Electrophoretically deposited polyaniline/ZnO nanoparticles for p–n heterostructure diodes

A p–n heterostructure diode of polyaniline (PANI) and ZnO nanoparticles was prepared by the electrophoretic deposition of PANI on ZnO nanoparticles thin film coated fluorine doped tin oxide (FTO) glass at room temperature. The morphological, structural and optical studies substantiated the penetration, bonding and the interaction of PANI molecules with ZnO nanoparticles thin film substrates. The prominent blue shift in UV-Vis spectra indicated the strong interaction between ZnO and PANI through the decreased degree of orbital overlap between π$\pi$ electrons of the phenyl rings with the lone pair of the nitrogen atom in the PANI molecules. The I–V$I\text{–}V$ characteristics of PANI/ZnO heterostructure diode showed weak rectifying behavior with non-linear nature of I–V$I\text{–}V$ curve of PANI/ZnO heterostructure device. The typical ohmic behavior was observed by the I–V$I\text{–}V$ characterization of PANI/ZnO heterostructure at the interface of PANI and ZnO thin film layer without top Pt thin layer contact.     

Influence of interface states on the temperature dependence and current–voltage characteristics of Ni/p-InP Schottky diodes

The ideality factor n$n$ and the barrier height _Φap${\Phi }_{ap}$ of the sputtered Ni/p-InP Schottky diodes have been calculated from their experimental Current–voltage (I–V)$\left(I\text{–}V\right)$ characteristics in the temperature range of 60–400 K with steps of 10 K. The n$n$ and _Φap${\Phi }_{ap}$ values for the device have been obtained as 1.27 and 0.87 eV at 300 K and 1.13 and 0.91 eV at 400 K, respectively. The n$n$ values larger than unity at high temperatures indicate the presence of a thin native oxide layer at the semiconductor/metal interface. The barrier height (BH) has been assumed to be bias dependent due to the presence of an interfacial layer and interface states located at the interfacial layer-semiconductor interface. Interfacial layer-thermionic emission current mechanism has been fitted to experimental I–V$I\text{–}V$ data by considering the bias-dependence of the BH at each temperature. The best fitting values of the series resistance _Rs$R_s$ and interface state density _Ns$N_s$ together with the bias-dependence of the BH have been used at each temperature, and the _Rs$R_s$ and _Ns$N_s$ versus temperature plots have been drawn. It has been seen that the experimental and theoretical forward bias I–V$I\text{–}V$ data are in excellent agreement with each other in the temperature range of 60–400 K. It has been seen that the _Rs$R_s$ and _Ns$N_s$ values increase with a decrease in temperature, confirming the results in the literature.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.     

The first Chevalley–Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations

In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle V^k$V^k$ to a decreasing family of k$k$ foliations _Fi$F_i$ on a manifold M$M$. We have shown that there exists a (1,1)$(1,1)$ tensor J$J$ of V^k$V^k$ such that J^k≠0$J^k\ne 0$, J^k+1=0$J^{k+1}=0$ and we defined by _LJ(V^k)$L_J\left(V^k\right)$ the Lie Algebra of vector fields X$X$ on V^k$V^k$ such that, for each vector field Y$Y$ on V^k$V^k$, [X,JY]=J[X,Y]$[X,JY]=J[X,Y]$.     

Effects of colored noise and noise delay on a calcium oscillation system

As a calcium oscillations system is in steady state, the effects of colored noise and noise delay on the system is investigated using stochastic simulation methods. The results indicate that: (1) the colored noise can induce coherence bi-resonance phenomenon. (2) there exist three peaks in the R–_τ0$R\text{–}{\tau }_0$ (R$R$ is the reciprocal coefficient of variance, and _τ0${\tau }_0$ is the self-correlation time of the colored noise) curves. For the same noise intensity Q=1$Q=1$, the Gaussian colored noise can induce calcium spikes but the white noise cannot do this. (3) the delay time can improve noise induced spikes regularity as _τ0${\tau }_0$ is small, and R$R$ has a significant minimum with increasing τ$\tau$ as _τ0${\tau }_0$ is large. (4) large values of ζ$\zeta$ reduce noise induced spikes regularity.     

On m-accretive Schrödinger-type operators with singular potentials on Riemannian manifolds

We consider a Schrödinger-type differential expression _HV=∇^∗∇+V$H_V={\nabla }^{\ast }\nabla +V$, where ∇$\nabla$ is a Hermitian connection on a Hermitian vector bundle E$E$ over a complete Riemannian manifold (M,g)$(M,g)$ with metric g$g$ and positive smooth measure dμ$d\mu$, and V$V$ is a locally integrable section of the bundle of endomorphisms of E$E$. We give a sufficient condition for m$m$-accretivity of a realization of _HV$H_V$ in L²(E)$L^2\left(E\right)$.     

Three PT-symmetric Hamiltonians with completely different spectra

We discuss three Hamiltonians, each with a central-field part H₀$H_0$ and a PT-symmetric perturbation igz$igz$. When H₀$H_0$ is the isotropic Harmonic oscillator the spectrum is real for all g$g$ because H$H$ is isospectral to H₀+g²/2$H_0+g^2/2$. When H₀$H_0$ is the Hydrogen atom then infinitely many eigenvalues are complex for all g$g$. If the potential in H₀$H_0$ is linear in the radial variable r$r$ then the spectrum of H$H$ exhibits real eigenvalues for 0<g<g_c$0<g<g_c$ and a PT phase transition at g_c$g_c$.     

Bertrand curves in the three-dimensional sphere

A curve α$\alpha$ immersed in the three-dimensional sphere S³${\mathbb{S}}^3$ is said to be a Bertrand curve if there exists another curve β$\beta$ and a one-to-one correspondence between α$\alpha$ and β$\beta$ such that both curves have common principal normal geodesics at corresponding points. The curves α$\alpha$ and β$\beta$ are said to be a pair of Bertrand curves in S³${\mathbb{S}}^3$. One of our main results is a sort of theorem for Bertrand curves in S³${\mathbb{S}}^3$ which formally agrees with the classical one: “Bertrand curves in S³${\mathbb{S}}^3$ correspond to curves for which there exist two constants λ≠0$\lambda \ne 0$ and μ$\mu$ such that λκ+μτ=1$\lambda \kappa +\mu \tau =1$”, where κ$\kappa$ and τ$\tau$ stand for the curvature and torsion of the curve; in particular, general helices in the 3-sphere introduced by M. Barros are Bertrand curves. As an easy application of the main theorem, we characterize helices in S³${\mathbb{S}}^3$ as the only twisted curves in S³${\mathbb{S}}^3$ having infinite Bertrand conjugate curves. We also find several relationships between Bertrand curves in S³${\mathbb{S}}^3$ and (1,3)-Bertrand curves in R⁴${\mathbb{R}}^4$.     

Resolutions of non-regular Ricci-flat Kähler cones

We present explicit constructions of complete Ricci-flat Kähler metrics that are asymptotic to cones over non-regular Sasaki–Einstein manifolds. The metrics are constructed from a complete Kähler–Einstein manifold (V,_gV)$(V,g_V)$ of positive Ricci curvature and admit a Hamiltonian two-form of order two. We obtain Ricci-flat Kähler metrics on the total spaces of (i) holomorphic C²/_Zp${\mathbb{C}}^2/{\mathbb{Z}}_p$ orbifold fibrations over V$V$, (ii) holomorphic orbifold fibrations over weighted projective spaces WCP¹${\mathbb{W}\mathbb{C}\mathbb{P}}^1$, with generic fibres being the canonical complex cone over V$V$, and (iii) the canonical orbifold line bundle over a family of Fano orbifolds. As special cases, we also obtain smooth complete Ricci-flat Kähler metrics on the total spaces of (a) rank two holomorphic vector bundles over V$V$, and (b) the canonical line bundle over a family of geometrically ruled Fano manifolds with base V$V$. When V=CP¹$V={\mathbb{C}\mathbb{P}}^1$ our results give Ricci-flat Kähler orbifold metrics on various toric partial resolutions of the cone over the Sasaki–Einstein manifolds Y^p,q$Y^{p,q}$.     

On analogues of black brane solutions in the model with multicomponent anisotropic fluid

A family of spherically symmetric solutions with horizon in the model with m  -component anisotropic fluid is presented. The metrics are defined on a manifold that contains a product of n−1$n-1$ Ricci-flat “internal” spaces. The equation of state for any s  -th component is defined by a vector Us$U^s$ belonging to Rn+1${\mathbb{R}}^{n+1}$. The solutions are governed by moduli functions Hs$H_s$ obeying non-linear differential equations with certain boundary conditions imposed. A simulation of black brane solutions in the model with antisymmetric forms is considered. An example of solution imitating M₂–M₅$M_2\text{–}{M}_5$ configuration (in D=11$D=11$ supergravity) corresponding to Lie algebra A₂$A_2$ is presented.     

Is space-time symmetry a suitable generalization of parity-time symmetry?

We discuss space-time symmetric Hamiltonian operators of the form H=H₀+igH^′$H=H_0+ig{H}^{\prime }$, where H₀$H_0$ is Hermitian and g$g$ real. H₀$H_0$ is invariant under the unitary operations of a point group G$G$ while H^′$H^{\prime }$ is invariant under transformation by elements of a subgroup G^′$G^{\prime }$ of G$G$. If G$G$ exhibits irreducible representations of dimension greater than unity, then it is possible that H$H$ has complex eigenvalues for sufficiently small nonzero values of g$g$. In the particular case that H$H$ is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<g_c$0<g<g_c$, where g_c$g_c$ is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H$H$ may exhibit real or complex eigenvalues for g>0$g>0$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.     

On the length of stabilograms: A study performed with detrended fluctuation analysis

The effects associated to the length of stabilograms, a measure of the time dependence of the center of pressure of an individual standing up, are analyzed. The fractal characteristics of 27 signals with a length of 2¹⁴$2^{14}$ points, each one corresponding to a different individual, are studied by using the Detrended Fluctuation Analysis technique. The properties of the complete signals are compared to those of various subsignals extracted from them. No differences have been found between the characteristic exponents found for x$x$ and y$y$ signals. The relation between the exponents of the position and velocity signals is accomplished by the 2¹⁴$2^{14}$ point signals, while subsignals with up to 2¹²$2^{12}$ points do not verify it. Using artificial signals with 2¹⁴$2^{14}$ points, generated for α$\alpha$ values given, it has been demonstrated that the exponents obtained from these signals take values larger than expected for α<0.3$\alpha <0.3$, while the exponents of the accumulated series are smaller than expected for 0.7<α$0.7<\alpha$. For CoP trajectories this indicates that DFA-1 provides feasible exponents for the short τ$\tau$-end region of the velocity signal and the large τ$\tau$-end region of the accumulated (position) one. It has been found that the characteristic exponents vary along the series. A slightly larger persistence is found in the last part of the signal for large frequencies in the x$x$ direction.     

On complete spacelike hypersurfaces with two distinct principal curvatures in Lorentz–Minkowski space

We investigate complete spacelike hypersurfaces in Lorentz–Minkowski space with two distinct principal curvatures and constant m$m$th mean curvature. By using Otsuki’s idea, we obtain the global classification result. As their applications, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in Lorentz–Minkowski (n+1)$(n+1)$-spaces (n≥3$n\ge 3$) of nonzero constant m$m$th mean curvature (m≤n−1$m\le n-1$) with two distinct principal curvatures λ$\lambda$ and μ$\mu$ satisfying inf(λ−μ)²>0$inf{(\lambda -\mu )}^2>0$ are the hyperbolic cylinders. We also obtain a global characterization for hyperbolic cylinder Hⁿ⁻¹(c)×R${\mathbb{H}}^{n-1}\left(c\right)\times \mathbb{R}$ in terms of square length of the second fundamental form.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.