3,3′‐Bi(1,2,4‐oxadiazoles) Featuring the Fluorodinitromethyl and Trinitromethyl Groups

Here we report on the preparation of two hydrogen atom free 3,3′‐bi(1,2,4‐oxadiazole) derivatives. 5,5′‐Bis(fluorodinitromethyl)‐3,3′‐bi(1,2,4‐oxadiazole) was synthesised by fluorination of diammonium 5,5′‐bis(dinitromethanide)‐3,3′‐bi(1,2,4‐oxadiazole). For our previously reported analogue 5,5′‐bis(trinitromethyl)‐3,3′‐bi(1,2,4‐oxadiazole), a new synthetic route starting from new 3,3′‐bi(1,2,4‐oxadiazolyl)‐5,5′‐diacetic acid was developed. In this course also hitherto unknown 5,5′‐dimethyl‐3,3′‐bi(1,2,4‐oxadiazole) was isolated. The compounds were characterised by multinuclear NMR spectroscopy, IR and Raman spectroscopy, elemental analysis as well as mass spectrometry. X‐ray diffraction studies were performed and the crystal structures for the 5,5'‐dimethyl and 5,5'‐(fluorodinitromethyl) derivatives are reported. The energetic 5,5'‐(fluorodinitromethyl) and 5,5'‐(trinitromethyl) compounds do not contain any hydrogen atoms and show remarkable high densities. Furthermore, the thermal stabilities and sensitivities were determined by differential scanning calorimetry (DSC) and standardised impact and friction tests. The heats of formation were calculated by the atomisation method based on CBS‐4M enthalpies. With these values and the room‐temperature X‐ray densities, several detonation and propulsion parameters, such as the detonation velocity and pressure as well as the specific impulse of mixtures with aluminium, were computed using the EXPLO5 code.     

Two applications of Brouwer’s fixed point theorem: in insurance and in biology models

In the first part of the article, a new interesting system of difference equations is introduced. It is developed for re-rating purposes in general insurance. A nonlinear transformation φ of a d-dimensional (d ≥ 2) Euclidean space is introduced that enables us to express the system in the form f^t+1:=φ( f^t), t = 0, 1, 2,. …. Under typical actuarial assumptions, existence of solutions of that system is proven by means of Brouwer’s fixed point theorem in normed spaces. In addition, conditions that guarantee uniqueness of a solution are given. The second, smaller part of the article is about Leslie–Gower’s system of d ≥ 2 difference equations. We focus on the system that satisfies conditions consistent with weak inter-specific competition. We prove existence and uniqueness of the equilibrium of the model under surprisingly simple and very general conditions. Even though the two parts of this article have applications in two different sciences, they are connected with similar mathematics, in particular by our use of Brouwer’s fixed point theorem.     

Adsorption of I2 by Macrocyclic Polyazadithiophenolato Complexes Mediated by Charge‐Transfer Interactions

The macrocyclic complex [Ni₂(L)(OAc)]ClO₄ ( 1 ) adsorbs up to 17 molar equivalents (>270 wt %) of iodine, although it does not exhibit permanent porosity. Vibrational spectroscopic and crystallographic studies reveal that two I₂ molecules are captured by means of thiophenolate→I₂ charge‐transfer interactions, which enable the diffusion and sorption of further I₂ molecules in a polyiodide‐like network. The efficient sorption and desorption characteristics make this material suitable for accommodation, sensing, and slow release of I₂.     

Polynitro Containing Energetic Materials based on Carbonyldiisocyanate and 2, 2‐Dinitropropane‐1, 3‐diol

New polynitro compounds containing a carbonyl biscarbamate moiety derived from the precursor carbonyldiisocyanate were synthesized. In addition, 2, 2‐dinitropropane‐1, 3‐diyl bis(2, 2,2‐trinitroethylcarbamate) and 2, 2‐dinitropropane‐1, 3‐diyl bis(2, 2,2‐trinitroethyl) dicarbonate, were synthesized using 2, 2‐dinitropropane‐1, 3‐diol as starting material. The compounds were characterized by using the analytical methods, single‐crystal X‐ray diffraction, vibrational spectroscopy (IR and Raman), multinuclear NMR spectroscopy, elemental analysis, and mass spectrometry. The thermal behavior was investigated with DSC measurements. The suitability of the compounds as potential oxidizers in energetic formulations was determined. The heats of formation of the compounds were calculated with GAUSSIAN 09. The detonation parameters such as the detonation pressure, velocity, energy, and temperature were computed using the EXPLO5 code. For a secure handling of the materials, the sensitivity towards impact, friction, and electrical discharge was tested using the BAM drop hammer, BAM friction tester as well as a small‐scale electrical discharge device, respectively.     

A constructive characterization ofQ o-matrices with nonnegative principal minors

In [2] we characterized the class of matrices with nonnegative principla minors for which the linear-complementarity problem always has a solution. That class is contained in the one we study here. Our main result gives a finitely testable set of necessary and sufficient conditions under which a matrix with nonnegative principal minors has the property that if a corresponding linear complementarity problem is feasible then it is solvable. In short, we constructively characterize the matrix class known asQ _o ∩P _o . Research partially supported by the National Science Foundation Grant DMS-8420623 and U.S. Department of Energy Contract DE-AA03-76SF00326, PA # DE-AS03-76ER72018.     

A note onQ-matrices

This paper concerns three classes of matrices that are relevant to the linear complementarity problem. We prove that within the class ofP ₀-matrices, theQ-matrices are precisely the regular matrices.Research supported by Department of Energy, Contract EY-76-S-03-0326 PA # 18.     

Development of CeO<Subscript>2</Subscript>- and TiO<Subscript>2</Subscript>-incorporated aluminium metal-composite matrix with high resistance to corrosion and biofouling

Cerium oxide (CeO₂) is a potential corrosion inhibitor for aluminium, and titanium oxide (TiO₂) is an efficient anti-fouling agent in the marine environment. The present study explored the possibility of incorporating CeO₂ and TiO₂ in aluminium to prepare a metal matrix composite that could have high corrosion and biofouling resistance under marine conditions. Such incorporation of CeO₂ and TiO₂ in pure aluminium offered high resistance to corrosion and biogrowth under marine conditions as evidenced during different tests. The specimens exhibited more anodic and stable open circuit potential throughout the period of the study. The optimum concentration of CeO₂ and TiO₂ was found to be 0.2 and 0.1%, respectively. The present results lay emphasis on the potential scope of the use of CeO₂- and TiO₂-incorporated aluminium in marine environments.     

Numerical modelling of sample–furnace thermal lag in dynamic mechanical analyser

Due to dynamic nature of processes taking place during the experiment (chemical reaction and physical processes, heat flow, gas flow, etc.) the results obtained by thermal methods may considerably depend on the conditions used during the experiment. Therefore, whenever the results of thermal analysis are reported, the experimental conditions used should be stated. In this paper we have studied the heat transfer from the furnace to the sample and through the sample during dynamic mechanical analysis measurements. Numerical modelling of the heat transfer was done using an own computer program based on the heat conduction equation, solved numerically applying the finite difference methods. The calculated values of the thermal lag between the furnace and the sample were compared with the values experimentally determined on samples of a composite polymeric energetic material (double-base rocket propellant). Also, the temperature distribution within the sample as a function of the heating rate was analysed using the same numerical model. It was found out that using this model and temperature dependent heat transfer coefficient, experimentally obtained values of the thermal lag between the furnace and the sample can be satisfactory described. It was also shown that even at slow heating rates, such is, e.g. 2 °C min⁻¹, the thermal lag between the furnace and the sample can reach several degrees, while the thermal gradient within 3-mm thick rectangular sample can reach 0.4 °C.     

The Topological Vertex

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kähler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the quantum Kodaira-Spencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.Acknowledgement We would like to thank D.-E.Diaconescu, R. Dijkgraaf, J. Gomis, A. Grassi, A. Iqbal, A. Kapustin, S. Katz, V. Kazakov, I. Kostov, C-C. Liu, H. Ooguri, J. Schwarz, S. Shenker and E. Zaslow for valuable discussions (and the cap!). The research of MA and CV was supported in part by NSF grants PHY-9802709 and DMS-0074329. In addition, CV thanks the hospitality of the theory group at Caltech, where he is a Gordon Moore Distinguished Scholar. M.A. is grateful to the Caltech theory group for hospitality during part of this work. A.K. is supported in part by the DFG grant KL-1070/2-1.