Effect of viscous damping on power transmissibility for the vibration isolation of building services equipment

Vibration isolation plays an important role in both the vibration and noise control of building services equipment. To evaluate vibration isolation performance, the force transmissibility method is commonly adopted. However, increasing the damping effect in the force transmissibility method reduces both the resonance peak value and the isolation performance in the “isolation region”. The limitation of the method is that the transmitted displacement of a floor structure and the interaction of mounting points are neglected. To include the floor displacement and the interaction of mounting points, Mak and Su recently proposed the power transmissibility method to assess the performance of vibration isolation. In this paper, the effect of viscous damping on power transmissibility is investigated. A practical procedure for experimentally determining the damping ratio is also given.     

High‐Nuclearity Silver Thiolate Clusters Constructed with Phosphonates

The n‐butylphosphonate ligand has been employed to construct three new silver(I) thiolate compounds. Single‐crystal X‐ray analysis revealed that complexes 1 and 2 are Ag₄₈ and Ag₅₁ coordination chain polymers, while 3 contains a discrete Ag₄₈ cluster, in which three different kinds of silver(I) thiolate cluster shells enclose three different phosphonate‐functionalized silver(I) cluster cores, respectively. The structures of clusters in 1 – 3 feature three three‐shell arrangements, S@Ag₁₂@(nBuPO₃)₉@Ag₃₆S₂₃, S@Ag₁₁@(nBuPO₃)₇(MoO₄)₂ @Ag₄₀S₂₇ and MoO₄@Ag₁₂@(nBuPO₃)₈S₆ @Ag₃₆S₂₄, respectively.     

Ratiometric fluorescent Zn chemosensor constructed by appending a pair of carboxamidoquinoline on 1,2-diaminocyclohexane scaffold

By appending a pair of carboxamidoquinoline pendants onto 1,2-diaminocyclohexane scaffold via N-alkylation, multifunctionalized ACAQ was designed and synthesized as a water soluble fluorescent ratiometric chemosensor for Zn²⁺. In 50% aqueous methanol buffer pH 7.4 solution, upon excitation at 316 nm, ACAQ (5 μM) displayed a selective ratiometric fluorescence changes with a shift from 410 to 490 nm in response to the interaction with Zn²⁺. After binding with 1 equiv of Zn²⁺, ACAQ exhibited a 12-fold enhancement in I₄₉₀/I₄₁₀ characterized by a clear isoemissive point at 440 nm. The metal sensor binding mode was established by Job’s plot and the combined fluorescence and ¹H NMR spectroscopic method. The selectivity of the probe toward biological relevant cations and transition metal ions was proven to be good. In addition, the interference caused by Cu²⁺ and Cd²⁺ in the quantitation of Zn²⁺ can be completely eliminated by the use of diethyldithiocarbamate as the screening agent. Exploitation of ACAQ as the sensing probe, ratiometric determination of Zn²⁺ with the limit of detection (LOD) at 28.3 nm can be realized. In addition, the unique responsive properties of the probe toward Fe³⁺ and Zn²⁺ were used to construct a fluorescent switch. The membrane permeability of ACAQ to living cells and bio-imaging of Zn²⁺ were demonstrated.     

Two-photon induced luminescence, singlet oxygen generation, cellular uptake and photocytotoxic properties of amphiphilic Ru(II) polypyridyl-porphyrin conjugates as potential bifunctional photodynamic therapeutic agents

Two Ru(II) polypyridyl-porphyrin and Zn(II) porphyrin conjugates (Ru-L and Ru-Zn-L) have been synthesized and their photophysical properties studied. The two conjugates, which contained a hydrophobic tetraphenylporphyrin L conjugated via an acetylide linker at its β-position with a hydrophilic Ru(II) polypyridyl complex, showed high singlet oxygen quantum yields (>70%) and substantial two-photon absorption cross-sections (~500 GM). Ru-L gave strong emissions at ~660 and ~733 nm through linear or two-photon excitation. Solvatochromism was observed in the fluorescence spectra of Ru-L and Ru-Zn-L, where in less polar solvents (i.e., toluene and dichloromethane) their fluorescence emissions became slightly blue-shifted with a 3-fold reduction in intensity relative to those observed in polar solvents (i.e., acetonitrile and methanol). Cell-based studies of these complex conjugates were conducted using human nasopharyngeal carcinoma HK-1 and cervical carcinoma HeLa cells on which Ru-L showed rapid cellular uptake, low dark-cytotoxicity, and high photo-cytotoxicity. Furthermore, Ru-L can be excited and emits in the "biological window"in vitro, making it a potential potent new generation photodynamic therapeutic agent capable of singlet oxygen generation and in vitro near-infrared emission.     

Strengthening of strong and approximate convexity?

Let X be a real linear space and $D\subseteq X$ be a nonempty convex subset. Given an error function E:[0,1]×(D?D)?????{+??} and an element $t\in\left]0,1\right[$ , a function f:D??? is called (E,t)-convex if $$f(tx+(1-t)y)\le tf(x)+(1-t)f(y)+E(t,x-y)$$ for all x,y??D. The main result of this paper states that, for all a,b??(???{0})+{0,t,1?t} such that {a,b,a+b}??????, every (E,t)-convex function is also $\big(F,\frac{a}{a+b}\big)$ -convex, where $$F(s,u):=\frac{{(a+b)}^2s(1-s)}{t(1-t)}E\left(t,\frac{u}{a+b}\right),\qquad (u\in (D-D), \, s\in\left]0,1\right[).$$ As a consequence, under further assumptions on E, the strong and approximate convexity properties of (E,t)-convex functions can be strengthened.     

On the Integrability of the Abel and of the Extended Liénard Equations

Acta Mathematicae Applicatae Sinica, English Series - We present some exact integrability cases of the extended Liénard equation y″ + f(y)(y′)n + k(y)(y′)m + g(y)y′ +...     

Some addition reactions of bisgermavinylidene

The reaction of bisgermavinylidene [(Me₃SiN?PPh₂)₂C?Ge→Ge?C(PPh₂?NSiMe₃)₂] ( 1 ) with AdNCO (Ad = Adamantyl) afforded the [2 + 2] cycloadditon product [(Me₃SiN?PPh₂)₂CGeC(O) NAd] ( 2 ). Similar reaction of 1 with Ph₃SiOH in tetrahydrofuran (THF) yielded the base‐stabilized germanium(II) triphenylsiloxide [H₂C(PPh₂?NSiMe₃)₂Ge(OSiPh₃)₂] ( 3 ). The results suggested that reactive germavinylidene may exist in solution and is capable of forming addition reaction products. The X‐ray structures of 2 and 3 were determined. Copyright © 2007 John Wiley & Sons, Ltd.     

Synthesis, crystal structure determination, spectroscopic and electrochemical studies of trans-[Ru(PPh3)2(bbpH2)Cl]Cl·CHCl3·H20 (bbpH2=2,6-bis(benzimidazolyl) pyridine) – an infinite double columnar supramolecule in the solid state

The synthesis, crystal structure, redox and spectroscopic properties of trans-[Ru(bbpH₂)(PPh₃)₂Cl]Cl are reported. In the crystalline solvate trans-[Ru(bbpH₂)(PPh₃)₂cCl]Cl CHCl₃ H₂O, the molecular components are connected by strong intermolecular hydrogen bonding to form an infinite double column.