Boundary conditions and mode jumping in the buckling of a rectangular plate

We show that mode jumping in the buckling of a rectangular plate may be explained by a secondary bifurcation — as suggested by Bauer et al. [1] — when clamped boundary conditions on the vertical displacement function are assumed. In our analysis we use the singularity theory of mappings in the presence of a symmetry group to analyse the bifurcation equation obtained by the Lyapunov-Schmidt reduction applied to the Von Kármán equations. Noteworthy is the fact that this explanation fails when the assumed boundary conditions are simply supported.Mode jumping in the presence of clamped boundary conditions was observed experimentally by Stein [9]; simply supported boundary conditions are frequently studied but are difficult — if not impossible — to realize physically. Thus, it is important to observe that the qualitative post-buckling behavior depends on which idealization for the boundary conditions one chooses.Research sponsored in part by the U.S. Army Contract DAAG29-75-C-0024 and the N.S.F. Grant MCS77-04148Research partially supported by the N.S.F. Grant MCS77-03685 and the Research Foundation of C.U.N.Y.     

Pulsed fourier transform NMR of substituted aryltrimethyltin derivatives : III. Proton data at 100 MHz and the derived Hammett σ-constant of the trimethyltin group

Proton NMR data at 100 MHz are reported for thirteen para- and meta-substituted phenyltrimethyltin compounds, XC₆H₄Sn(CH₃)₃, where X = para-N(CH₃)₂, para-OCH₃, para-OC₂H₅, para-CH₃, meta-CH₃, -H, para-F, meta-OCH₃, para-Cl, para-Br, meta-F, meta-Cl and para-Sn(CH₃)₃. Correlation coefficients with Hammett σ-constants of greater than 0.95 are obtained with the methyltin proton chemical shifts and coupling constants to carbon [¹J(¹³C¹H)] and tin [²J(SnC¹H)]. Solvent effects and other extraneous factors invalidate comparisons of ? values in terms of the relative attenuation of the transmission of substituent effects through homologous carbon, silicon, germanium and tin systems, but coupling constant data reflect a diminution of ca. one tenthfold per bond in the order ?[C(1)Sn] > ? [SnC] > ? [CH]. Satisfactory correlations (r > 0.95) are obtained in this series of closely-related compounds among the conventionally recorded two-bond, ²J(SnC¹H) and the constituent, one-bond ¹J (Sn¹³C) and J(¹³C¹H) coupling constants, but the correlation coefficient for the comparison between the two one-bond couplings, ¹J(Sn¹³C) and ¹J(¹³C¹H) is lower (r = 0.872). Changes in the couplings at the methyltin carbon bond tin-119 atoms are interpreted in terms of isovalent hybridization; a model based upon effective nuclear charges is tested with respect to both NMR coupling constants and ¹¹⁹Sn Mössbauer Isomer shifts at tin and is invalidated. Proton and carbon-13 NMR, chemical shift and coupling constant data are used to derive a Hammett σ-constant for the para-trimethyltin group of ?0.14, and the significance of this value is discussed.     

Purine acyclic nucleosides. Unambiguous synthesis of acyclovir via a furazano[3,4-d]pyrimidine

Acyclovir was synthesized in five steps from 7-formamido-5-methylthiofurazano[3,4-d]pyrimidine 2 . Alkylation of 2 with 2-(benzoyloxy)ethoxymethyl chloride, followed by reductive cleavage of the furazan ring gave 9-[[2-(benzoyloxy)ethoxy]methyl]-2-(methylthio)adenine 5 . Hydrolysis of the 6-amino group of 5 , followed by amination of 7 with ammonia gave 9-[(2-hydroxyethoxy)methyl]guanine ( 1 , acyclovir).     

Selection of a synthetic glycan oligomer from a library of DNA-templated fragments against DC-SIGN and inhibition of HIV gp120 binding to dendritic cells

We report the synthesis of a nucleic acid-encoded carbohydrate library, its combinatorial self-assembly into 37,485 pairs and a screen against DC-SIGN leading to the identification of consensus ligand motifs. A prototypical example from the selected pairs was shown to have enhanced binding. A dendrimer incorporating the selected motifs inhibited gp120's binding to dendritic cells with higher efficiency than mannan.     

Polymeric thiols as enzyme activators of serum creatine phosphokinase

Several hydrophilic polymeric thiols were prepared from aminoactivated polymeric supports by reaction with N-acetylhomocysteinethiolactone. Supports include agaroses, cellulose, Glycophase™ controlled-pore glass, and Matrex™ acrylic beads. Thiol content in these polymers was 3–72 μmol SH/g dry polymer. Several were effective solid-phase activators of the sulfhydryl-dependent enzyme creatine phosphokinase at concentrations comparable to that of monomeric thiol required for enzyme activation. The kinetic activation curves for the polymeric and the monomeric (thioglucose) activators were similar, suggesting unhindered interaction of the enzyme with the polymeric activator.     

Nonlinear behavior of model equations which are linearly ill-posed

We discuss two model equations of nonlinear evolution which demonstrate that linearly ill-posed problems may be well-posed in a mild sense. For the nonlocal equation (1.4), smooth solutions exist for all time, are unique, and depend continuously on the initial data in low norms. For the partial differential equation (1.1), solutions always exist; we do not know whether they are unique, but if they are, they also have continuous dependence on data. The large-time behavior of solutions and other qualitative properties are discussed     

Lexicographic generation of projective spaces

Lexicographic or first choice constructions of geometric objects sometimes lead to amazingly good results. Usually it is difficult to determine the precise identity of the resulting geometries. Here we find infinitely many cases where the identification actually can be accomplished.