Small degree out‐branchings

Using a suitable orientation, we give a short proof of a strengthening of a result of Czumaj and Strothmann 4 : Every 2‐edge‐connected graph G contains a spanning tree T with the property that for every vertex v. As an analogue of this result in the directed case, we prove that every 2‐arc‐strong digraph D has an out‐branching B such that . A corollary of this is that every k‐arc‐strong digraph D has an out‐branching B such that , where . We conjecture that in this case would be the right (and best possible) answer. If true, this would again imply a strengthening of a result from 4 concerning spanning trees with small degrees in k‐connected graphs when k ≥ 2. We prove that for acyclic digraphs the existence of an out‐branching satisfying prescribed bounds on the out‐degrees of each vertex can be checked in polynomial time. A corollary of this is that the existence of arc‐disjoint branchings , , where the first is an out‐branching rooted at s and the second an in‐branching rooted at t, can be checked in polynomial time for the class of acyclic digraphs © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 297–307, 2003     

Metal scrambling in the trinuclear (Pt(2)Se(2)M)(M = Pt, Pd, Au) system using an electrospray mass spectrometry (ESMS) directed synthetic methodology; isolation and crystallographic characterization of (Pt(2)(mu(3)-Se)(2)(PPh(3))(4)[Pt(cod)])(PF(6))(2) and (Pt(mu(3)-Se)(2)(PPh(3))(2)[Pt(cod)](2))(PF(6))(2) (cod = cyclo-octa-1,5-diene)

Pt(2)(mu-Se)(2)(PPh(3))(4) reacts with PtCl(2)(cod) to give (Pt(2)(mu(3)-Se)(2)(PPh(3))(4)[Pt(cod)])(2+) and an unexpected cod-rich product that arises from metal scrambling, viz. (Pt(mu(3)-Se)(2)(PPh(3))(2)[Pt(cod)](2))(2+). The formation of these species was detected and followed by electrospray mass spectrometry (ESMS) and subsequently verified by batch synthesis and crystallographic characterization. Other metal-scrambled aggregate products were successfully detected.     

Metastable transitions in the mass spectra of ketals and ketones. Competition between loss of small and large radicals

An investigation of competing metastable transitions in the mass spectra of ethylene ketals R_SR_LC(OCH₂)₂ (where R_L is a larger n-alkyl group than R_S) has established that in most cases R_S is lost with a lower activation energy than R_L. This technique has also been applied to ketones R_SR_LC?O, to show again that R_S is usually lost with the lower activation energy (thus supporting earlier data based on relative daughter ion abundances at the threshold). In the classes of compounds so far investigated, although [M⁺ ? R_S] ions are formed with lower activation energies than [M⁺ ? R_L] ions, the ion yield of [M⁺ ? R_S] ions is anomalously low from ions of high internal energy. Factors which may influence the [M⁺ ? R_S]/[M⁺ ? R_L] ratio of daughter ion intensities are examined. It is suggested that at the threshold [M⁺ ? R_S] and [M⁺ ? R_L] ions may be formed with rearrangement, or from an electronic state that cannot be effectively populated from molecular ions of high internal energies.     

Novel 53/106 GHz Dual-Band MMW LC Oscillator Implemented in SiGe BiCMOS Technology

In this Paper, we present a fully integrated millimeter wave LC voltage-controlled oscillator (VCO), which employs a novel topology, operating at dual-band frequency of 53.22 GHz-band and 106.44 GHz-band. The low-phase noise performance of –107.3 dBc/Hz and –106.1 dBc/Hz at the offset frequency of 600 kHz, –111.8 dBc/Hz and –110.6 dBc/Hz at the offset frequency of 1 MHz around 53.22 GHz and 106.44 GHz are achieved using IBM BiCMOS-6HP technology, respectively. Two tuning ranges, of 52.7 - 53.8 GHz and 105.4 - 107.6 GHz for the proposed LC VCO are obtained. The output voltage swing of this VCO is around 1.8 V_p-p at the operation frequency of 53.22 GHz and 0.45 V_p-p at 106.44 GHz; the total power consumption is about 16.5 mW. To our knowledge, this is the first oscillator which operates at dual-band frequency above 50 GHz with the best preformance.     

The combined use of ab initio molecular orbital theory and matrix isolation infrared spectroscopy in the study of molecular interactions

The infrared spectra of a linear (C_s) and a cyclic (C_i) water dimer and a linear (C_s) and a cyclic (C_2h) ammonia dimer have been calculated, at the second order level of MØller-Plesset perturbation theory, using the 6-31G^** basis set. The calculated spectra have been compared with the spectra of water and ammonia isolated in nitrogen and argon matrices. In the case of water, theory predicts the linear to be the more stable isomer, and the observed spectrum can only be interpreted in terms of the linear structure. For ammonia, while the experimentally determined spectrum fits the calculated spectrum of the linear dimer fairly closely, the prediction of which is the more stable structure is still ambiguous.     

The intramolecular Baylis-Hillman reaction: easy preparation of versatile substrates, facile reactions, and synthetic applications

We have developed a general and highly efficient method for the preparation of diverse [small omega]-formyl-[small alpha],[small beta]-unsaturated carbonyl compounds and optimized the conditions for the intramolecular Baylis-Hillman reactions of these compounds to provide various biologically important polycyclic compounds.     

A new imidazolium cavitand for the recognition of dicarboxylates

[structure: see text] A new cavitand bearing four imidazolium groups was synthesized for the recognition of anions through (C-H)+...X- hydrogen bond formation. The binding properties toward various anions including dicarboxylates were examined on the basis of 1H NMR spectroscopic experiments.