Sets on which the modulus of an entire function is bounded from belowSiberian Mathematical Journal -doi:10.1007/BF00969939Kluwer Academic Publishers-Plenum PublishersSiberian Mathematical Journal
For instance, the function f(x1, x2) = 2x21 − 6x1x2 + x22 − 2x1 + x2 + 1 is a quadratic function. We have: [6.1]fx=x1x22−3−31x1x2+−21x1x2+1 We will show below that the derivative of f at point x is an affine function. In our example, the derivative ...
is a vectorial Boolean function with coordinate functionsf1= (01010101),f2= (00100001), andf3= (11000010); we list here vectors of values of them. Note that the component functions ofFaref1,f2,f3,f1⊕f2= (01110100),f1⊕f3= (10010111),f2⊕f3= (11100011), andf1⊕f2⊕f3= (10110110)....
Searching for possible biochemical networks that perform a certain function is a challenge in systems biology. For simple functions and small networks, this can be achieved through an exhaustive search of the network topology space. However, it is difficult to scale this approach up to larger netwo...
The function log |x| playsthe same role when n = 2 that |x|2n 49、plays when n > 2. Notice thatlimx log |x|= , but limx |x|2n = 0; note also that log |x| is nei-ther bounded above nor below, but |x|2n is always positive. Thesefacts hint at the contrast between ...
A spline f(X) will be a smooth function, satisfying certain differentiability properties mentioned below, such that f(X) is a polynomial of degree d. Wooden or metal splines have continuous derivatives of all orders since they are a physical object. This is not true for statistical splines. ...
We consider an infinitesimal version of the Bishop-Gromov relative volume comparison condition as generalized notion of Ricci curvature bounded below for A... KAZUHIRO KUWAE,TAKASHI SHIOYA - 《Comm.anal.geom》 被引量: 50发表: 2007年 Constant-sign and sign-changing solutions of a nonlinear eigenva...
The present paper is dealt with a predator–prey model in which the growth of the prey population is influenced by the Allee effect while the predator species are contended with the prey population following the Crowley–Martin type response function. Th
Different partitions of the interval [a, b] (that is, different choices of points of division xi) yield, generally speaking, different sums. If the set of these sums is bounded above, we say that the function f (x) is of bounded variation on the interval [a, b]. The least upper bo...
Using the universal approximation property of NN, and our Theorem 3 for approximation of jump functions, there is a two-layer NN such that (77)f(x)=W1Tσ(V1Tx)+W2Tφ(V2Tx)+ε with the approximation error bounded on a compact set by ||ε|| < εN, with εN a known bound. W1...