where for i = 1,2, φi: R → R is an increasing homeomorphism such that φi(0) = 0, ai is a measurable function with ai(t) > 0 a.e. t in some interval of (0, ∞) and the nonlinearity fi: R ×(0, ∞)4 → R is continuous, and may exhibit singula...
We prove that signals with bounded ( r + 1)st derivative can be quantized using a uniform c-level quantizer with the sample quantization error bounded by B... GW Wasilkowski - 《Journal of Complexity》 被引量: 0发表: 1990年 Note on quantization for signals with bounded (r + 1) No ab...
This starts from the case of a domain Ω that is starlike with respect to all points in a ball B. Then one chooses a bump function (a non-negative function whose integral is 1) θ with support in B and averages the operators coming from (6) for the points x0∈B with a weight ...
where TT is transmissivity [L²/T], SS is storativity [-], tt is time since pumping began [T] and w(u)w(u) is the Theis well function [-]. Similarly, drawdown due to the image well located at a distance r2r2 from the observation well is given by: s2=Q4πTw(u2)s2=Q4πT...
adjective.having bounds or limits. Mathematics. (of a function) having a range with an upper bound and a lower bound. Can unbounded sequence converge? Sounbounded sequence cannot be convergent. Can a divergent sequence be bounded? Abounded sequence cannot be divergent....
When the domain over which the operator d|x|α acts is unbounded, the fractional derivative has a simple de?nition in terms of its Fourier transform dα iqx e = ?|q|α eiqx . d|x|αα α (3) (1) d In Eq. (1), d|x|α is the Riesz–Feller derivative of fractional order ...
ed logarithmic derivative f (x) = g ′(x) Y ′ (x) ? g(x) Y (x) (2) where the function g(x) is chosen so that f (x) is analytic at x = 0 and therefore can be expanded in a Taylor series ∞ f (x) = j=0 fj xj (3) Notice that the coe?cients fj depend on E....
We consider a related inequality between the uniform norm of the kth order derivative of a function, the norm of the function in the space predual for the space of multipliers in Lr, and the L∞-norm of the nth order derivative; this inequality is an analogue of the Kolmogorov inequality...
A functionU :\partial \Omega \rightarrow \mathbb {R}satisfies thebounded slope conditionwith constantQ>0if for anyx_o \in \partial \Omegathere exist two affine functionsw_{x_o}^\pm :\mathbb {R}^n \rightarrow \mathbb {R}with Lipschitz constants[w_{x_o}^\pm ]_{0,1} \le Qsuch...
, etc. depending on the input data in the spdes. in general, the function spaces that we will adopt as those where to look for the solutions to ( 1.1 ) and ( 1.2 ) will be of the form $$\begin{aligned} l^2(i,g_k)\otimes (s)_{-1}, \quad k\in {\mathbb {z}}, \end...