Semi infinite Orthotropic Cantilevered Strips and the Foundations of Plate Theories

Elastostatic problems of semiinfinite orthotropic cantilevered strips with traction-free edges and loading at infinity are reduced to the solution of a single scalar Fredholm integral equation of the first kind with a generalized Cauchy kernel. The known complex variable method for equations with a Cauchy type kernel is extended to handle the singularities in the solution for the generalized Cauchy kernel. The reduced problem lends itself to a more efficient numerical solution scheme than all existing methods. Moments of stresses at the root of the cantilever are accurately evaluated and used for the correct formulation of displacement boundary conditions for a plate theory solution (or the actual interior solution) of the elastostatics of thin flat bodies.     

Normal state spaces of Jordan and von Neumann algebras

Normal state spaces of Jordan and von Neumann algebras are characterized among convex sets. The normal state spaces of JBW-algebras are precisely those which are spectral and elliptic; along these the normal state spaces of von Neumann algebras are distinguished by the global 3-ball property.     

A cyclopentadienyl functionalized silylene – a flexible ligand for Si- and C-coordination

The synthesis of a 1,2,3,4-tetramethylcyclopentadienyl (Cp⁴) substituted four-membered N-heterocyclic silylene [{PhC(NtBu)₂}Si(C₅Me₄H)] is reported first. Then, selected reactions with transition metal and a calcium precursor are shown. The proton of the Cp⁴-unit is labile. This results in two different reaction pathways: (1) deprotonation and (2) rearrangement reactions. Deprotonation was achieved by the reaction of [{PhC(NtBu)₂}Si(C₅Me₄H)] with suitable zinc precursors. Rearrangement to [{PhC(NtBu)₂}(C₅Me₄)SiH], featuring a formally tetravalent silicon R₂C Si(R′)–H unit, was observed when the proton of the Cp⁴ ring was shifted from the Cp⁴-ring to the silylene in the presence of a Lewis acid. This allows for the coordination of the Cp⁴-ring to a calcium compound. Furthermore, upon reaction with transition metal dimers [MCl(cod)]₂ (M = Rh, Ir; cod = 1,5-cyclooctadiene) the proton stays at the Cp⁴-ring and the silylene reacts as a sigma donor, which breaks the dimeric structure of the precursors.

A cyclopentadienyl functionalized silylene or its derivatives can be coordinated in all three forms: silylene (A), anion (B), and sila fulvene (C).     

Phospholidines incorporating a beta N-sulfonylaminoalcohol moiety: first observed selectivity of phosphorus heterocycle aminolysis in the presence of water

Eleven 2-oxo or 2-thioxo 3-sulfonyl 1,3,2-oxazaphospholidines were synthesized in one step by condensing P(IV) dichlorides with N-sulfonyl-ethanolamines, or -aminothexylalcohols or -ortho-aminophenols. These compounds, in contrast to all other phosphorus heterocycles studied so far, reacted easily with amines, sometimes selectively in the presence of water, leading to the corresponding amides. The results are rationalized by the involvement of the addition-elimination mechanism of phosphorylation with direct collapse of the primary zwitterionic intermediate formed by the amine attack on phosphorus.     

Derivatives of 3-(2-hydroxyethyl)2-benzothiazolinone and related compounds

The reaction of the appropriate 2-benzothiazolinone with 2-chloroethanol or 3-chloropropanol under basic conditions afforded 3-(2-hydroxyethyl or 3-hydroxypropyl)-2-benzothiazolinone and related compounds 1–7. The reaction of the alcohols 1,4, 5 or 7 with potassium hydroxide and excess carbon disulfide furnished the potassium salts of xanthic acid 8–11 which upon oxidation gave the disulfides 12–15. Esters of xanthic acid 16–23 were prepared by the reaction of 8 or 11 with various halogen compounds. Esters of acetic acid 24–28 were prepared by the reaction of the appropriate 2-benzothiazolinone with 2-bromoethyl acetate under basic conditions. Esterification of 1 with various acids afforded the esters 25, 29–32.     

Synthesis and characterization of thermosensitive copolymers for oral controlled drug delivery

Poly(N-isopropylacrylamide) (PNIPAAm) copolymers were synthesized in order to obtain co-polymers with a phase transition temperature slightly higher than the physiological temperature, as required by a new drug delivery concept described in a previous paper. Six hydrophilic comonomers bringing about a rise of the phase transition temperature were evaluated. The synthesized copolymers were characterized and the influence of the type and of the amount of the used comonomer on the phase transition temperature was discussed. Among the comonomers, Acrylamide (AAm), N-methyl-N-vinylacetamide (MVA), N-vinylacetamide (NVA), and N-vinyl-2-pyrrolidinone (VPL) were found to be capable to raise the phase transition temperature to a value slightly higher than 37 °C and to have adequate phase transition behavior. The selected four copolymers were subjected to an additional purification step that should make them fit to use as a controlling agent in drug delivery systems.     

Modular forms arising from spherical polynomials and positive definite quadratic forms

The dimension over the complex numbers of the vector space of θ-series

$\text{Φ(τ;P,Q)=∑n?Z}{}^{\mathrm{r}}\text{P(n)e}{}^{\mathrm{2\pi iQ(n)\tau }}\text{,}$

where P(X) is a “spherical polynomial” with respect to the positive definite quadratic form Q(X) is computed for binary forms. A sufficient condition that θ(τ; P, Q) be identically zero is proved, and its necessity is also proved for binary forms.     

A study of EWOD-driven droplets by PIV investigation

Despite the recent interest in droplet-based microfluidics using electrowetting-on-dielectric (EWOD), fundamental understanding of the fluid dynamics remains limited to two-dimensional (2D) reduction of the Navier-Stokes equation. Experimental data are in dire need to verify the predictions and advance the field. We report an investigation of the flow inside droplets actuated by EWOD in air using micro particle image velocimetry (micro-PIV). Using the continuity equation, we reconstruct the 3D velocity field from the 2D PIV experimental data. We present some fundamental findings and build valuable insights that will help design sophisticated EWOD microfluidic devices. For example, the results confirm that efficient mixing in a droplet may be achieved by moving the droplet along an irreversible pattern that breaks the symmetry of the two circulating inner flows.     

Millisecond denaturation dynamics of fluorescent proteins revealed by femtoliter container on micro-thermodevice

Real-time observation of biomolecular behavior focusing on high speed temperature response is an essential endeavor for further biological study at the molecular level. This is because most of the important biological functions at the molecular level happen at the sub-second time scale. We used our own on-chip microheaters and microcontainers to observe the denaturation dynamics of fluorescent proteins at the millisecond time scale. The microheater controls the temperature in 1 ms under the microscope. Fluorescent proteins were contained in 28 fL PDMS microcontainers to prevent them from diffusing into the solution. The proteins were denatured by high temperatures and observed by a high speed CCD camera with 5 ms per frame. Hence, denaturation speeds of red fluorescent proteins (rDsRed and rHcRed) were measured to be 5-10 ms. Green fluorescent proteins (rAcGFP and rGFPuv) denatured with bi-exponential decay. rAcGFP denatured with time constants of 5 ms and 75 ms while rGFPuv denatured with 10 ms and 130 ms. This may be the reverse process of a two step renaturation of GFP observed in a previous report. This micro-thermodevice is applicable to other biomaterials such as nucleic acids or other proteins. It does not require any chemical treatment nor mutation to the biomaterial itself. Therefore, the methodology using this general purpose device gives access to biomolecular studies in short time scales and acts as a powerful tool in molecular biology.