straight lines. We propose a new triangular Hermite element with 13 degrees of freedom. It is used in combination with the Bogner-Fox-Schmit element near the boundary of an arbitrary polygonal domain and provides continuous differentiability of an approximate solution in the whole domain up to the boundary.
基金support from the National Key R&D Program of China(Grant No.2020YFB1805901)the National Natural Science Foundation of China(Grant No.62105274)+1 种基金the Technology and Innovation Commission of Shenzhen Municipality(Grant No.JCYJ20210324133406018)the Research Grants Council,University Grants Committee of Hong Kong SAR(Grant No.PolyU15301022).
文摘The statistical dynamics of partially incoherent ultrafast lasers are complex and chaotic,which is significant for fundamental research and practical applications.We experimentally and theoretically reveal the statistical dynamics of the spectral evolutions and correlations in an incoherent noise-like rectangle pulse laser(NLRPL).Based on statistical histogram analysis,the probability distribution asymmetry of the spectral intensity fluctuation is decayed with the wavelength far away from the spectral peak due to the detection noise.The full-spectral correlation values indicate that the spectral similarity between two round trips is exponentially weakened as the round-trip offset increases.By studying the correlation map of spectral components,we find that the area of the high-correlation region is relevant to the pump power,which is reduced by increasing the pump power.The mutual information of the spectra demonstrates that two spectral components with symmetry about the spectral peak have a statistical dependence.Experimental observations and statistical properties can coincide well with theoretical numerical simulations.We reveal the pump-dependent spectral correlation of the NLRPL and provide multiple statistical methods for the characterizations of chaotic dynamics in incoherent light sources.
