Determination of the source parameter in a heat equation with a non-local boundary condition

AbstractIn this article we consider the inverse problem of identifying a time dependent unknown coefficient in a parabolic problem subject to initial and non-local boundary conditions along with an overspecified condition defined at a specific point in the spatial domain. Due to the non-local boundary condition, the system of linear equations resulting from the backward Euler approximation have a coefficient matrix that is a quasi-tridiagonal matrix. We consider an efficient method for solving the linear system and the predictor–corrector method for calculating the solution and updating the estimate of the unknown coefficient. Two model problems are solved to demonstrate the performance of the methods

Quantum Hall Effect on the Flag Manifold F_2

The Landau problem on the flag manifold ${\bf F}_2 = SU(3)/U(1)\times U(1)$ is analyzed from an algebraic point of view. The involved magnetic background is induced by two U(1) abelian connections. In quantizing the theory, we show that the wavefunctions, of a non-relativistic particle living on ${\bf F}_2$, are the SU(3) Wigner ${\cal D}$-functions satisfying two constraints. Using the ${\bf F}_2$ algebraic and geometrical structures, we derive the Landau Hamiltonian as well as its energy levels. The Lowest Landau level (LLL) wavefunctions coincide with the coherent states for the mixed SU(3) representations. We discuss the quantum Hall effect for a filling factor $\nu =1$. where the obtained particle density is constant and finite for a strong magnetic field. In this limit, we also show that the system behaves like an incompressible fluid. We study the semi-classical properties of the system confined in LLL. These will be used to discuss the edge excitations and construct the corresponding Wess-Zumino-Witten action.Comment: 23 pages, two sections and references added, misprints corrected, version to appear in IJMP

On the solution of non linear systems.

SIGLEAvailable from British Library Document Supply Centre- DSC:D37560/81 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schr\"odinger cat states

A recursive approach to determine the Hilbert-Schmidt measure of pairwise quantum discord in a special class of symmetric states of $k$ qubits is presented. We especially focus on the reduced states of $k$ qubits obtained from a balanced superposition of symmetric $n$-qubit states (multiqubit Schr\"odinger cat states) by tracing out $n-k$ particles $(k=2,3, \cdots ,n-1)$. Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the party grouping $(k-1)$ qubits is explicitly derived. This uses recursive relations between the Fano-Bloch correlation matrices associated with subsystems comprising $k$, $k-1$, $\cdots$ and $2$ particles. A detailed analysis is given for two, three and four qubit systems. In the second scheme, the subsystem comprising the $(k-1)$ qubits is mapped into a system of two logical qubits. We show that these two bipartition schemes are equivalents in evaluating the pairwise correlation in multi-qubits systems. The explicit expressions of classical states presenting zero discord are derived.Comment: 26 page

Number of Spanning Trees of Different Products of Complete and Complete Bipartite Graphs

Spanning trees have been found to be structures of paramount importance in both theoretical and practical problems. In this paper we derive new formulas for the complexity, number of spanning trees, of some products of complete and complete bipartite graphs such as Cartesian product, normal product, composition product, tensor product, symmetric product, and strong sum, using linear algebra and matrix theory techniques

The efficacy and side effects of topiramate on refractory epilepsy in infants and young children: A multi-center clinical trial

SummaryObjectives:This study has been conducted to assess the efficacy and safety of topiramate in refractory epilepsies in infants and young children.Methods:A prospective clinical trial was performed in three tertiary care hospitals, on 47 children aged 6–60 months with refractory epilepsy. Topiramate was added to at least two baseline anti-epileptic drugs. The efficacy was rated according to seizure type, frequency and duration.Results:Children with refractory epilepsy were classified according to their clinical, neuro-imaging, and neurophysiological profile into infantile spasms (IS) (9 cases, 19%), Lennox–Gastaut syndrome (LGS) (25 cases, 53%) and other epilepsies (13 cases, 28%). Children were also classified into cryptogenic and symptomatic epilepsy. Topiramate was introduced as add-on therapy in a daily dose of 1mg/kg/day for 2 weeks, followed by increments of 1–3mg/kg/day at 2-week intervals, up to a maximum of 10mg/kg/day. After a minimum treatment period of 6 months, 28 (60%) of the children had a satisfactory response (completely seizure free, or more than a 50% seizure reduction). The remaining 19 children (40%) had an unsatisfactory response (50% or less reduction in seizure frequency, no change or increased seizure frequency).Topiramate appeared to be equally effective in infantile spasms, Lennox–Gastaut syndrome and children with other types of epilepsy, with no significant difference between those with a satisfactory and an unsatisfactory response (p=0.089). There was also no significant difference in response between patients with cryptogenic and symptomatic epilepsy (p=0.360).Mild to moderate adverse effects, mainly somnolence, anorexia and nervousness, were present in 25 (53%) of children. One of the children developed hypothyroidism.Conclusion:Although the long term safety and possible adverse effects of topiramate have not been fully established in infants and young children, this study has shown that it is a useful option for children with frequent seizures unresponsive to standard anti-epileptic drugs