查询词典 necessary and sufficient conditions

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we inducted the absolute value norm in the two-dimensional vector interspace, and also proved the two-dimensional vector interspace is a Banach Interspace. Thirdly, we define two-dimensional vector-valued functions on a interval by the definition of -fine partitions in part 1. Then, some sufficient and necessary conditions of integrabel are given, and discuss the property of the integral on two-dimensional vector-valued functions.

主要包括以下内容：在第一部分，我们介绍了本文所用到的几个基本概念和引理；第二部分，我们在二维向量空间中引入了绝对值范数，并且证明了二维向量空间是一个Banach空间；在第三部分中，通过第一部分关于-精细分划的定义，我们给出了在某区间上二维向量值函数积分的定义以及可积的充分必要条件，并讨论了二维向量值函数积分的一些性质。

Here conditions (1) and (2) are each on their own necessary conditions for bachelorhood and together they are jointly sufficient for bachelorhood.

在这里，条件（1）和（2）各自是单身汉身份的必要条件，合起来构成单身汉身份的充分条件。

Laws must be sufficient to determine the will as will, even before I ask whether I have power sufficient for a desired effect, or the means necessary to produce it; hence they are categorical: otherwise they are not laws at all, because the necessity is wanting, which, if it is to be practical, must be independent of conditions which are pathological and are therefore only contingently connected with the will.

简译：laws必须足以把意志作为意志来规定，即使并没有进行这个（即'我问我自己是否拥有足以实现所欲求的后果的能力或产生该后果所必须的工具'）；因此它们是范畴性的categorical定言的，否则它们就不是laws，因为它缺乏必然性，而如果这个原理要被实践的话，这必然性是和'诸如习惯喜好等（由此是偶然关联于意志的）条件'无关的/相独立的。

These conditions can be used to prove the sufficient and necessary conditions of the weak controllable property.

它是定常解析非线性系统弱能控充要条件的证明和受控对称性分析的基础，并在定常非线性系统的能控性分析中得到应用。

Dress beauty to a woman is a necessary condition is not sufficient and necessary conditions.

服饰美容是做好一个女人的必要条件，不是充要条件。

Dress beauty is a woman do the necessary conditions are not sufficient and necessary conditions.

服饰美容是做好一个女人的必要条件，不是充要条件。

Based on the theory of B spline,this paper discusses the sufficient and necessary conditions of G 1 continuity between two patches of bi cubic tensor product non uniform B spline surfaces in a special type,and gives a kind of sufficient condition of G 1 continuity so as to satisfy the need of application.

依据有关B样条理论，研究了一种特定类型的双三次张量积非均匀B样条曲面间G1光滑拼接的充要条件，且给出了此种类型的两张双三次张量积非均匀B样条曲面间G1光滑拼接的一个充分条件，以满足实际应用的需

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

Subject to the conditions of this section and to such terms and conditions as the Administrator determines to be necessary to carry out the purposes of this title, the Administrator is authorized to guarantee, and to make commitments to guarantee, the principal and interest (including interest accruing between the date of default and the date of the payment in full of the guarantee) of any loan, obligation, or participation therein of any State, municipality, or intermunicipal or interstate agency issued directly and exclusively to the Federal Financing Bank to finance that part of the cost of any grant-eligible project for the construction of publicly owned treatment works not paid for with Federal financial assistance under this title, which project the Administrator has determined to be eligible for such financial assistance under this title, including, but not limited to, projects eligible for reimbursement under section 206 of this title. No guarantee, or commitment to make a guarantee, may be made pursuant to this section—(1) unless the Administrator certifies that the issuing body is unable to obtain on reasonable terms sufficient credit to finance its actual needs without such guarantee; and (2) unless the Administrator determines that there is a reasonable assurance or repayment of the loan, obligation, or participation therein. A determination of whether financing is available at reasonable rates shall be made by the Secretary of the Treasury with relationship to the current average yield on outstanding marketable obligations of municipalities of comparable maturity.

依于这个部分的条件和对如此期限和条件象管理员确定是必要执行这个标题的目的，管理员被批准保证，并且做承诺保证，主要和兴趣(包括兴趣累积在缺省日期和付款的日期之间充分保证)的任何贷款，义务，或参与在其中任何状态，自治市，或intermunicipal 或跨境代办处直接地和完全被发布对联邦财务银行提供经费一部分的任何授予合格的项目的费用为公开地拥有的治疗工作的建筑没被支付以联邦经济援助在这个标题之下，哪个项目管理员确定是有资袼这样的经济援助在这个标题之下没有保证，或承诺做保证，可以被做寻求这个部分(1)除非管理员证明发布的身体无法获得在合理的期限充足的信用提供经费给它的实际需要没有这样的保证；并且(2)除非管理员确定有贷款的合理的保证或偿还，义务，或参与在其中。

We get the sufficient and necessary conditions for the reaction process to be stochastic monotonic under certain conditions e.g.

第三部分推广了[29]中的结果，对较广的有限系统证明了若干泛函不等式与底过程对应的泛函不等式的等价性以及不等式常数之间的关系。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。