Duality in disjunctive programming via vector optimization

In this paper, we develop a new duality theory for families of linear programs with an emphasis on disjunctive linear optimization by proposing a vector optimization problem as dual problem. We establish that the well-known relations between primal and dual problems hold in this context. We show that our method generalizes the duality results of Borwein on families of linear programs, of Balas on disjunctive programs, and of Patkar and Stancu-Minasian on disjunctive linear fractional programs. Moreover, we can derive some duality results for integer and for fractional programs where the denominator is not assumed (as usual) to be greater than zero for each feasible point.     

On Bandt's tangential distribution for self-similar measures

It is shown that the local geometry of a self-similar measure as captured by Bandt's average tangential distribution is the same at -almost all points of the underlying space. Moreover, for a self-similar measure explicit formulas for Bandt's tangential distribution as well as for the average density of Bedford and Fisher are derived.     

Limit theorems for probability measures on simply connected nilpotent lie groups

LetX ₁,X ₂,... be i.i.d. random variables with values in a simply connected nilpotent Lie groupG. Assume the laws of to be weakly convergent to a probability measure onG, _n Aut(G), and (k _n)_n strictly increasing in. In this paper we want to characterize the possible limit laws. We obtain that every limit law is continuously embeddable and we prove a kind of functional limit theorem. Further, we study the connections between two different concepts of stability (resp. semistability) and limit laws. Finally, we describe the various domains of attraction of measures (resp. of convolution semigroups).     

Furylvinylhalogenides,XII: Reactions of β-chloro-α-cyano-β-(5-nitrofur-2-yl)-acrylic acid derivatives with malonic acid derivatives

Summary Reactions of -chloro--cyano--(5-nitrofur-2-yl)-acrylic acid derivatives with malonic acid derivatives in the presence of collidine yield the allyl anions3a–d. The pyridines4, 8 or9 are formed by cyclization of3 under acidic conditions. The 2-chloropyridine4a reacts with nucleophiles under substitution. The treatment of ethyl dichloropropionate1b with C-H-acidic compounds provided the cyclopropanes11 or12, the configurations of which were determined by¹³C-NMR spectroscopy. The results of the X-ray structure analysis of8c are discussed.

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Furylvinylhalogenide, 12. Mitt.: Reaktionen von -Chlor--(5-nitrofur-2-yl)--cyanacrylsäurederivaten mit Malonsäurederivaten

Zusammenfassung Die Umsetzung von -Chlor--cyan--(5-nitrofur-2-yl)-acrylsäurederivaten mit Malonsäurederivaten in Gegenwart von Collidin führt zu Allylanionen3a–d. Unter sauren Bedingungen cyclisiert3 zu den Pyridinen4, 8 oder9. Das 2-Chlorpyridin4a reagiert mit Nukleophilen unter Substitution. Setzt man den Dichlorpropionsäureester1b mit C-H-aciden Verbindungen in Gegenwart von Collidin um, so werden die Cyclopropane11 bzw.12 gebildet, deren Konfigurationen mit Hilfe der¹³C-NMR-Spektroskopie bestimmt wurden. Die Ergebnisse der Röntgenkristallstrukturanalyse von8c werden diskutiert.

     

Intermittency in the Navier-Stokes dynamics

Intermittency effects in high Reynolds number turbulence (Re10³–10⁶) are calculated from the Navier-Stokes equation in Fourier-Weierstrass approximation. First, the probability density functions (PDF) of scale resolved turbulent signals is found to be Gaussian for large scales, whereas for smaller scales the PDF changes (in agreement with experiment) to a more and more stretched exponential type. This is due to intermittent small scale fluctuations which are caused by the competition between turbulent energy transfer downscale and viscous energy loss. Second, we calculate the moments of ther-averaged energy dissipation rate _r (x) and theirr-scaling exponents (m/3). Our results well agree with experiment and numerical simulations of the full Navier-Stokes equations ((2)=0.29±0.02). We analytically show that the common identification between the (m/3) and the corrections (m) to classical scaling of the velocity structure functions (Kolmogorov's refined similarity hypothesis) is doubtful, because even Gaussian ₁ u ₁-PDFs (characterizing non intermittent flow) lead to (m/3)0.     

Microstructure analysis of a bronze–steel electron beam weld

An electron beam welded joint of bronze and steel has been investigated by scanning electron microscopy and energy-dispersive X-ray spectroscopy. The phases and the resulting microstructure in the different zones of the joint have been characterised in detail and compared to hardness. The fine grained microstructure of the weld zone is partly dominated by the directed solidification of the melt. It mainly consists of the α-copper solid solution phase, the intermetallic δ phase Cu₃₁>Sn₈> as well as the bainitic and the martensitic steel phase. This mixture results in a considerably increase in hardness compared to base materials. The heat affected zone of bronze shows a refinement of the used dendritic cast material in a very small area. In the heat affected zone of the mild steel the change of microstructure depends on the distance from the weld zone due to the influence of thermal energy impact and heat dissipation. A maximum of hardness is reached nearby the weld due to the formation of bainite and martensite. The resulting hardness profile is asymmetrical.     

Über basische Aluminiumsalze und ihre Lösungen. X. NMR-Untersuchungen am tridekameren Al-oxo-hydroxo-Kation

Basic Aluminum Salts and their Solutions. X. NMR-Investigations on the Tridecameric Al-Oxo-Hydroxo Cation Using solid-state high resolution ²⁷Al-NMR it is shown that in the basic aluminum chloride with a degree of alkalinity r = OH/Al = 2.5 cations of the [Al₁₃O₄(OH)₂₅(H₂O)₁₁]⁶⁺ type exist. The ¹H-NMR detects besides the constitutional water still an amount of mobile, enclosed H₂O molecules which can be removed by thermal treatment at 104°C. The ²⁷Al spectrum of the aqueous solutions of the chloride shows only one peak at 62.5 ppm which is characteristic for the tridecameric cation. Adding HCl to the solution causes a decomposition to low-molecular species (peak at 0 ppm). Adding NaOH to the aqueous solution of the chloride effects a rearrangement of the tridecameric cations to higher molecular particles which are no more accessible by ²⁷Al-NMR.     

Double-chip protein arrays: force-based multiplex sandwich immunoassays with increased specificity

Protein assays provide direct access to biologically and pharmacologically relevant information. To obtain a maximum of information from the very smallest amounts of complex biological samples, highly multiplexed protein assays are needed. However, at present, cross-reactions of binding reagents restrict the use of such assays to selected cases and severely limit the potential for up-scaling the technology. Here we describe a double-chip format, which can effectively overcome this specificity problem for sandwich immunoassays. This format consists of a capture array and a reference array with fluorescent labeled detection antibodies coupled to the reference array via DNA duplexes. This format allows for the local application of the labeled detection antibodies onto their corresponding specific spots on the capture array. Here we show that this double-chip format allows for the use of cross-reactive antibodies without generating false positive signals, and an assay for the parallel detection of seven different cytokines was set up. Even without further optimization, the dynamic range and the limit of detection for interleukin 8 were found to be comparable to those obtained with other types of multiplexed sandwich immunoassays.     

Formation and dissociation kinetics of Cu(II) and Ni(II) complexes with N2S2-macrocycles

The kinetics of the formation and dissociation of the Cu(2+) and Ni(2+) complexes with a series of N(2)S(2) macrocycles, in which the ring size and the geometry of the arrangement of the donor groups have been varied, have been measured at 25 [degree]C and I= 0.5 (KNO(3)). Both the deprotonated (L) and the monoprotonated (LH(+)) form of the ligands are reactive species in the formation step. In their deprotonated form, first bond formation, in some cases supported by an ICB effect, is rate determining, independently of the ring size. In the monoprotonated form, we find slower rates, due to the charge repulsion and/or conformation changes induced by hydrogen bonds. In contrast the mechanism of the dissociation is very dependent on the ring size. The complexes with the smaller rings react as flexible open-chain ligands directly with H(+). In contrast, the complexes with the larger rings react in a similar way as rigid ligands: first the metal amine bond slowly dissociates so that the free electron pair of the amine can take the "out conformation" and then it is protonated. The 14-membered macrocycle L(3) forms complexes in which the metal ions are ideally coordinated so that their dissociation becomes extremely slow.