Element-Free Methods

Element-free methods Meshfree methods Particle methods... 

Abstract Bis(3-methylbutantio) maleonitril has been obtained from the reaction of disodium salt, l-bromo-3 methylbiitan in acetone under nitrogen for 11 hours. MgPz has been synthesized through the cyclotetramerization reaction of magnesium and n-butanol with bis(3-methylbutantio) maleonitril. The metal free pophyrazine derivative was obtained by its treatment with trifluroacetic acid and further reaction of this product with cobalt(II) acetate, nickel(II) acetate and zinc(II) acetate led to the metal porphyrazine (MPz, M = Co, Ni ve Zn). These new compounds have been investigated and characterized by UV, FT-IR, H NMR, GC-MS and elemental analysis methods. 

Abstract Magnesium porphyrazines substituted with eight (phenyl-propene) groups on the peripheral positions have been prepared by cyclotetramerization of l,2-bis(3-phenyl-2-propenethio) maleonitrile and then achieved porphyrazine by 3-bromo-l-phenyl-l-propene. Metal-free derivative was obtained by its treatment with trifluoroacetic acid. The new compounds have been characterized by FT-IR, H-NMR, UV-VIS and elemental analysis methods. 

For numerical investigations of stress localizations in laminates, the discretizational effort can be reduced significantly if only the boundary needs to be discretized, as it is for e -ample the case in the classical boundary element method (BEM). But in this method a fundamental solution is needed which is in many cases difficult to achieve or even unknown. The Boundary Finite Element Method (BFEM) to be presented here does not require such a fundamental solution, because the element formulation is based on the finite element method (FEM), Thus the BFEM can be characterized to be a finite element based boundary discretization method. This method was originally developed from Wolf and Song [10] under the name Consistent Finite Element Cell Method for time-dependent problems in soil-mechanics. The basic assumption of this method is that a stiffness matrix describing the force-displacement relation at discrete degrees of freedom at the boundary of the continuum is scalable with respect to one point in three-dimensional space, the so-called similarity center, if similar contours within the continuum are considered. In contrast to this, the current work deals with the case of equivalent cross-sectional properties, i.e., that cross-sections parallel to the boundary can be described by the same stiffness matrix, which is the appropriate formulation for the case of the free-edge effect and the matrix crack problem. The boundary stiffness matrix results from a Matrix-Riccati equation. The field quantities inside of the continuum can be calculated from an ordinary differential equation. 

The commutator expressions, Eqs (120) and (121), are sufficient to derive expressions for the matrix elements required for the MCSCF optimization process. This results from the fact that both the orbital transformation and the Hamiltonian operator are written in terms of the generators and generator products of Eq. (117). Since all of these operators involve explicit references only to the spatial orbitals, and not to the spin orbitals, it would be possible to eliminate reference to the spin-orbitals entirely if the expansion kets could be represented in such a spin-free method and if matrix elements of these spin-free operators could be calculated without reference to the spin orbitals. 

The white disulfide, only slightly soluble in toluene or mesitylene, is a useful reagent for the sulfurization of phosphines. The range of applicability for the sulfur transfer reagent has not yet been tested. In comparison with the known R2BS2BR2 boranes, the (9-BBN)2S2 compound is more readily available and can be synthesized in a pure form, free of monosulfide and thiol. The disulfide can be prepared in two different ways from (9-H-9-BBN)2 or 9-1-9-BBN, respectively, with elemental sulfur (methods A and B). 

An alternative approach to the intrinsic DNA electrochemical activity utilizes electroactive species as redox indicators of the presence of immobilized DNA as well as its interaction events such as hybridization, damage, and association with another substance [14]. This mode was also used in a pioneering work on the DNA biosensor used for sequence detection [7]. In this case, it is still a label-free method in the sense that DNA probes or targets are not chemically modified by a special label however, as the indicator has to be added to a test S5 em as an additional reagent, we cannot speak more about the reagent-less technique. Redox indicators typically possess electrochemical responses at a "safe" electrode potential and often reversibly. The terms redox probe and redox marker are sometimes used in the literature to mean the redox indicator, which is confusable with the DNA capture probe used as a recognition element at hybridization and with markers used in medical diagnostics [8]. 

Galerkin methods, which are used in element-free Galerkin method, reproducing kernel particle method, etc. 

Liu GR (2003) Mesh free methods moving beyond the finite element method. CRC Press, Boca Raton... 

QSARs include statistical methods to relate biological activities (most often expressed by logarithms of equipotent molar activities) with structural elements (Free Wilson analysis), physicochemical properties (Hansch analysis), or fields (3D QSAR). The parameters used in a QSAR model are also called (molecular) descriptors. Classical QSAR analyses (Hansch and Free Wilson analyses) consider only 2D structures. Their main field of application is in substituent variation of a common scaffold. 3D-QSAR analysis (CoMFA) has a much broader scope. It starts from 3D structures and correlates biological activities with 3D-property fields (McKinney et al. 2000). 

Tanaka et al [43] have studied the effect of nanotubes thickness on the equivalent thermal conductivity of composites which has been evaluated by element free Galerkin method using different length of nanotube. The result of this study is shown in figures 9 10 ... 

Petera, J. and Nassehi, V., 1996. Finite element modelling of free surface viscoelastic flows with particular application to rubber mixing. Int. J. Numer. Methods Fluids 23, 1117-1132. 

---