A sufficient condition for a graph to be hamiltonian

Those non-hamiltonian graphsG withn vertices are characterized, which satisfy the Ore-type degree-conditiond(x)+d(y)n–2 for each pairx,yM of different nonadjacent vertices whereM consists of two vertices ofG. As an application a theorem on hamiltonian connectivity of graphs is given. Furthermore, a condition is presented which is sufficient for the existence of a covering of a graph by two disjoint paths with prescribed set of startpoints and prescribed set of endpoints. A class of graphs is described which have no covering of this kind.     

Über Mittelwerte multiplikativer zahlentheoretischer Funktionen mehrerer Variablen

In [8] the author extended the concept of neighbouring functions (cp. [9]) to the case of several variables. Using these results it is shown that under some weak conditions a multiplicative functionf in two variables has a mean-value different from zero if and only if the two multiplicative functionsf ₁(n)=f(n, 1) andf ₂(n)=f(1,n) have mean-values different from zero. Applications to theorems ofDelange [3],Elliott [6] andDaboussi [1] are given.     

Approximations of inventory models

Summary A general procedure is presented for constructing approximations of discrete review single product dynamic inventory models. Bounds are derived for the approximations and compared with the ones ofHinderer [1978],Whitt [1978] for the approximation of a general dynamic program. Good order-policies are constructed. Finally, conditions are given under which the sequence of bounds associated with a sequence of approximating models converges to zero.

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Zusammenfassung Es wird ein allgemeines Verfahren zur Approximation periodisch inspizierter dynamischer Ein-Produkt-Lagerhaltungsmodelle betrachtet. Dazu werden Fehlerschranken gegeben. Diese werden verglichen mit denen vonHinderer [1978],Whitt [1978] für ein allgemeines dynamisches Entscheidungsmodell. Außerdem werden gute Bestellpolitiken konstruiert und hinreichende Bedingungen gegeben, unter denen die Fehlerschranken einer Folge von approximierenden Modellen gegen Null konvergiert.

     

Facile Synthesis and Palladium‐Catalyzed Cross‐Coupling Reactions of 2,3‐Bis(pinacolatoboryl)‐1,3‐butadiene

Treatment of 1,1‐bis(pinacolatoboryl)ethene with an excess of 1‐bromo‐1‐lithioethene gave 2,3‐bis(pinacolatoboryl)‐1,3‐butadiene in high yield. Palladium‐catalyzed cross‐coupling of the resulting diborylbutadiene with aryl iodides took place smoothly in the presence of a catalytic amount of Pd(OAc)₂/PPh₃ and aqueous KOH to give 2,3‐diaryl‐1,3‐butadienes in good yields. The coupling reaction with commercially available 4‐acetoxyphenylmethyl chloride under the same conditions followed by hydrolysis of the acetyl groups gave anolignan B in a one‐pot manner. A variety of [3]‐ to [6]dendralenes were synthesized by palladium‐catalyzed coupling of the diene or 1,1‐bis(pinacolato)borylethene with alkenyl or dienyl halides, respectively, in good yields.     

(Me2NH2)[(Ph3Sn)3(MoO4)2], ein Triorganozinnmolybdat mit Schichtstruktur

(Me₂NH₂)[(Ph₃Sn)₃(MoO₄)₂], a Triorganotin Molybdate with Layer Structure The reaction of [(Ph₃Sn)₂MoO₄] with (Me₂NH₂)Cl in an acetonitrile/water mixture leads to the formation of (Me₂NH₂)[(Ph₃Sn)₃(MoO₄)₂] ( 1 ). ( 1 ) crystallizes in the space group Pca2₁ with a = 1967.0(4), b = 1353.1(2) and c = 2176.6(5) pm. In the crystal structure of 1 Ph₃SnO₂ bipyramides and MoO₄ tetrahedra are linked by corner sharing to give a layer structure. Additionally the layers are connected by O···H···N hydrogen bridges between MoO₄ groups and [Me₂NH₂]⁺ ions to give a 3D network structure.     

Microfluidic three-dimensional biomimetic tumor model for studying breast cancer cell migration and invasion in the presence of interstitial flow

Cell migration and invasion are critical steps in cancer metastasis, which are the major cause of death in cancer patients. Tumor-associated macrophages(TAMs) and interstitial flow(IF) are two important biochemical and biomechanical cues in tumor microenvironment, play essential roles in tumor progression. However, their combined effects on tumor cell migration and invasion as well as molecular mechanism remains largely unknown. In this work, we developed a microfluidic-based 3 D breast cancer model by co-culturing tumor aggregates, macrophages, monocytes and endothelial cells within 3 D extracellular matrix in the presence of IF to study tumor cell migration and invasion. On the established platform, we can precisely control the parameters related to tumor microenvironment and observe cellular responses and interactions in real-time. When co-culture of U937 with human umbilical vein endothelial cells(HUVECs) or MDA-MB-231 cells and tri-culture of U937 with HUVECs and MDA-MB-231 cells, we found that mesenchymal-like MDA-MB-231 aggregates activated the monocytes to TAM-like phenotype macrophages. MDA-MB-231 cells and IF simultaneously enhanced the macrophages activation by the stimulation of colony-stimulating factor 1(CSF-1). The activated macrophages and IF further promoted vascular sprouting via vascular endothelial growth factor(VEGFα) signal and tumor cell invasion. This is the first attempt to study the interaction between macrophages and breast cancer cells under IF condition. Taken together, our results provide a new insight to reveal the important physiological and pathological processes of macrophages-tumor communication. Moreover, our established platform with a more mimetic 3 D breast cancer model has the potential for drug screening with more accurate results.     

Thermochemistry of the ternary solid complex Gd(C5H8NS2)3(C12H8N2)

The novel ternary solid complex Gd(C₅H₈NS₂)₃(C₁₂H₈N₂) has been obtained from the reaction of hydrous gadolinium chloride, ammonium pyrrolidinedithiocarbamate (APDC), and 1,10-phenanthroline (o-phen · H₂O) in absolute ethanol. The complex was described by an elemental analysis, TG-DTG, and an IR spectrum. The enthalpy change of the complex formation reaction from a solution of the reagents, Δ_r H _m ^ϑ (sol), and the molar heat capacity of the complex, c _m , were determined as being − 15.174 ± 0.053 kJ/mol and 72.377 ± 0.636 J/(mol K) at 298.15 K by using an RD496-III heat conduction microcalorimeter. The enthalpy change of a complex formation from the reaction of the reagents in a solid phase, Δ_r H _m ^ϑ (s), was calculated as being 52.703 ± 0.304 kJ/mol on the basis of an appropriate thermochemical cycle and other auxiliary thermodynamic data. The thermodynamics of the formation reaction of the complex was investigated by the reaction in solution. Fundamental parameters, the activation enthalpy (ΔH _≠ ^ϑ ), the activation entropy (ΔS _≠ ^ϑ ), the activation free energy (ΔG _≠ ^ϑ ), the apparent reaction rate constant (k), the apparent activation energy (E), the preexponential constant (A), and the reaction order (n), were obtained by the combination of the thermochemical data of the reaction and kinetic equations, with the data of thermokinetic experiments. The constant-volume combustion energy of the complex, Δ_c U, was determined as being −17588.79 ± 8.62 kJ/mol by an RBC-II type rotatingbomb calorimeter at 298.15 K. Its standard enthalpy of combustion, Δ_c H _m ^ϑ , and standard enthalpy of formation, Δ_f H _m ^ϑ , were calculated to be −17604.28 ± 8.62 and −282.43 ± 9.58 kJ/mol, respectively. The text was submitted by the authors in English.     

SPME-GC-MSD for Determination of Nine Phenyl Compounds in Snow Water in Beijing China

Solid phase microextraction (SPME) then capillary gas chromatography with mass spectrometric detection have been used for determination of nine phenyl compounds in snow water in Beijing City. Headspace extraction with a fiber coated with 100 µm PDMS was used to extract the compounds. Extraction and desorption times were optimized at 8 and 2 min, respectively. Relative standard deviation (RSD) of the analytical method was found to be less than 5%. The linear range was wide and limits of detection were less than 5 ng mL⁻¹ for the nine target analytes. Several phenyl compounds at ng mL⁻¹ levels were detected in snow samples in Beijing, indicating the corresponding air pollution.     

O(3P)原子和硅烷化学反应动力学研究

本文报道了用流动放电-化学发光技术测定O(~3P)和硅烷化学反应速率常数.在293—413K范围内, 结果为k=(1.05±0.36)×10~(-10)exp[(-3.06±0.10) kcal·mol~(-1) /RT] cm~3·molecule~(-1)·s~(-1)并用过渡态理论将上述实验结果外推到200—2000 K范围内. 计算结果以三参数公式表示为: k=7.67×10~(-19) T~(2.59) exp(-720 cal·mol~(-1)/RT) cm~3·molecule~(-1)·s~(-1).