Parliament membership during the single-party system in Turkey (1925-1945)

The official legitimization of the single-party regime in Turkey lay with Parliament, which, as a representative of the people, controlled the legislature, the executive and the judiciary. However, the parliamentary period after 1925 was highlighted by a lack of freedom of speech, with scope for political discussion limited. This paper aims to establish the role of MPs during this period. At the head of the single-party system, the President was free to choose every party member for Parliament. This meant competition was very restricted, be it in the form of short-lived opposition parties or independent candidates. During the selection process, some social classes, for example high-ranking officer and bureaucrats were privileged. These two groups were the most common in Parliament. On the other hand, local ties were sometimes respected by the regime: rural notables with close relations with party headquarters were easily elected, and remained in Parliament. A MPs’ chance of re-election was significant if he performed his duty with loyalty to the party. The author underlines a stabilization of political personnel throughout this period

Special functions with mod n symmetry and kaleidoscope of quantum coherent states

The set of mod $n$ functions associated with primitive roots of unity and discrete Fourier transform is introduced. These functions naturally appear in description of superposition of coherent states related with regular polygon, which we call kaleidoscope of quantum coherent states. Displacement operators for kaleidoscope states are obtained by mod $n$ exponential functions with operator argument and non-commutative addition formulas. Normalization constants, average number of photons, Heinsenberg uncertainty relations and coordinate representation of wave functions with mod n symmetry are expressed in a compact form by these functions.Comment: 12 pages, 4 figures, talk in The 32nd International Colloquium on Group Theoretical Methods in Physics (Group32), Prague, Czech Republic, 9-13 July 201

Systematic Search of Exactly Solvable Non-Central Potentials

Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the effectiveness of the present formalism.Comment: 7 pages, no figure

Explicit Solutions for N-Dimensional Schrodinger Equations with Position-Dependent Mass

With the consideration of spherical symmetry for the potential and mass function, one-dimensional solutions of non-relativistic Schrodinger equations with spatially varying effective mass are successfully extended to arbitrary dimensions within the frame of recently developed elegant non-perturbative technique, where the BenDaniel-Duke effective Hamiltonian in one-dimension is assumed like the unperturbed piece, leading to well-known solutions, whereas the modification term due to possible use of other effective Hamiltonians in one-dimension and, together with, the corrections coming from the treatments in higher dimensions are considered as an additional term like the perturbation. Application of the model and its generalization for the completeness are discussed.Comment: 8 pages, no figure

The Geometry of Self-dual 2-forms

We show that self-dual 2-forms in 2n dimensional spaces determine a $n^2-n+1$ dimensional manifold ${\cal S}_{2n}$ and the dimension of the maximal linear subspaces of ${\cal S}_{2n}$ is equal to the (Radon-Hurwitz) number of linearly independent vector fields on the sphere $S^{2n-1}$. We provide a direct proof that for $n$ odd ${\cal S}_{2n}$ has only one-dimensional linear submanifolds. We exhibit $2^c-1$ dimensional subspaces in dimensions which are multiples of $2^c$, for $c=1,2,3$. In particular, we demonstrate that the seven dimensional linear subspaces of ${\cal S}_{8}$ also include among many other interesting classes of self-dual 2-forms, the self-dual 2-forms of Corrigan, Devchand, Fairlie and Nuyts and a representation of ${\cal C}l_7$ given by octonionic multiplication. We discuss the relation of the linear subspaces with the representations of Clifford algebras.Comment: Latex, 15 page