【摘 要】
：
While considering a mirror and light rays coming either from a point source or from infinity, the reflected light rays may have an envelope, called a caustic curve. In this paper, we study developable surfaces as mirrors. These caustic surfaces, described
【机 构】
：
Institute of Mathematics and Computer Science,Eszterházy Károly University,Eger 3300,Hungary;Departm
论文部分内容阅读
While considering a mirror and light rays coming either from a point source or from infinity, the reflected light rays may have an envelope, called a caustic curve. In this paper, we study developable surfaces as mirrors. These caustic surfaces, described in a closed form, are also developable surfaces of the same type as the original mirror surface. We provide efficient, algorithmic computation to find the caustic surface of each of the three types of developable surfaces (cone, cylinder, and tangent surface of a spatial curve). We also provide a potential application of the results in contemporary free-form architecture design.
其他文献
This paper presents a novel multiple-outlier-robust Kalman filter (MORKF) for linear stochastic discrete-time systems. A new multiple statistical similarity measure is first proposed to evaluate the similarity between two random vectors from dimension to
能量对电弧行为具有重要影响,开展高压环境下GMAW电弧能量耗散研究对指导焊接工艺和提升电弧稳定性具有重要意义.电弧的能量损失难以直接测量,为此创建以电弧中心一定距离的圆柱面的热流量作为参考,比较不同压力GMAW电弧的能量损失,基于流体力学和传热学理论,建立高压GMAW数值分析模型,计算电弧局部区域对外能量传输情况.建立了高压GMAW能量耗散测量试验平台,通过采集1/16圆柱面的能量传输量进行换算,获得整个圆柱面的能量传输情况,并采用圆管自然对流传热模型,对测量结果加以修正.将模拟和试验结果对比,分析环境压
Recently, graph neural networks (GNNs) have achieved remarkable performance in representation learning on graph-structured data. However, as the number of network layers increases, GNNs based on the neighborhood aggregation strategy deteriorate due to the
低碳钢/高强钢组合结构能够在保证承载能力的前提下减少合金元素用量,降低成本.文中提出了一种高效、稳定的双丝双钨极氩弧增材制造方法,在400 A大熔敷电流参数下,将低碳钢丝H08Mn2Si与高强钢丝H06MnNi3CrMoA同时送进,开展了熔敷金属的成分调控研究.结果表明,该方法的熔敷效率达到了2.4 kg/h,通过调整双丝的送丝速度比,在不影响电弧状态的前提下,准确获得了所需的熔敷金属成分,并且熔敷金属的抗拉强度、屈服强度、显微硬度随高强钢含量的增加而线性增加,其调节范围分别为565～914,441～80
以45钢为基体,采用感应钎涂工艺在其表面制备金刚石/镍基合金复合涂层,通过洛氏硬度计、磨粒磨损试验机对涂层进行硬度和耐磨性测试,采用超景深显微镜、扫描电子显微镜对涂层、钎料和金刚石形貌进行观察,采用EDS对金刚石表面微区进行成分分析,初步研究了复合涂层的微观形貌、磨损规律及机制.结果表明,金刚石颗粒在镍基合金复合涂层中弥散分布,与钎料合金实现了良好的冶金结合.随着金刚石含量增加,可显著提高复合涂层的硬度及耐磨性.当金刚石质量分数为20％时,涂层的宏观硬度达到63 HRC,较纯钎料涂层提高1.5倍;在相同的
Analyzing network robustness under various circumstances is generally regarded as a challenging problem. Robustness against failure is one of the essential properties of large-scale dynamic network systems such as power grids, transportation systems, comm
探索MIG电弧增材制造6061铝合金构件的工艺成形性,并对成形件不同区域的微观组织及力学性能开展研究.结果表明,当送丝速度/焊接速度的比值P在0.5～1之间,且送丝速度在5～7 m/min之间时,可获得良好焊道形貌;堆积焊道层与层之间交界处为结合层,其余区域为沉积层,结合层和沉积层呈现出沿堆积高度方向灰白色带依次交替的形貌,并都呈现出各种尺寸大小的气孔多发的状态;显微硬度和拉伸测试发现:沿着堆积方向硬度变化不大,结合层硬度低于沉积层,且硬度波动性更大;不同区域水平方向强度差异不大,堆积方向强度比水平方向略
The H∞ control method is an effective approach for attenuating the effect of disturbances on practical systems, but it is difficult to obtain the H∞ controller due to the nonlinear Hamilton–Jacobi–Isaacs equation, even for linear systems. This study deals
Driving behavior normalization is important for a fair evaluation of the driving style. The longitudinal control of a vehicle is investigated in this study. The normalization task can be considered as mapping of the driving behavior in a different environ
An X-band monopulse antenna based on trans-mitarray with light-weight and low-cost features is designed, fabricated, and measured. The proposed antenna is composed of a transmitarray lens, a feed source which combines aperture-coupled microstrip antennas,