Rh(II)-Catalyzed Isomerizations of Cyclopropenes Evidence for Rh(II)-Complexed Vinylcarbene Intermediates

The thermocatalytic rearrangements of cyclopropenes 1-4 have been investigated in the presence of Rh(IT) perfiuorobutyrate. 1, 2, 3-Triphenylcyclopropene ( 1a ) undergoes rearrangement lo diphenylindene 5a or, with alkoxycyclopropene derivatives, to α, β-unsaturated ketone 6. Furan formation occurs with 2, 3-diphenylcyclo-propenecarboxylate 2, but the diethyl counterpart 3 rearranges to dienoate 8. 2-Alkylcyclopropenecarboxylates 4 afforded (E)-methylidenecyclopentane derivatives 9 as the only isolable product in yields of ca. 35 %. A mechanism involving regio- and stereospecific cyclopropene ring opening to a Rh-complexed vinylcarbene and insertion of the latter into the C? H bond to give 9 is proposed. An analogous mechanism should account for the rearrangement products of 1 to 3 .     

Modification of the GV-MSA model in obtaining the activity and osmotic coefficients of aqueous electrolyte solutions

In this work a modified form of the Ghotbi–Vera Mean Spherical Approximation model (MGV-MSA) has been used to correlate the mean ionic activity coefficients (MIAC) for a number of symmetric and asymmetric aqueous electrolyte solutions at 25 °C. In the proposed model the hard sphere as well as the electrostatic contributions to the MIAC and the osmotic coefficient of the previously GV-MSA model has been modified. The results of the proposed model for the MIAC of the electrolyte solutions studied in this work are used to directly calculate the values of the osmotic coefficients without introducing any new adjustable parameter. In the MGV-MSA model the cation diameter as well as the relative permittivity of water depends on the electrolyte concentration. Having considered such dependency for both cation and relative permittivity for water in an electrolyte solution the modification of the GV-MSA has been made. It should be stated that in the MGV-MSA model the anion diameter in the solution similar to that in the GV-MSA model remains constant and independent of the electrolyte concentration. The results obtained from the proposed model have been favorably compared with those of the GV-MSA model. The results showed that the MGV-MSA model can more accurately correlate the MIAC of the single electrolyte solutions than those of the GV-MSA model. The same comparison has been observed in case of the osmotic coefficients for the electrolyte solutions studied in this work. It should be noted that in order to do an unequivocal comparison between the results obtained from the models used in this work the same minimization procedure and the same experimental data for the MIAC and the osmotic coefficients have been used. Also it should be mentioned that in the MGV-MSA model the conversion from the McMillan–Mayer (MM) framework to that of the Lewis–Randall (LR) has been performed. It has been concluded that such transformation can affect the results in particular at higher electrolyte concentrations.     

Synthesis,Characterization and Crystal Structures of new Coordination Polymers of Cerium(III) and Samarium(III) Containing 2,6‐Pyridinedicarboxylic Acid

The reaction of 2,6‐pyridinedicarboxylic acid ( 1 , LH₂) with CeCl₃·7H₂O and Sm(NO₃)₃·6H₂O in the presence of triethylamine led to the coordination polymer complexes [M(L)(LH)(H₂O)₂]·4H₂O [M = Ce ( 2 ) and Sm ( 3 )]. Both complexes were characterized by elemental analyses, IR spectroscopy and the crystal structures of 2 and 3 . Crystal data for 2 at ?80 °C: monoclinic, space group P2₁/c, a = 1404.6(1), b = 1122.1(1), c = 1296.1(1) pm, β = 102.09(1)°, Z = 4, R₁ = 0.0217 and for 3 at ?80 °C: monoclinic, space group P2₁/c, a = 1395.1(1), b = 1120.1(1), c = 1282.8(1) pm, β = 102.71(1)°, Z = 4, R₁ = 0.019.     

Synthesis,Characterization, and Crystal Structure of Thallium(I) Complex containing Monodeprotonated 2,6‐Pyridinedicarboxylic Acid

The reaction of an ethanolic solution 2,6‐pyridinedicarboxylic acid ( 1 , LH₂) with TlNO₃ in the presence of triethylamine led to the coordination polymer [Tl(LH)]_n ( 2 ). The complex was characterized by elemental analysis, IR spectroscopy and single‐crystal X‐ray diffraction. Crystal data for 2 at –80 °C: monoclinic, space group I2/a, a = 696.1(1), b = 1190.6(2), c = 931.0(2) pm, β = 103.28(1)°, Z = 4, R₁ = 0.0256.     

Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory

Abstract

This article contains the nonlocal elasticity theory to capture size effects in functionally graded (FG) nano-rod under magnetic field supported by a torsional foundation. Torque effect of an axial magnetic field on an FG nano-rod has been defined using Maxwell’s relation. The material properties were assumed to vary according to the power law in radial direction. The Navier equation and boundary conditions of the size-dependent FG nano-rod were derived by the Hamilton’s principle. These equations were solved by employing the generalized differential quadrature method (GDQM). Presented model has the ability to turn into the classical model if the material length scale parameter is taken to be zero. The effects of some parameters, such as inhomogeneity constant, magnetic field and small-scale parameter, were studied. As an important result of this study can be stated that an FG nano-rod model based on the nonlocal elasticity theory behaves softer and has smaller natural frequency.     

Comment on “Delayed luminescence of biological systems in terms of coherent states” [Phys. Lett. A 293 (2002) 93]

Popp and Yan [F.A. Popp, Y. Yan, Phys. Lett. A 293 (2002) 93] proposed a model for delayed luminescence based on a single time-dependent coherent state. We show that the general solution of their model corresponds to a luminescence that is a linear function of time. Therefore, their model is not compatible with experimental delayed luminescence. Moreover, the functions that they use to describe the oscillatory behaviour of delayed luminescence are not solutions of the coupling equations to be solved.     

Hybrid Proximal Point Algorithm and Applications to Equilibrium Problems and Convex Programming

The problem of finding minima of weakly sequentially lower semicontinuous functions on reflexive Banach spaces is studied by means of convex and nonconvex subdifferentials. Finding a descent direction for a non-stationary point is a question of importance for many optimization algorithms. The existence or non-existence of such a direction is clarified through several theorems and a series of selective examples. For the general problem, a notion called radius of descent is proposed and shown to be useful for the analysis related to descent directions.     

A Heuristic Insight on End-Point Calculation and a New Phase Interference Parameter in Two-Phase Relative Permeability Curves for Horizontal Fracture Flow

Relative permeability curves of two-phase flow in a fracture have been a subject of study in recent years. The importance of these curves have been widely observed in multidisciplines, such as water subsurface resources, geothermal energy and underground hydrocarbon resources, especially fractured oil and gas reservoirs. Extensive experimental studies have been cited alongside the numerical studies in this area. However, simple analytical and practical solutions are still attractive. In the current study, wettability effects and phase interference explicitly were tried to be implemented in a simple analytical formula. The wettability effects are represented by residual saturations which resulted in direct calculation of relative permeability end points. In addition, the phase interference part affected the shape of the curves that allowed to quantify the degree of phase interference from no phase interference, assigned as zero, to ultimate phase interference, assigned as infinity. The results were compared and validated with the available experimental data in the literature. The proposed formulation is applicable for both smooth and rough fracture assemblies.     

Active transient elasto-acoustic response damping of a thick-walled liquid-coupled piezolaminated cylindrical vessel

The linear 3D piezoelasticity theory in conjunction with the versatile transfer matrix approach and the wave equation for the internal acoustic domain are employed for active non-stationary vibroacoustic response control of an arbitrarily thick, tri-laminate, fluid-filled, simply supported, piezocomposite cylindrical tank, excited by arbitrary (non-axisymmetric) time-dependent on-surface mechanical loads. The smart structure is composed of a supporting core layer of functionally graded orthotropic material perfectly bonded to inner and outer spatially distributed radially polarized functionally graded piezoceramic sensor and uniform force actuator (FGPM) layers. Active vibration damping is implemented by transferring the accumulated voltage on the sensor layer to the piezoelectric actuator layer in context of proportional and derivative control laws. Durbin's numerical inverse Laplace transform scheme is utilized to calculate the time response histories of the relevant interface displacement/stress components, center-point acoustic pressure, and actuator voltage, for selected loading configurations (i.e., concentrated step, impulse, and moving external loads). Numerical simulations demonstrate the effectiveness of the adopted distributed sensing/actuation configuration together with the active damping control strategy in suppressing the vibroacoustic response of a three-layered (Ba₂NaNb₅O₁₅/Al/PZT4) water-filled piezoelastic cylindrical tank. Limiting cases are considered and the validity of results is established by comparison with the available data as well as with the aid of a commercial finite element package.