Some studies on TiO2 films deposited by sol-gel technique

TiO2 films are extensively used in various applications including optical multi-layers, sensors, photo catalysis, environmental purification, and solar cells etc. These are prepared by both vacuum and non-vacuum methods. In this paper, we present the results on TiO2 thin films prepared by a sol-gel spin coating process in non-aqueous solvent. Titanium isopropoxide is used as TiO2 precursor. The films were annealed at different temperatures up to 3000 C for 5 hours in air. The influence of the various deposition parameters like spinning speed, spinning time and annealing temperature on the thickness of the TiO2 films has been studied. The variation of film thickness with time in ambient atmosphere was also studied. The optical, structural and morphological characteristics were investigated by optical transmittance-reflectance measurements, X-ray diffraction (XRD) and scanning electron microscopy (SEM) respectively. The refractive index and extinction coefficient of the films were determined by envelope technique and spectroscopic ellipsometry. TiO2 films exhibited high transparency (92%) in the visible region with a refractive index of 2.04 at 650 nm. The extinction coefficient was found to be negligibly small. The X-ray diffraction analysis showed that the TiO2 film deposited on glass substrate changes from amorphous to crystalline (anatase) phase with annealing temperature above 2500 C. SEM results show that the deposited films are uniform and crack free.

Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

Structural and optical investigations of TiO2 films deposited on transparent substrates by sol-gel technique

An inexpensive and effective simple method for the preparation of nano-crystalline titanium oxide (anatase) thin films at room temperature on different transparent substrates is presented. This method is based on the use of peroxo-titanium complex, i.e. titanium isopropoxide as a single initiating organic precursor. Post-annealing treatment is necessary to convert the deposited amorphous film into titanium oxide (TiO2) crystalline (anatase) phase. These films have been characterized for X-ray diffraction (XRD) studies, atomic force microscopic (AFM) studies and optical measurements. The optical constants such as refractive index and extinction coefficient have been estimated by using envelope technique. Also, the energy gap values have been estimated using Tauc's formula for on glass and quartz substrates are found to be 3.35 eV and 3.39 eV, respectively. (C) 2008 Elsevier B.V. All rights reserved.

Separability in relativistic Hamiltonian particle dynamics

The problem of separability in recent models of classical relativistic interacting particles is examined. This physical requirement is shown to be more subtle than naive separability of all the constraints defining the system: it is adequate to be able to canonically transform the time-fixing constraints from an unseparated to a separated form when clusters emerge. Viewing separability in this way, and within a specific framework, we are led to a new no-interaction theorem which states the incompatibility of nontrivial interaction with relativistic invariance, separability, and invariant world lines for more than two particles.

Do H-functions always increase during Violent Relaxation

Recent work on the violent relaxation of collisionless stellar systems has been based on the notion of a wide class of entropy functions. A theorem concerning entropy increase has been proved. We draw attention to some underlying assumptions that have been ignored in the applications of this theorem to stellar dynamical problems. Once these are taken into account, the use of this theorem is at best heuristic. We present a simple counter-example.

Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.

Asymptotic behaviour of point processes with Markov-dependent intervals

This splitting techniques for MARKOV chains developed by NUMMELIN (1978a) and ATHREYA and NEY (1978b) are used to derive an imbedded renewal process in WOLD's point process with MARKOV-correlated intervals. This leads to a simple proof of renewal theorems for such processes. In particular, a key renewal theorem is proved, from which analogues to both BLACKWELL's and BREIMAN's forms of the renewal theorem can be deduced.

Structure of 5-Bromo-2',3'-O-isopropylideneuridine, C12H15BrN206

Mr= 363.17, orthorhombic, P21212 ~, a= 5.251(4), b=14.962(5), c=19.112(5)A, U= 1501.41/k 3, Z=4, Dx=1.61Mgm -3, /t(CuKa)= 3.02 mm -1, 2(Cu Ka)= 1.5418/~, final R = 7.0% for 1091 reflections with Fo> 2e(Fo). The glycosidic torsion angle ZCN is 13"1 (12) °. The ribose has a C (3')-exo,C (4)-endo twist geometry. The dioxolane ring assumes an envelope conformation with 0(3') displaced by 0.453 (10)/k from the plane of the other four atoms. The conformation about the C(4')-C(5') bond is gauche-gauche. The structure is stabilized by two hydrogen bonds between screw-axis-related molecules. The crystal packing and the conformation of the molecule are very similar to those found in the structure of 2',3'-O-isopropylideneuridine which lacks the Br atom at the 5-position.

Structure of 2',3'-O-Isopropylidene-5'-O-tosyluridine, C19H22N 2Oas

M r = 438.45, trigonal, P32, a = b = 13.385 (4), c = 9.900 (5) A,, V = 1536.0 A 3, Z = 3, D x = 1.42, D m = 1.42 Mg m -3, 2(Cu Ka) = 1.5418 A,,g(CuKa) = .800mm -], T=290K, F(000)=690, R=6.0% for 1222 unique reflections with F o>_2o(Fo). This is the first 2',3'-O-isopropylidene pyrimidine nucleoside with the base in a syn orientation with respect to the ribose [Xcy= 116.0(7)°]. The ribose has a C(3')-endo conformation with the phase angle of pseudorotation P = 16.36 (2) °. The dioxolane ring assumes an envelope conformation with 0(2') displaced from the best four-atom plane by 0.50 (1) k. The crystal structure is possibly stabilized by a bifurcated hydrogen bond between N(3) and the 0(2) and 0(4) atoms of screw-related molecules.

Forms of relativistic dynamics with World Line Condition and separability

he Dirac generator formalism for relativistic Hamiltonian dynamics is reviewed along with its extension to constraint formalism. In these theories evolution is with respect to a dynamically defined parameter, and thus time evolution involves an eleventh generator. These formulations evade the No-Interaction Theorem. But the incorporation of separability reopens the question, and together with the World Line Condition leads to a second no-interaction theorem for systems of three or more particles. Proofs are omitted, but the results of recent research in this area is highlighted.

On the invariants of coloured Petri Nets

In this paper, we develop a theorem that enables computation of the place invariants of the union of a finite collection of coloured Petri Nets when the individual nets satisfy certain conditions and their invariants are known. We consider the illustrative examples of the Readers-Writers problem, a resource sharing system, and a network of databases and show how this theorem is a valuable tool in the analysis of concurrent systems.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

We analyze aspects of symmetry breaking for Moyal spacetimes within a quantization scheme which preserves the twisted Poincare´ symmetry. Towards this purpose, we develop the Lehmann-Symanzik- Zimmermann (LSZ) approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone’s theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.

4-(4-Methoxyphenyl)-1-phenylpyridine-2,6(1H,3H)-dione

In the title compound, C18H15NO3, the pyridine-2,6-dione ring adopts an envelope conformation. The phenyl ring lies approximately perpendicular to the mean plane of the pyridine-2,6-dione ring [dihedral angle =81.5 (1)degrees], while the methoxyphenyl ring is tilted to the same plane by a dihedral angle of 34.8 (1)degrees. Intermolecular C-H center dot center dot center dot O interactions link the molecules into chains along [100].

Application of Maclaurin Series in Structural Analysis

In the simple theory of flexure of beams, the slope, bending moment, shearing force, load and other quantities are functions of a derivative of y with respect to x. It is shown that the elastic curve of a transversely loaded beam can be represented by the Maclaurin series. Substitution of the values of the derivatives gives a direct solution of beam problems. In this paper the method is applied to derive the Theorem or three moments and slope deflection equations. The method is extended to the solution of a rigid portal frame. Finally the method is applied to deduce results on which the moment distribution method of analyzing rigid frames is based.

WISENOM. A formal organic chemical nomenclature system

A formal chemical nomenclature system WISENOM based on a context-free grammar and graph coding is described. The system is unique, unambiguous, easily pronounceable, encodable, and decodable for organic compounds. Being a formal system, every name is provable as a theorem or derivable as a terminal sentence by using the basic axioms and rewrite rules. The syntax in Backus-Naur form, examples of name derivations, and the corresponding derivation trees are provided. Encoding procedures to convert connectivity tables to WISENOM, parsing, and decoding are described.