Scattering in three-dimensional fuzzy space

We develop scattering theory in a non-commutative space defined by a $su(2)$ coordinate algebra. By introducing a positive operator valued measure as a replacement for strong position measurements, we are able to derive explicit expressions for the probability current, differential and total cross-sections. We show that at low incident energies the kinematics of these expressions is identical to that of commutative scattering theory. The consequences of spacial non-commutativity are found to be more pronounced at the dynamical level where, even at low incident energies, the phase shifts of the partial waves can deviate strongly from commutative results. This is demonstrated for scattering from a spherical well. The impact of non-commutativity on the well's spectrum and on the properties of its bound and scattering states are considered in detail. It is found that for sufficiently large well-depths the potential effectively becomes repulsive and that the cross-section tends towards that of hard sphere scattering. This can occur even at low incident energies when the particle's wave-length inside the well becomes comparable to the non-commutative length-scale.Comment: 12 pages, 6 figure

Equivalence of robust stabilization and robust performance via feedback

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation (LFT) models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified $L^{2}$-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to Linear Matrix Inequality (LMI) conditions.Comment: 20 page

Interpreting the theology of Barth in light of Nietzsche’s dictum “God is dead”

Karl Barth responded with his theology to Nietzsche’s dictum “God is dead” by stating that God is the living God. God does not need the human race to exist. God reveals God self to humankind whenever God wills. Barth agreed with Nietzsche that the god of the nineteenth century was a “Nicht-Gott”. The article aims to discus Karl Barth’s respons to Nietzsche’s impulse towards the development of a concept of God that would lead to neither atheism nor theism. The article argues that Barth paved the way for talking about God by defining God as the “communicative God”

Karl Barth’s role in church and politics from 1930 to 1935

Karl Barth saw in natural theology a threat to the church of Christ. He was convinced that the so-called “German Christians” under the influence of the National Socialist Party practised natural theology. He advocated the need for the church of Christ to be church according to the Word of God. The church can be true church of Christ when it listens to and obeys the true calling of God. Barth’s critique of an exclusive “Volkskirche” can serve as a corrective for the definition of the Nederduitsch Hervormde Kerk as a “volkskerk”

Die vroeg-Christelike doop as kultureelrituele simbool

Early Christian baptism as a cultural, ritual symbol This article describes baptism as a cultural, ritual symbol. Baptism is seen as a symbol consisting of reason, value and meaning. The reason why baptism functions as a symbol has a historical basis in the death and resurrection of Jesus. For the first Jesus followers the value of being baptized was that they became part of a new value system. This value system gave meaning to the lives of the baptized and others who stood in relationship with them. The initiation into this alternative lifestyle (through baptism) was made possible by an altered state of consciousness

Spectrum of the three dimensional fuzzy well

We develop the formalism of quantum mechanics on three dimensional fuzzy space and solve the Schr\"odinger equation for a free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits. A high energy cut-off is found for the free particle spectrum, which also results in the modification of the high energy dispersion relation. An ultra-violet/infra-red duality is manifest in the free particle spectrum. The finite well also has an upper bound on the possible energy eigenvalues. The phase shifts due to scattering around the finite fuzzy potential well have been calculated