A novel derivative free algorithm with seventh order convergence for solving systems of nonlinear equations

We present a seventh order iterative method for solving systems of nonlinear equations. The algorithm is derivative free per full iteration. A comparison between the computational efficiencies of proposed technique and existing techniques of similar nature is made. It is shown that for large system the new method is more efficient. The performance is tested through numerical experimentation which also confirms the theoretical results.     

Taylor‐Galerkin B‐spline finite element method for the one‐dimensional advection‐diffusion equation

The advection‐diffusion equation has a long history as a benchmark for numerical methods. Taylor‐Galerkin methods are used together with the type of splines known as B‐splines to construct the approximation functions over the finite elements for the solution of time‐dependent advection‐diffusion problems. If advection dominates over diffusion, the numerical solution is difficult especially if boundary layers are to be resolved. Known test problems have been studied to demonstrate the accuracy of the method. Numerical results show the behavior of the method with emphasis on treatment of boundary conditions. Taylor‐Galerkin methods have been constructed by using both linear and quadratic B‐spline shape functions. Results shown by the method are found to be in good agreement with the exact solution. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Thiocarboxylato Complexes of Biscyclopentadienyl and Bisindenyl Titanium (IV)

Reactions of biscyclopentadienyl (and bisindenyl) titanium (IV) dichlorides with sodium salts of various thiocarboxylic acids in tetrahydrofuran medium, yield the complexes of the general formula (D) ²Ti(SCOR) ² where D is cyclopentadienyl or indenyl group and R? H, CH₃, C₂H₅, C⁴H⁵ or p-C⁴H⁴CH³ group. The foul smelling complexes are monomeric in nature. The IR spectra, thermal stabilities and Some physical characteristics of these complexes have been studied.     

Generalized slant Toeplitz operators on H2

For an integer k ≥ 2, k^th‐order slant Toeplitz operator U_φ [1] with symbol φ in L^∞(??), where ?? is the unit circle in the complex plane, is an operator whose representing matrixM = (α_ij ) is given by α_ij = 〈φ, z^ki–j〉, where 〈. , .〉 is the usual inner product in L²(??). The operator V_φ denotes the compression of U_φ to H²(??) (Hardy space). Algebraic and spectral properties of the operator V_φ are discussed. It is proved that spectral radius of V_φ equals the spectral radius of U_φ, if φ is analytic or co‐analytic, and if T_φ is invertible then the spectrum of V_φ contains a closed disc and the interior of the disc consists of eigenvalues of infinite multiplicities. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Minimal quadratic residue cyclic codes of length 2 n

LetF be a finite field of prime power orderq(odd) and the multiplicative order ofq modulo 2 ⁿ (n>1) be ?(2 ⁿ )/2. Ifn>3, thenq is odd number(prime or prime power) of the form 8m±3. Ifq=8m?3, then the ring $$R_{2^n } = F\left[ x \right]/< x^{2^n } - 1 > $$ has 2n primitive idempotents. The explicit expressions for these primitive idempotents are obtained and the minimal QR cyclic codes of length 2 ⁿ generated by these idempotents are completely described. Ifq=8m+3 then the expressions for the 2n?1 primitive idempotents ofR ₂ ⁿ are obtained. The generating polynomials and the upper bounds of the minimum distance of minimal QR cyclic codes generated by these 2n?1 idempotents are also obtained. The casen=2, 3 is dealt separately.     

Experimental investigation of mean flow characteristics of slot jet impingement on a cylinder

An experimental investigation is made to study the flow characteristics of slot jet impingement on a cylinder. The velocity profiles and pressure distribution around the cylinder are reported for various parameters namely, the flow rate, width of the nozzle, distance of the cylinder from the jet exit and eccentricity of the cylinder to the jet axis.

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Experimentelle Untersuchung über die Strömungseigenschaften eines Düsenstrahls, der auf einen Zylinder aufprallt

Zusammenfassung Es wurde eine experimentelle Untersuchung gemacht, um die Strömungseigenschaften eines Düsenstrahls zu unterschen, der auf einen Zylinder prallt. Die Geschwindigkeitsprofile und die Druckverteilungen an dem Zylinder wurden für unterschiedliche Parameter dokumentiert. Die Parameter sind die Strömungsgeschwindigkeit, Düsengröße, Abstand zwischen Zylinder und Strahlaustritt und die Exzentrizität von Zylinder und Strahlachse.

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Nomenclature B breadth of the nozzle at the exit - D diameter of the cylinder - C _p pressure coefficient - g acceleration due to gravity - L distance of the cylinder from jet exit - P _a atmospheric pressure - P _c static pressure along the jet center-line - P ₀ stagnation pressure - P _W wall static pressure - Re _D Reynolds numberu _j D/ _a - Re _W Reynolds numberu _j W/ _a - r distance measured from cylinder surface in radial direction - r _m position of maximum velocity from cylinder surface - r _0.5 half width of the jet - u mean velocity - u _j mean velocity at the jet exit - u _m maximum velocity - W width of the nozzle - _a density of air - _m density of mercury - _w density of water - absolute viscosity - kinematic viscosity     

Modelling of displacement washing of pulp fibers using orthogonal collocation on finite elements

Flow of fluid through packed bed of porous particles is modelled with the help of Peclet number (Pe) and Biot number (Bi). Packed bed is divided into three zones, flowing liquor, intrapore solute present in pores of particles and solute adsorbed on particle surface. Langmuir isotherm is used to describe the relationship between intrapore solute concentration and concentration of solute adsorbed on particle surface, whereas the bulk fluid concentration and the intrapore solute concentration are related by linear adsorption isotherm. Model predicted values are also compared with the experimental values. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nano-graphitic clustering and break down of phonon selection rule in diamond-like carbon films

Diamond-like carbon films are deposited on silicon substrates at different substrate bias using ECR-CVD technique. Raman spectroscopic studies show the presence of broad G and D peaks. In contrast to the position of D peak, the G peak shows a systematic red-shift with increase in the bias voltage. From the analysis it is found that an increase in bias voltage decreases the sp² cluster diameter. Furthermore, two additional Raman peaks at around 690 and 880 cm^?1 are also observed. These peaks, forbidden in the first order Raman scattering, arise due to the breakdown of phonon selection rule in graphitic nanoclusters.