TiO_{2} nano particles were synthesized in Rutile and Anatase phases by sol-gel method using two kind of complex agents, acidic (Citric Acid) and organic complex agent (acetyl acetone) at 400°C, 500°C, 650°C sintering temperatures. The structural analysis by XRD diffraction confirmed phase formation of titanium oxide. Particles sizes were determined by using Scherrer formula. TEM was employed to confirm nano particles formation. The size of nano particles as well as Phase formation can be controlled by the type of complex agent and sintering temperature. Acetyl Acetone causes a more crystalline structure and more uniformity of size distribution in 400°C sintering temperatures. Moreover, it results in obtaining single phase TiO_{2} nanoparticles at 400°C and 650°C sintering temperature. On the other hand, at high sintering temperature, the particles obtained from polymeric agent tend to agglomerate larger in size than the acidic product.

Abstract:
It has been reported theoretically that the intercalation of nitrogen in the voids of the rather open cubic structure of bulk Cu3N build up a magnetic structure. In an extended effort to study this system, we have investigated spin polarization in bulk and thin films of nitrogen intercalated Cu3N (Cu3N2) structure by means of first-principles calculations based on Kohn-Sham density functional theory and ultrasoft pseudopotentials technique. Contrary to the previous study, the results show that after an accurate structural relaxation of the system, magnetism in the bulk structure vanishes. This effect is due to the migration of the intercalated nitrogen atom from the body center of the cell to the nearness of one of the cell faces. Similar study for the thin films of 5, 7, 9 and 11 monolayers thickness was performed and it was found that initial relaxation of structures with 7 and 11 monolayers show a net magnetic moment of 2.6 {\mu}B. By a more extended survey of the energy surfaces, the film with 7 monolayers loses its magnetic moment similar to the bulk structure but the film with 11 monolayers maintains its magnetic moment. It is possibly a new quantum size effect that keeps the intercalated nitrogen atom of the middlemost cell at the body center site. Electron density map of this film clearly confirms the spin polarization upon the intercalated atom.

Abstract:
We present a detailed study of the representations of the algebra of functions on the quantum group $ GL_q(n) $. A q-analouge of the root system is constructed for this algebra which is then used to determine explicit matrix representations of the generators of this algebra. At the end a q-boson realization of the generators of $ GL_q(n) $ is given.

Abstract:
We extend our previous analysis of the classical integrable models of Calogero in several respects. Firstly we provide the algebraic resaons of their quantum integrability.Secondly we show why these systems allow their initial value problem to be solved in closed form . Furthermore we show that due to their similarity with the above models the classical and quantum Heisenberg magnets with long rang interactions in a magnetic field are also intergrable. Explicit expressions are given for the integrals of motion in involution in the classical case and for the commuting operators in the quantum case.

Abstract:
Within the Matrix Product Formalism we have already introduced a multi- species exclusion process in which different particles hop with different rates and fast particles stochastically overtake slow ones. In this letter we show that on an open chain, the master equation of this process can be exactly solved via the coordinate Bethe ansatz. It is shown that the N-body S-matrix of this process is factorized into a product of two-body S-matrices, which in turn satisfy the quantum Yang-Baxter equation (QYBE). This solution is to our knowledge, a new solution of QYBE.

Abstract:
There are only two quantum group structures on the space of two by two unimodular matrices, these are the $SL_q(2)$ and the $SL_h(2)$ [9-13] quantum groups. One can not construct a differential geometry on $ SL_q(2)$, which at the same time is bicovariant, has three generators, and satisfies the Liebnitz rule. We show that such a differential geometry exists for the quantum group $SL_h(2)$ and derive all of its properties.

Abstract:
We study the Kitaev model on a ladder network and find the complete spectrum of the Hamiltonian in closed form. Closed and manageable forms for all eigenvalues and eigenvectors, allow us to calculate the partition function and averages of non-local operators in addition to the reduced density matrices of different subsystems at arbitrary temperatures. It is also briefly discussed how these considerations can be generalized to more general lattices, including three-leg ladders and two dimensional square lattices.

Abstract:
{Although q-oscillators have been used extensively for realization of quantum universal enveloping algebras,such realization do not exist for quantum matrix algebras ( deformation of the algebra of functions on the group ). In this paper we first construct an infinite dimensional representation of the quantum matrix algebra $ M_q ( 3 ) $(the coordinate ring of $ GL_q (3)) $ and then use this representation to realize $ GL_q ( 3 ) $ by q-bosons.}

Abstract:
It is shown that the finite dimensional ireducible representations of the quantum matrix algebra $ M_q(3) $ ( the coordinate ring of $ GL_q(3) $ ) exist only when q is a root of unity ( $ q^p = 1 $ ). The dimensions of these representations can only be one of the following values: $ p^3 , { p^3 \over 2 } , { p^3 \over 4 } $ or $ { p^3 \over 8 } $ . The topology of the space of states ranges between two extremes , from a 3-dimensional torus $ S^1 \times S^1 \times S^1 $ ( which may be thought of as a generalization of the cyclic representation ) to a 3-dimensional cube $ [ 0 , 1 ]\times [ 0 , 1 ]\times [ 0 , 1 ] $ .

Abstract:
It is shown that the finite dimensional irreducible representaions of the quantum matrix algebra $ M_{ q,p}(2) $ ( the coordinate ring of $ GL_{q,p}(2) $) exist only when both q and p are roots of unity. In this case th e space of states has either the topology of a torus or a cylinder which may be thought of as generalizations of cyclic representations.