Visualizing functions is an omnipresent task in many sciences and almost every day we are confronted with diagrams in newspapers and magazines showing functions of all possible flavours. Usually such functions are visualized by plotting their function graph inside an appropriate coordinate system, with the probably most prominent choice being the cartesian coordinate system. This allows us to g...

A group of small spacecraft able to change their relative position and attitude through the use of the potential function method is discussed. The spacecraft shapes, sizes and manoeuvring capabilities are not identical, although all are assumed to manoeuvre using continuous thrusters. A hyperbolic form of the attractive potential function is used to reduce actuator effort by using natural orbit...

lim h→0 f(z + h)− f(z) h if this limit exists. If the derivative of f exists at z, we denote its value by f ′(z), and we say f isholomorphic at z. If f is holomorphic at every point of an open set U we say that f is holomorphic on U . This definition naturally leads to several basic remarks. First, the definition formally looks identical to the limit definition of a derivative of a function of ...

The canonical coherent states are expressed as infinite series in powers of a complex number z in their infinite series version. In this article we present classes of coherent states by replacing this complex number z by other choices, namely, iterates of a complex function, higher functions and elementary functions. Further, we show that some of these classes do not furnish generalized oscilla...

and Applied Analysis 3 Definition 1.1 Hadamard product or convolution . For functions f and g in the class A, where f z of the form 1.1 and g z is given by g z z ∞ ∑ k 2 ckz , 1.8 the Hadamard product or convolution f ∗ g z is defined by ( f ∗ g z z ∞ ∑ k 2 akbkz k ( g ∗ f z , z ∈ U. 1.9 Definition 1.2 subordination principle . For analytic functions g and hwith g 0 h 0 , g is said to be subord...