Heavier Tetrylenes as Single Site Catalysts

An overview of the development of compounds with heavier low-valent group 14 elements (known as tetrylenes) as single component catalyst for organic transformation has been provided. Compounds with heavier group 14 elements possess stereochemically active lone pairs and energetically accessible π-antibonding orbitals, thereby resembling the electronic configuration of transition-metal compounds. Such compounds with low-valent group 14 elements has been known for small molecule activation since Power's report of dihydrogen activation by a digermyne, but their utilization in catalysis remained as a “Holy Grail” in main group chemistry. In recent years, numerous methodologies have been discovered epitomizing the use of Si(II), Ge(II) and Sn(II) compounds as single site catalysts for hydroboration of aldehydes, ketones, pyridines, cyanosilylation of aldehydes and ketones, N-formylations aromatic amines, dehydrocoupling reactions. This mini-review highlights these significant developments with an emphasis on the mechanistic investigation.     

On the numerical solution of tracked vehicle dynamic equations

In this investigation, the solution of the nonlinear dynamic equations of the multibody tracked vehicle systems are obtained using different procedures. In the first technique, which is based on the augmented formulation that employes the absolute Cartesian coordinates and Lagrange multipliers, the generalized coordinate partitioning of the constraint Jacobian matrix is used to determine the independent coordinates and the associated independent differential equations. An iterative Newton-Raphson algorithm is used to solve the nonlinear constraint equations for the dependent variables. The numerical problems encountered when one set of independent coordinates is used during the simulation of large scale tracked vehicle systems are demonstrated and their relationship to the track dynamics is discussed. The second approach employed in this investigation is the velocity transformation technique. One of the versions of this technique is discussed in this paper and the numerical problems that arise from the use of inconsistent system of kinematic equations are reported. In the velocity transformation technique, the tracked vehicle system is assumed to consist of two kinematically decoupled subsystems; the first subsystem consists of the chassis, the rollers, the sprocket and the idler, while the second subsystem consists of the track which is represented as a closed kinematic chain that consists of rigid links connected by revolute joints. It is demonstrated that the use of one set of recursive equations leads to numerical difficulties because of the change in the track configuration. Singular configurations can be avoided by repeated changes in the recursive equations. The sensitivity of the predictor-corrector multistep numerical integration schemes to the method of formulating the state equations is demonstrated. The numerical results presented in this investigation are obtained using a planner tracked vehicle model that consists of fifty four rigid bodies.     

Solanopubamine,a rare steroidal alkaloid from Solanum schimperianum: Synthesis of some new alkyl and acyl derivatives,their anticancer and antimicrobial evaluation

Solanopubamine (3β-amino-5α, 22αH, 25βH-solanidan-23β-ol), a steroidal alkaloid was isolated from the alkaloidal fraction of Solanum schimperianum in significant yield. Its structure was established by IR, positive ESI-MS, 1D and 2D NMR. The presence of -3β-NH₂ and -23β-OH groups was achieved through methylation, acetylation or coupling with octadecanoic and undec-11-enoic acids to produce six derivatives (2–7). Their structures were confirmed by spectroscopic analyses. Solanopubamine and semi-synthetic analogs are investigated for their in vitro cytotoxicity against a panel of human cancer cell lines and anti-microbial activity. Solanopubamine showed good antifungal activity only against Candida albicans and C. tenuis with MIC of 12.5 μg/mL. Semi-synthesized compounds (2–7) have failed to show anti-tumor and anti-microbial activities.     

On crystallization and phase separation phenomena in PEN/PHBA copolyesters

Two different etching techniques that reveal the semicrystalline morphology of polyesters have been developed and applied to an analysis of the phase structure of copolyesters made by reacting poly(hydroxybenzoic acid) (PHBA), and poly(ethylene naphtha-lene-dicarboxylate) (PEN). One technique is based on oxidation with acidic permanganate solutions and is used to study the macroscopic distribution of different phases. The other is based on sa-ponification with alkaline reagents and reveals more detailed structure within the various phases. Etching and electron microscopic examinations have been carried out for three different PEN-co-PHBA compositions. Three different types of solid phase are revealed: (1) a phase rich in PEN; (2) a phase containing roughly equal proportions of the two components, liquid crystalline at high temperatures; (3) a solid phase of crystalline HBA-rich molecules, which segregate into laminar regions. These observations are consistent with the previously published thermal, x-ray, and dynamic mechanical analyses of these materials.     

STUDIES ON ORGANOPHOSPHORUS COMPOUNDS. PART VI.† THE REACTION OF ALKOXIDES WITH 2,4-BIS(4-METHOXYPHENYL)-1,3,2,4-DITHIADIPHOSPHETANE 2,4-DISULFIDE (LR). A NEW APPROACH FOR THIO-INEZIN

Abstract

Sodium alkoxide, a hard nucleophile, reacts with 2,4-bis(4-methoxyphenyl)-1,3,2,4-dithiadiphosphetane 2,4-disulfide (LR) on phosphorus to give O-alkyl S-sodium-(4-methoxyphenyl) phosphonothiolothionate 5 as an intermediate. Compound 5 reacts with benzyl (or benzoyl) chloride to give good yields of O-alkyl S-benzyl (benzoyl) (4-methoxy-phenyl)phosphonothiolothionate (6a–e).     

Sparse matrix implicit numerical integration of the Stiff differential/algebraic equations: Implementation

The finite element absolute nodal coordinate formulation (ANCF) is often used in modeling very flexible bodies in multibody system (MBS) applications. This formulation leads to a constant mass matrix, allowing for an efficient sparse matrix implementation. Nonetheless, the use of the ANCF finite elements to model stiff structures can lead to high frequencies associated with ANCF coupled deformation modes, as discussed in the literature. Implicit numerical integration methods can be effectively used to develop efficient procedures for the solution of MBS differential/algebraic equations. Most existing implicit integration algorithms, however, require numerical differentiation of the equations of motion, and some of these integration methods do not ensure that the kinematic algebraic constraint equations are satisfied at all levels (position, velocity, and acceleration). Because of these limitations, existing implicit integration methods can be less accurate and less efficient when used to solve large scale MBS applications. In order to circumvent this problem, the two-loop implicit sparse matrix numerical integration (TLISMNI) method was proposed for the solution of MBS differential/algebraic equations. The TLISMNI method does not require numerical differentiation of the forces and allows for an efficient sparse matrix implementation. This paper discusses TLISMNI implementation issues including the step size selection, the error control, and the effect of the numerical damping. The relation between the step size selection and the structure stiffness is also discussed. The use of the computer implementation described in this paper is demonstrated by solving very stiff structure problems using the Hilber?CHughes?CTaylor (HHT) method, which includes numerical damping. An eigenvalue analysis and Fast Fourier Transform (FFT) are performed in order to identify the fundamental modes of deformation and demonstrate that the contributions of these fundamental modes can be erroneously damped out when some other implicit integration methods are used. The TLISMNI method, on the other hand, captures the contributions of these fundamental modes. The results, obtained using the TLISMNI method, are compared with the results obtained using other methods including the implicit HHT-I3 and the explicit Adams integration methods. The results obtained show that the TLISMNI method can be five times faster than the other two methods when no numerical damping is considered.     

Study of nonlinear system stability using eigenvalue analysis: Gyroscopic motion

General computational multibody system (MBS) algorithms allow for the linearization of the highly nonlinear equations of motion at different points in time in order to obtain the eigenvalue solution. This eigenvalue solution of the linearized equations is often used to shed light on the system stability at different configurations that correspond to different time points. Different MBS algorithms, however, employ different sets of orientation coordinates, such as Euler angles and Euler parameters, which lead to different forms of the dynamic equations of motion. As a consequence, the forms of the linearized equations and the eigenvalue solution obtained strongly depend on the set of orientation coordinates used. This paper addresses this fundamental issue by examining the effect of the use of different orientation parameters on the linearized equations of a gyroscope. The nonlinear equations of motion of the gyroscope are formulated using two different sets of orientation parameters: Euler angles and Euler parameters. In order to obtain a set of linearized equations that can be used to define the eigenvalue solution, the algebraic equations that describe the MBS constraints are systematically eliminated leading to a nonlinear form of the equations of motion expressed in terms of the system degrees of freedom. Because in MBS applications the generalized forces can be highly nonlinear and can depend on the velocities, a state space formulation is used to solve the eigenvalue problem. It is shown in this paper that the independent state equations formulated using Euler angles and Euler parameters lead to different eigenvalue solutions. This solution is also different from the solution obtained using a form of the Newton-Euler matrix equation expressed in terms of the angular accelerations and angular velocities. A time-domain solution of the linearized equations is also presented in order to compare between the solutions obtained using two different sets of orientation parameters and also to shed light on the important issue of using the eigenvalue analysis in the study of MBS stability. The validity of using the eigenvalue analysis based on the linearization of the nonlinear equations of motion in the study of the stability of railroad vehicle systems, which have known critical speeds, is examined. It is shown that such an eigenvalue analysis can lead to wrong conclusions regarding the stability of nonlinear systems.     

Higher order representation of the beam cross section deformation in large displacement finite element analysis

Most existing beam formulations assume that the cross section of the beam remains rigid regardless of the amplitude of the displacement. The absolute nodal coordinate formulation (ANCF); however, allows for the deformation of the cross section and leads to a more general beam models that capture the coupling between different modes of displacement. This paper examines the effect of the order of interpolation on the modes of deformation of the beam cross section using ANCF finite elements. To this end, a new two-dimensional shear deformable ANCF beam element is developed. The new finite element employs a higher order of interpolation, and allows for new cross section deformation modes that cannot be captured using previously developed shear deformable ANCF beam elements. The element developed in this study relaxes the assumption of planar cross section; thereby allowing for including the effect of warping as well as for different stretch values at different points on the element cross section. The displacement field of the new element is assumed to be cubic in the axial direction and quadratic in the transverse direction. Using this displacement field, more expressions for the element extension, shear and the cross section stretch can be systematically defined. The change in the cross section area is measured using Nanson’s formula. Measures of the shear angle, extension, and cross section stretch can also be systematically defined using coordinate systems defined at the element material points. Using these local coordinate systems, expressions for a nominal shear angle are obtained. The differences between the cross section deformation modes obtained using the new higher order element and those obtained using the previously developed lower order elements are highlighted. Numerical examples are presented in order to compare the results obtained using the new finite element and the results obtained using previously developed ANCF finite elements.