查询词典 strictly convex function

The uniqueness of solution of field point, inside a convex region due to singular source with kernel function decreasing with distance increasing, outside-region-distribution such that the boundary condition expressed by the response of the source is satisfied, is proved by using the condition of kernel function decreasing with distance increasing and an integral inequality.

应用奇源解的核函数沿距离递减的条件和积分不等式，可证这类奇源在凸域外分布只要满足以它产生的响应来表达的边界条件时，所引起相应的域内场点解是唯一的。

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

Certain mold components (for example convex-concave mold) the shapeand the size by the product decided thus is unable in the moduledesign time foresees, therefore only can according to the common shapedesign module (for example circular or rectangular drift), is suitablethe surface to be narrow; Certain mold components (for example flush压模work piece localization components) although mutuallycoordinates to carry out some function, but their space arrangesdifficult to seek the rule and the general character, therefore evenif divides according to the function cannot have the module.

某些模具零件的形状和尺寸由产品决定因而无法在模块设计时预见到，所以只能按常见形状设计模块，适用面窄；某些模具零件（如冲压模的工件定位零件）虽然互相配合执行某一功能，但它们的空间布置难寻规律与共性，因此即使按功能划分也不能产生模块。

Let G be the domain whose inverse image is the cross section of u definedin (H1) where the mapping is affine,g and ψ are smooth functions and g＞0,thenthere is a unique smooth convex-monotone function which satisfies the followingproblem 〓Furthermore,if 〓 where C is a constant,ψis an affine function,〓 is astrictly interior sub-domain of G in the sense of"parabolic distance",then

若G为按（H1）中定义的u的截影经仿射变换而得的区域，g和〓为光滑函数且〓，则〓存在惟一的凸单调光滑解。若〓常数，〓仿射函数，〓为G在&抛物距离&下的严格内子域，则

In the context of signal processing it is often referred to as the unit impulse function. Note that the Dirac delta is not strictly a function. While for many purposes it can be manipulated as such, formally it can be defined as a distribution that is also a measure .

在物理上，通常用于代表脉冲函数，或者呈点分布的物理量，例如质点、点电荷等；另外，delta函数常用于表示对物理量在某点的抽样，这一点不仅在数学物理方法这样的理论学科中常用，在实际的工程通信中也很常用，这时delta函数被用作采样函数。

Based on the speciality of the spectral function, we provide the sufficient conditions such that the spectral function are K—increasing (strictly K—increasing) in Euclidean Jordan algebra, and establish the relationship between the spectral scalar solution set and the K— efficient solution set of the Euclidean Jordan algebra vector optimization problem.

基于谱函数的特殊性，刻画了谱标量函数满足K-增性的充分条件，继而建立了谱标量解集与欧几里德若当代数向量优化问题K-弱有效解集和K-有效解集的包含关系。

We construct a kind of special matrix function, which is used to characterize the minimization property of this iterative method, and prove that the approximate solution, generated by this iterative method, minimizes this kind of matrix function over a special affine subspace, which means that the Frobenius norm of the residual sequence is strictly monotone decreasing.

通过构造一类特殊的矩阵函数来刻画该迭代方法的极小化性质，并证明了由该迭代方法计算出来的逼近解，可使得这类矩阵函数在一个仿射子空间上达到极小，而且所得到的残差序列的Frobenius范数是严格单调递减的。

As the objective function is not strictly concave in the path rate, the penalty function method is applied to transform the primal problem into a new formulation to obtain the optimal solution based on the subgradient method. And the multiPath congestion control algorithm is also proposed.

由于多径效用最大化问题中的目标函数对路径速率而言不是严格凹的，所以运用罚函数法将此最大化问题转化成新的等价形式，再运用次梯度法获得了原问题的最优解，由此提出了用于Ad hoc网络的多径路由优化拥塞控制算法MPCC。

While the standard Airy function, used frequently in the uniform asymptotic formulas for classical orthogonal polynomials, behaves like the exponential function on one side and the trigonometric functions on the other side of an extreme zero,the q-Airy polynomial behaves like the q-Airy function on one side and the q-Theta function on the other side.

在经典正交多项式的一致渐近公式中我们通常要用到Airy函数，这个Airy函数在一个极端零点的一边表现为指数函数，另一边又表现为三角函数。同样地，q-Airy多项式在一边表现为q-Airy函数，另一边又表现为q-Theta函数。

This paper compares periodic set with almost periodic set, and properties of periodic function with that of almost periodic function through analysing the definitions of periodic function and almost perodic function, and then draws some important conclusions.

利用周期函数与概周期函数的定义，把周期函数的周期集与概周期函数的概周期集进行了比较，把周期函数与概周期函数的性质进行了比较，并得出一些重要结论。

But Severus escaped the hands of those that Julianus had sent to murder him and sent a letter to the praetorian guard, giving them the signal either to desert Julianus or to kill him.

赛维鲁总算逃过了尤利阿努斯派来的杀手，并写了一封信给罗马的禁卫军，向他们发出信号，要么抛弃尤利阿努斯，要么干掉他。他们立即服从了。

This text is in terms of this of " human nature ", it is under the influence of western literature human nature thought to probe into, awakening in human nature of novel works and all sorts of limitations that affectionate The school of Mandarin Duck and butterfly.

本文便是从"人性"这一角度，探讨在西方文学人性思想的影响下，清末民初鸳鸯蝴蝶派的言情、哀情小说作品在人性方面的觉醒与种种局限。