Inverse spectral theory for Jacobi matrices and their almost periodicity

In this paper we consider the inverse problem for bounded Jacobi matrices with nonempty absolutely continuous spectrum and as an application show the almost periodicity of some random Jacobi matrices. We do the inversion in two different ways. In the general case we use a direct method of reconstructing the Green functions. In the special case where we show the almost periodicity, we use an alternative method using the trace formula for points in the orbit of the matrices under translations. This method of reconstruction involves analyzing the Abel-Jacobi map and solving of the Jacobi inversion problem associated with an infinite genus Riemann surface constructed from the spectrum.     

Azo-hydrazo Tautomerism and Inclusion Complexation of 1-phenylazo-2-naphthols with Various Solvents and β-cyclodextrin

Spectral characteristics of sudan I (SDI), sudan II (SDII) and mordant violet-5 (MV5) have been studied in various solvents and β-cyclodextrin (β-CD). The inclusion complex of the above molecules with β-CD was analyzed by UV-visible, fluorometry, and DFT methods. The solvent study shows that azo-hydrazo tautomer is present in these molecules. The increase in the fluorescence intensity and a large bathochromic shift in the S₁ state indicate these molecules forms 1:1 inclusion complex with β-CD.     

Supramolecular stabilization of hydroxylamine TEMPOH by complexation with an amphiphilic calixarene

In an ethanol/water mixture, the nitroxyl radical TEMPO abstracts a hydrogen atom from a phenolic OH group of the amphiphilic para-hexanoylcalix[4]arene, and the hydroxylamine TEMPOH formed yields a stable inclusion complex with another molecule of the calixarene.     

X-ray attenuation around <Emphasis Type="Italic">K</Emphasis>-edge of Zr,Nb, Mo and Pd: A comparative study using proton-induced X-ray emission and <Superscript>241</Superscript>Am gamma rays

Mass attenuation coefficients (μ/ρ) for Zr, Nb, Mo and Pd elements around their K-edges are measured at 14 energies in the range 15.744–28.564 keV using secondary excitation from thin Zr, Nb, Mo, Rh, Pd, Cd and Sn foils. The measurements were carried out at the K _α and K _β energy values of the target elements by two techniques: (1) Proton-induced X-ray emission (PIXE) and (2) ²⁴¹Am (300 mCi) source. In PIXE, 2 MeV proton-excited X-rays were detected by a Si(Li) detector. In the second case, X-rays excited by 59.54 keV photons from the targets were counted by an HPGe detector under a narrow beam good geometry set-up with sufficient shielding. The results are consistent with theoretical values derived from the XCOM package and indicate that the PIXE data have better statistical accuracy.     

An alternative technique for solving a coupled PDE system in interphase heat transfer

Recently an accelerated iterative procedure was studied for solving a coupled partial differential equation system in interphase heat transfer to improve some existing iterative procedures in the literature. In that procedure, at each step of the iteration one has to evaluate the derivative of a well-known function at a new point. In this paper, an alternative approach is proposed in which one has to evaluate the derivative only once throughout the procedure. The proposed new iterative scheme also has the same order of convergence and takes lesser number of iterations for certain benchmark problems. An interesting theoretical study on the monotone convergence as well as error estimate of the proposed iterative procedure are provided for continuous as well as discretized problems. The proposed iterative procedure also supplements the existence and uniqueness of the solution in both the cases. A comparative numerical study is also done to demonstrate the efficacy of the proposed scheme.     

Various passport options and their valuation

The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the writer is liable for the loss. Multi-asset passport options and passport options with discrete constraints are studied. For the first ones the pricing equations are Hamilton-Jacobi-Bellman equations. For those with discrete constraints, a linear complementary problem must be solved in order to price the option. The gain by selling passport options to utility maximizing investors and to investors who guess the market a certain percentage of the time is also examined.     

On Singular Artin Monoids and Contributions to Birman's Conjecture

ABSTRACT

Baez and Birman introduced the singular braid monoid on n + 1 strings, 𝒮B _n+1, which Birman uses in understanding knot invariants. 𝒮? _n+1 is the type A _n case of an infinite class of monoids known as singular Artin monoids and denoted by 𝒮G _M for a Coxeter matrix M. Birman conjectured, and Paris proved, that 𝒮B _n+1 embeds in the complex algebra of the braid group under the desingularisation map or Vassiliev homomorphism, η. In effect, Birman's conjecture generalizes to arbitrary types since, as noted by Corran, the Vassiliev homomorphism from 𝒮G _M to the algebra of the corresponding Artin group is well defined. We deduce general combinatorial results regarding divisibility in positive singular Artin monoids, and when M is of finite type, a well-defined positive form for 𝒮G _M is produced. These facts are then invoked to infer that, when M is of finite type, η is injective on pairs of words such that a common multiple exists for their positive form.     

The Natural Embedding of Positive Singular Artin Monoids

We explore some combinatorial properties of singular Artin monoids and invoke them to prove that a positive singular Artin monoid of arbitrary Coxeter type necessarily injects into the corresponding singular Artin monoid. This is an extension of L. Pari' result that positive Artin monoids embed in the correpsonding Artin groups: Adjoining inverses of the generators does not produce any new identities between words that do not involve those inverses.     

Elastic stability of all edges simply supported,stepped and stiffened rectangular plate under Biaxial loading

In this paper using finite difference method the lower bound buckling load for simply supported (a) stepped and stiffened rectangular thin plate (b) linear and non-linear variation of thickness (c) uniformly distributed compressive forces in both directions (d) uniformly distributed compressive force in y direction and non-uniform distribution of compressive force in x-direction is discussed. The thin plate is divided into 900 rectangular meshes. The partial derivatives are approximated using central difference formula. Eight hundred and forty one equations are formed and using the program developed and the least eigenvalue is obtained. The buckling coefficients are calculated for different types of stepped and non prismatic plates and the results are presented in tables and graphs for ready use by designers. Buckling factors for some cases are presented in the form of three separate tables and compared with the values obtained by Xiang, Wei and Wang. The results are in close agreement.