Lattice Dynamics Study of Microstructures of Electrorheological Fluids

The lattice dynamics method is used to study the stability of the chain structures formed in electrorheological (ER) fluids. The appearance of the soft modes in the phonon dispersion of the structures indicates that the chains tend to distort and aggregate into thicker columns due to the electrostatic attractive forces and thermal generated forces between them. The results show that the stability of the chains relies on their width and the separation between them. The complete chain structures are more stable than the chains with defects. The results can be used to elucidate the densification phenomenon of the chains in the structuring process of ER fluids in the quiescent state.     

Linear independence of pseudo-splines

In this paper, we show that the shifts of a pseudo-spline are linearly independent. This is stronger than the (more obvious) statement that the shifts of a pseudo-spline form a Riesz system. In fact, the linear independence of a compactly supported (refinable) function and its shifts has been studied in several areas of approximation and wavelet theory. Furthermore, the linear independence of the shifts of a pseudo-spline is a necessary and sufficient condition for the existence of a compactly supported function whose shifts form a biorthogonal dual system of the shifts of the pseudo-spline.

     

Generalized Shift-Invariant Systems

A countable collection $X$ of functions in $L_2(\mbox{\footnotesize\bf R})$ is said to be a Bessel system if the associated analysis operator $$ \txs{X}:L_2(\mbox{\smallbf R}^d)\to \ell_2(X) : f\mapsto (\inpro{f,x})_{x\in X} $$ is well-defined and bounded. A Bessel system is a fundamental frame if $\txs{X}$ is injective and its range is closed. This paper considers the above two properties for a generalized shift-invariant system $X$. By definition, such a system has the form $$ X=\bigcup_{j\in J} Y_j, $$ where each $Y_j$ is a shift-invariant system (i.e., is comprised of lattice translates of some function(s)) and $J$ is a countable (or finite) index set. The definition is general enough to include wavelet systems, shift-invariant systems, Gabor systems, and many variations of wavelet systems such as quasi-affine ones and nonstationary ones. The main theme of this paper is the fiberization of $\txs{X}$, which allows one to study the frame and Bessel properties of $X$ via the spectral properties of a collection of finite-order Hermitian nonnegative matrices.     

Convergence of cascade algorithms associated with nonhomogeneous refinement equations

This paper is devoted to a study of multivariate nonhomogeneous refinement equations of the form where is the unknown, is a given vector of functions on , is an dilation matrix, and is a finitely supported refinement mask such that each is an (complex) matrix. Let be an initial vector in . The corresponding cascade algorithm is given by In this paper we give a complete characterization for the -convergence of the cascade algorithm in terms of the refinement mask , the nonhomogeneous term , and the initial vector of functions .

     

An unprecedented intramolecular coupling of o-carboranyl and cyclopentadienyl. Synthesis and structural characterization of a ruthenium complex containing a novel doubly-bridged cyclopentadienyl-carboranyl ligand

A novel ruthenium-mediated coupling reaction of a carboranyl with a cyclopentadienyl was discovered for the first time, leading to a brand new doubly-bridged cyclopentadienyl-carboranyl ligand bearing two five-membered rings and to a new type of chiral ruthenium complex.     

Facile Synthesis of N‐Carboranyl Amines through an ortho‐Carboryne Intermediate

The efficient o‐carboryne precursor 1‐Li‐2‐OTf‐o‐C₂B₁₀H₁₀ reacts with lithium amides at room temperature to give a series of N‐carboranyl amines in moderate to high isolated yields. This reaction is compatible with a broad substrate scope from primary to secondary, alkyl to aryl amines. The reaction mechanism is also proposed on the basis of experimental results and DFT calculations. This represents the first general and efficient method for the synthesis of 1‐NR¹R²‐o‐carboranes.     

Synthesis, structure, reactivity, and thermal isomerization of boron-substituted 13-vertex cobaltacarboranes (eta5-Cp)Co(eta6-R2C2B10Me8H2) (R = H, Et)

Reduction of boron-substituted carboranes o-R2C2B10Me8H2 (R = H, Et), thermal isomerization, and nucleophilic reaction of the resultant 13-vertex cobaltacarboranes were studied. Reaction of o-C2B10Me8H4 (1) with excess potassium metal in tetrahydrofuran (THF) gave, after recrystallization from a THF solution of 18-crown-6 ether, [[K(18-crown-6)(THF)2][K(18-crown-6)]][[4-(18-crown-6)-2,3,5,8,9,11,12,13-Me8-4,1,6-KC2B10H4]2] (2) in 78% yield. Interaction of 1 with excess sodium or potassium metal in THF, followed by treatment with CoCl2/CpNa and then aerobatic oxidation, afforded two boron-substituted 13-vertex cobaltacarboranes, 4-Cp-2,3,5,8,9,11,12,13-Me8-4,1,6-CoC2B10Me8H4 (3) and 4-Cp-2,3,5,9,10,11,12,13-Me8-4,1,6-CoC2B10Me8H4 (4), in 15% and 8% yield, respectively. Subsequently, thermal isomerization of 3 and 4 yielded another two new isomers, 4-Cp-2,3,5,6,8,11,12,13-Me8-4,1,9-CoC2B10Me8H4 (5) and 4-Cp-2,3,5,6,7,11,12,13-Me8-4,1,9-CoC2B10Me8H4 (6). Treatment of 3 or 4 with strong bases such as nBuLi and MeLi generated unexpected nucleophilic substitution products 4-nBuCp-2,3,5,8,9,11,12,13-Me8-4,1,6-CoC2B10Me8H4 (7), 4-nBuCp-2,3,5,9,10,11,12,13-Me8-4,1,6-CoC2B10Me8H4 (8a), and 4-MeCp-2,3,5,9,10,11,12,13-Me8-4,1,6-CoC2B10Me8H4 (8b) in good yields. Under the same reaction conditions, however, only one 13-vertex cobaltacarborane, 4-Cp-1,9-Et2-2,5,6,7,8,11,12,13-Me8-4,1,9-CoC2B10Me8H4 (10), was isolated when o-Et2C2B10Me8H2 (9) was used as the starting material. Complex 10 is a thermodynamically stable product and has a substitution pattern different from that of 3-6. These results show that the substituents on either the cage carbon or boron atoms have an important effect on the formation and thermal stability of the 13-vertex metallacarboranes. The formation of these complexes can be rationalized by the diamond-square-diamond mechanism.     

Ph3As-catalyzed wittig-type olefination of aldehydes with diazoacetate in the presence of Na2S2O4

In the presence of sodium hydrosulfite and a catalytic amount of AsPh3 and Fe(TCP)Cl, aldehydes react with ethyl diazoacetate to give the corresponding alpha,beta-unsaturated esters in high yields with excellent stereoselectivities (E/Z > 50/1).     

Ti-amide catalyzed synthesis of cyclic guanidines from di-/triamines and carbodiimides

A titanacarborane monoamide catalyzed, one-step synthesis of mono/bicyclic guanidines from commercially available di/triamines and carbodiimides is reported. The reaction mechanism is also proposed.     

Selective cage boron/carbon extrusion reaction of 13-vertex carborane μ-1,2-(CH2)3-1,2-C2B11H11: formation of nido-CB10, closo-CB10, and closo-C2B10 species

The nature of nucleophiles greatly influences the reactivity patterns of 13-vertex carboranes. μ-1,2-(CH(2))(3)-1,2-C(2)B(11)H(11) reacts with Et(3)N/MeOH, pyridine or bipyridine to give cage-boron and -carbon extrusion products nido-CB(10) or closo-CB(10), or a cage-boron extrusion compound closo-C(2)B(10) while the cage-carbon extrusion species closo-CB(11) monoanions are produced by treatment with MeOH or Ph(3)P.