According to the principle of continuity If the fluid is in streamline flow and is in-compressible then we can say that mass of fluid passing through different cross sections are equal. From the above situation, we can say the mass of liquid inside the container remains the same. The rate ...
Optimal controlEnsemble controlImpulsive controlLinear transport equationPontryagin's Maximum PrincipleFeedback controlsIterative methods for optimal controlThe paper deals with an optimal control problem for the simplest version of a "reduced" linear impulsive continuity equation. The latter is introduced in...
We call a continuous and strictly increasing function \(\omega (\cdot ): R_{+}\rightarrow R_{+}\) a modulus of continuity if \(\omega (0)=0\).Definition 2.1[8] The fractional integral of order \(\alpha >0\) for a function \(\phi :[0,T]\rightarrow R\) is defined by ...
1.PASSAGE ARRANGEMENT OPTIMIZATION OF MULTI-STREAM HEAT EXCHANGER BASED ON STRUCTURE-PERFORMANCE CONTINUITY PRINCIPLE基于结构性能连续性原理的多股流换热器通道排列优化 2.On the Original Functional Continuity of Sectional-continuous Function and Its Application关于分段连续函数的原函数的连续性及其应用 3.It is ...
To determine the principal organic constituent of a living being in order of relative abundance, we will analyze each option provided:1. Understanding the Question: We need to identify the most abundant organic constituent in l
(2) Flow rate characteristics: According to the mass continuity law, the mass flow rate in the preceding stage must be the same as that in the following stage, but the volume flow rate of the preceding International Journal of Refrigeration 149 (2023) 35–48 stage is significantly higher ...
I provide a new proof of uniqueness of equilibrium in a wide class of global games. I show that the joint best-response in these games is a contraction. The uniqueness result then follows as a corollary of the contraction principle. Furthermore, the contraction-mapping approach provides an int...
Removing the integral signs, we obtain the well-known continuity equation; the differential equation form of the law of conservation of mass: (2.10)∂ρ∂t+div(ρv→)=0 This equation can be expanded both for Cartesian and cylindrical coordinates: (2.11)∂ρ∂t+∂∂x(ρvx)+∂...
whereW˙is white in time and fractional in space with Hurst parameterH∈(14,12). Recently, Hu and Wang (Ann Inst Henri Poincaré Probab Stat 58(1):379–423, 2022) have studied the well-posedness of this equation without the technical condition ofσ(0)=0which was previously assumed in ...
. hence, by continuity, we find \(\epsilon >0\) (where \([0,\epsilon )\subset v\) ) so that $$\begin{aligned} |x_{j_0}'(a)|\ge \frac{\sup _{a\in [0,1]}\sup _{x\in k(a)}|\partial _at_a(x)|}{\lambda -1}+2l,\qquad \forall a\in (0,\epsilon ). \end{...