Let an infinite family of functions F = f ( x ) be defined on the segment [ a, b ].
For any real-valued function f defined on the segment ([x,y]), there exists an associated function (g_{x,y}: [0,1] rightarrowmathbb{R}) with g_{x,y}(t)=fbigl[ 1-t x+tybigr].
We write the solution of the system (1.2), depending from n − p arbitrary scalar functions α i ( t ) defined on the segment [ 0, T ], in the following form: y ¯ ( t, α p + 1, …, α n ) = α p + 1 ( t ) c p + 1 ( t ) + ⋯ + α n ( t ) c n ( t ) + y ˜ 0 ( t ), (1.4).
We consider the orbits of the maps f defined on the unit segment I = [ 0, 1 ] and the limiting (as the order m of differences tends to +∞) behavior of their difference series H ( m ).
Let f : I → I be a map defined on the numerical segment I and X be an orbit, X = ( f ( 0 ) ( x ), f ( 1 ) ( x ), …, f ( n ) ( x ), … ), that is, we put in (1) f n = f ( n ) ( x ), where f ( n ) ( f ( 0 ) ( x ) ≡ x, f ( n + 1 ) = f ∘ f ( n ) ), n ≥ 0 denote the iterates of the map f.
The training was then defined on the target study to be segmented in the following way.
In Frequency Domain Decomposition (FDD), several segments are defined on the bridge and the measurement is performed using two instrumented axles.
Our parallel approach is independent of the number of segments and objects, since instead of graph representation of these components, image features are defined on the pixel level.
Neutrophils were defined on the size/CD16+ gate.
Intuitively, our algorithm of supertree construction resembles an algorithm of finding the minimum of a function of one variable defined on a segment.
For any convex function defined on a segment ([x,y] subset X), we have the Hermite-Hadamard integral inequality (cf. Dragomir [14, p.2] and Dragomir [15, p.2]): f biggl(frac{x+y}{2} biggr) leqint_{0}^{1}f bigl[ 1-t x+tybigr],dtleqfrac {f(x)+f(y)}{2},quad x,yin X, (9) which can bigl[ 1-t x+tybigr]lassical Hermite-Hadamard inequality (8) for the convex function (g_{x,dtleqfracightarrowmathbb {f}).
