The main aim of this article is to survey and discuss the existing state of art concerning the assignability by a feedback of numerical characteristics of linear continuous and discrete time-varying systems. Most of the results present necessary or sufficient conditions for different formulation of the Lyapunov spectrum assignability problem. These conditions are expressed in terms of various controllability types and optimalizability of the controlled systems and certain properties of the free system such as: regularity, diagonalizability, boundness away, integral separation and reducibility.
It is shown that in uncontrollable linear system ẋ = Ax + Bu it is possible to assign arbitrarily the eigenvalues of the closed-loop system with state feedbacks u = Kx, K ∈ ℜn⨉m if rank [A B] = n. The design procedure consists in two steps. In the step 1 a nonsingular matrix M ∈ ℜn⨉m is chosen so that the pair (MA,MB) is controllable. In step 2 the feedback matrix K is chosen so that the closed-loop matrix Ac = A − BK has the desired eigenvalues. The procedure is illustrated by simple example.
The situation of transsexual persons in Poland is not precisely known; there are only estimates determining the scale of the phenomenon. The lack of information fosters stereotypes and, not infrequently, injurious appraisal; fear of the unknown is also produced, and is gradually turning into widespread prejudice. A social analysis of the phenomenon of transsexuality is hampered by the predominance of the hetero-normative discourse, including in scholarly spheres. The basic issue addressed by the author is the acceptance of transsexual persons, viewed from the perspective of their own personal experiences. These observations concern both the sphere of personal life as well as functioning in the macro-social space (school, work, etc.). In each of these spheres, a change of gender produces complications with which transsexual persons must grapple as they strive to live in harmony with their psychologically intuited gender.
In cellular networks, cells are grouped more densely around highly populated areas to provide more capacity. Antennas are pointed in accordance with local terrain and clutter to reduce signal shadows and interference. Hardware parameters are easily set during installation but difficult to change thereafter. In a dynamic environment of population migration, there is need to continuously tune network parameters to adapt the network performance. Modern mobile equipment logs network usage patterns and statistics over time. This information can be used to tune soft parameters of the network. These parameters may include frequency channel assignment or reuse, and transmitter radiation power assignment to provide more capacity on demand. The paper proposes that by combining the frequency and power assignments, further optimisation in resource allocation can be achieved over a traditional frequency assignment. The solution considers the interference, traffic intensity and use of priority flags to bias some edges. An Edge Weight Power and Frequency Assignment Algorithm is presented to solve the resource allocation problem in cellular networks. The paper also analyses the performance improvements obtained over that of the Edge Weight Frequency Assignment Algorithm. The results show that the proposed algorithm improves the performance of the Edge Weight Frequency Assignment Algorithm depending on the initial structure of the graph.