The Combinatorics of Laguerre,Charlier, and Hermite Polynomials

This paper describes several combinatorial models for Laguerre, Charlier, and Hermite polynomials, and uses them to prove combinatorially some classical formulas. The so-called “Italian limit formula” (from Laguerre to Hermite), the Appel identity for Hermite polynomials, and the two Sheffer identities for Laguerre and Charlier polynomials are proved. We also give bijective proofs of the three-term recurrences. These three families form the bottom triangle in R. Askey's chart classifying hypergeometric orthogonal polynomials.     

Electrophoresis of a rigid sphere in a Carreau fluid normal to a large charged disk

The electrophoresis of a rigid sphere in a Carreau fluid normal to a large disk is analyzed theoretically under the conditions of low surface potential and weak applied electric field. Previous analyses are extended to the case where a disk can be charged, and a more realistic electrostatic force formula is applied. We show that the qualitative behavior of a sphere depends largely on its distance from a disk, the thickness of double layer, and the nature of a fluid. In general, the presence of a disk has the effect of increasing the conventional hydrodynamic drag on a sphere, and a decrease in the thickness of the double layer surrounding a sphere has the effect of enhancing the shear-thinning effect. However, this might not be the case if a sphere is uncharged and a disk is charged, where the osmotic pressure field and the induced charge on the sphere surface can be significant. The shear-thinning effect is important only if the thickness of double layer is sufficiently thick. This result can play a significant role in practice such as in electrophoretic deposition, where the deposition electrode is charged and the fluid medium is usually of shearing-thinning nature.     

Isocratic Separation of Dansylated Biogenic Amines on a C8‐Bonded Silica Column under the LC Elution of Methanol‐Based Mobile Phase

Under the elution of methanol‐based mobile phase, the isocratic resolution of 12 biogenic amines, including 1 aromatic, 2 heterocyclic and 9 aliphatic amines, as the dansylated derivatives has been accomplished in less than 25 minutes on a 15 cm C₈‐bonded column. The resolution can not be reproduced on other examined alkyl‐bonded phases (e.g., C₄ and C₁₈) under the same chromatographic conditions, or in the reversed‐phase mode. The retention, mainly as a result of hydrophobic interaction between analyte and stationary phase, can be adjusted by varying the percentage of methanol in the mobile phase. Also, incorporating acetic acid as additive to the mobile phase to protonate the analyte and silanol groups that are little shielding on the surface of silica gel reduces the dipole‐dipole interaction, and thus the retention scale, which in turn deteriorates the resolution. Furthermore, the elution reversal is plausible for some of analytes as a greater percent of acetic acid is used in the elution. Values of correlation coefficients (R²) range between 0.9995 and 0.9996, indicating good linearity.     

Biodegradable and pH-sensitive hydrogels: Synthesis by crosslinking of N,N-dimethylacrylamide copolymer precursors

Novel pH-sensitive hydrogels containing azoaromatic crosslinks were synthesized by the crosslinking of polymeric precursors. First, a reactive polymeric precursor was synthesized by copolymerization of N,N-dimethylacrylamide, N-tert-butylacrylamide, acrylic acid, and N-methacryloylglycylglycine p-nitrophenyl ester. The hydrogel was prepared in the second step by the reaction of the polymeric precursor with N,N′-(ω-aminocaproyl)-4,4′-diaminoazobenzene. The hydrogels were characterized by the network structure, (that is, content of crosslinks, unreacted pendent groups, and cycles), the equilibrium swelling ratio as a function of pH, modulus of elasticity in compression, and the degradability in vitro. The results obtained indicated that the hydrogel network structure strongly depends on the reaction conditions such as polymer concentration, and the ratio of the reactive groups during the crosslinking reaction. The swelling and mechanical properties of hydrogels can be controlled by the modification of polymer backbone structure and/or the crosslinking density. The rates of hydrogel degradation depended on their degree of swelling. The higher the degree of swelling, the higher the degradability. The properties of the hydrogels suggest that they have a potential as carriers for colon-specific drug delivery. © 1994 John Wiley & Sons, Inc.     

Square-free-preserving and primitive-preserving homomorphisms

The aim of this paper is to investigate homomorphisms which reserve square-free languages or primitive languages. A characterization of square-free-preserving homomorphisms is presented. We show that every square-free-preserving homomorphism is primitive-preserving. Strongly cube-free-preserving homomorphisms are also studied.     

CH Oxidation of Ingenanes Enables Potent and Selective Protein Kinase C Isoform Activation

Ingenol derivatives with varying degrees of oxidation were prepared by two‐phase terpene synthesis. This strategy has allowed access to analogues that cannot be prepared by semisynthesis from natural ingenol. Complex ingenanes resulting from divergent C? H oxidation of a common intermediate were found to interact with protein kinase C in a manner that correlates well with the oxidation state of the ingenane core. Even though previous work on ingenanes has suggested a strong correlation between potential to activate PKCδ and induction of neutrophil oxidative burst, the current study shows that the potential to activate PKCβII is of key importance while interaction with PKCδ is dispensable. Thus, key modifications of the ingenane core allowed PKC isoform selectivity wherein PKCδ‐driven activation of keratinocytes is strongly reduced or even absent while PKCβII‐driven activation of neutrophils is retained.     

Insight into the dinuclear {Fe(NO)2}10{Fe(NO)2}10 and mononuclear {Fe(NO)2}10 dinitrosyliron complexes

The reversible redox transformations [(NO)(2)Fe(S(t)Bu)(2)](-) ? [Fe(μ-S(t)Bu)(NO)(2)](2)(2-) ? [Fe(μ-S(t)Bu)(NO)(2)](2)(-) ? [Fe(μ-S(t)Bu)(NO)(2)](2) and [cation][(NO)(2)Fe(SEt)(2)] ? [cation](2)[(NO)(2)Fe(SEt)(2)] (cation = K(+)-18-crown-6 ether) are demonstrated. The countercation of the {Fe(NO)(2)}(9) dinitrosyliron complexes (DNICs) functions to control the formation of the {Fe(NO)(2)}(10){Fe(NO)(2)}(10) dianionic reduced Roussin's red ester (RRE) [PPN](2)[Fe(μ-SR)(NO)(2)](2) or the {Fe(NO)(2)}(10) dianionic reduced monomeric DNIC [K(+)-18-crown-6 ether](2)[(NO)(2)Fe(SR)(2)] upon reduction of the {Fe(NO)(2)}(9) DNICs [cation][(NO)(2)Fe(SR)(2)] (cation = PPN(+), K(+)-18-crown-6 ether; R = alkyl). The binding preference of ligands [OPh](-)/[SR](-) toward the {Fe(NO)(2)}(10){Fe(NO)(2)}(10) motif of dianionic reduced RRE follows the ligand-displacement series [SR](-) > [OPh](-). Compared to the Fe K-edge preedge energy falling within the range of 7113.6-7113.8 eV for the dinuclear {Fe(NO)(2)}(9){Fe(NO)(2)}(9) DNICs and 7113.4-7113.8 eV for the mononuclear {Fe(NO)(2)}(9) DNICs, the {Fe(NO)(2)}(10) dianionic reduced monomeric DNICs and the {Fe(NO)(2)}(10){Fe(NO)(2)}(10) dianionic reduced RREs containing S/O/N-ligation modes display the characteristic preedge energy 7113.1-7113.3 eV, which may be adopted to probe the formation of the EPR-silent {Fe(NO)(2)}(10)-{Fe(NO)(2)}(10) dianionic reduced RREs and {Fe(NO)(2)}(10) dianionic reduced monomeric DNICs in biology. In addition to the characteristic Fe/S K-edge preedge energy, the IR ν(NO) spectra may also be adopted to characterize and discriminate [(NO)(2)Fe(μ-S(t)Bu)](2) [IR ν(NO) 1809 vw, 1778 s, 1753 s cm(-1) (KBr)], [Fe(μ-S(t)Bu)(NO)(2)](2)(-) [IR ν(NO) 1674 s, 1651 s cm(-1) (KBr)], [Fe(μ-S(t)Bu)(NO)(2)](2)(2-) [IR ν(NO) 1637 m, 1613 s, 1578 s, 1567 s cm(-1) (KBr)], and [K-18-crown-6 ether](2)[(NO)(2)Fe(SEt)(2)] [IR ν(NO) 1604 s, 1560 s cm(-1) (KBr)].     

Circular shallow spherical shells with central circular hole under simultaneous actions of arbitrary unsteady temperature field and arbitrary dynamic normal load

In this paper, under assumption that tempeature is linearly distributed along the thickness of the shell, we deal with problems as indicated in the title and obtain general solutions of them which are expressed in analytic form.In the first part, we investigate free vibration of circular shallow spherical shells with circular holes at the center under usual arbitrary boundary conditions. As an example, we calculate fundamental natural frequency of a circular shallow spherical shell whose edge is fixed (m=0). Results we get are expressed in analytic form and check well with E. Reissner’s [1]. Method for calculating frequency equation is recently suggested by Chien Wei-zang and is to be introduced in appendix 3.In the second part, we investigate forced vibration of shells as indicated in the title under arbitrary harmonic temperature field and arbitrary harmonic dynamic normal load.In the third part, we investigate forced vibration of the above mentioned shells with initial conditions under arbitrary unsteady temperature field and arbitrary normal load.In appendix 1 and 2, we discuss how to express displacement boundary conditions with stress function and boundary conditions in the case m=1.     

Enhancement of buckling characteristics for sandwich structure with fiber reinforced composite skins and core made of aluminum honeycomb and polyurethane foam

This experimental study is concerned with enhancing the buckling characteristics of sandwich structure when the 6061-T6 aluminum skins are replaced by carbon fiber reinforced composite for the same aluminum honeycomb and polyurethane core. Such an improvement can be attributed to the high strength to weight ratio of the composite skin while the softer core material acts on a relative base as a better energy absorbent and hence tends to stabilize the failure. This results in much higher post-buckling loads which corresponds to the remaining strength of the structure after the onset of buckling.Sandwich structures with core made of polyurethane foam with different densities were also tested in compression. The buckling load increased with the density of polyurethane up to 280 kg/m³ while deattachment of the core and skin occurred when the density is decreased below 100 kg/m³. Compatibility of the skin and core material is shown to play an important role in the buckling behavior of sandwich structure.     

Facile and efficient synthesis of 1-[2-(6,7-dimethyl-3,4-dihydronaphthalen-2-yl)ethyl]pyrrolidine hydrochloride

An efficient and facile procedure for the preparation of 1-[2-(6,7-dimethyl-3,4-dihydronaphthalen-2-yl)ethyl]pyrrolidine hydrochloride from 6,7-dimethyl-1,2,3,4-tetrahydronaphtalen-1-one in four steps is proposed. It includes one-step synthesis of 1-(6,7-dimethyl-1,2,3,4-tetrahydronaphthalen-2-yl)acetic acid as key intermediate and subsequent transformations of functional groups therein. Published in Russian in Zhurnal Organicheskoi Khimii, 2008, Vol. 44, No. 3, pp. 449–453. The text was submitted by the authors in English.