Delay Equations with Non-negativity Constraints Driven by a Hölder Continuous Function of Order \beta \in \left(\frac13,\frac12\right)

In this note we prove an existence and uniqueness result of solution for multidimensional delay differential equations with normal reflection and driven by a Hölder continuous function of order \(\beta \in (\frac13,\frac12)\) . We also obtain a bound for the supremum norm of this solution. As an application, we get these results for stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H \(\in (\frac13,\frac12)\) .     

A DFT Study on the Mechanism of the Cycloaddition Reaction of CO2 to Epoxides Catalyzed by Zn(Salphen) Complexes

The reaction mechanism for the Zn(salphen)/NBu₄X (X=Br, I) mediated cycloaddition of CO₂ to a series of epoxides, affording five‐membered cyclic carbonate products has been investigated in detail by using DFT methods. The ring‐opening step of the process was examined and the preference for opening at the methylene (C_β) or methine carbon (C_α) was established. Furthermore, calculations were performed to clarify the reasons for the lethargic behavior of internal epoxides in the presence of the binary catalyst. Also, the CO₂ insertion and the ring‐closing steps have been explored for six differently substituted epoxides and proved to be significantly more challenging compared with the ring‐opening step. The computational findings should allow the design and application of more efficient catalysts for organic carbonate formation.     

Energetic salts of the binary 5-cyanotetrazolate anion ([C2N5]-) with nitrogen-rich cations

The reaction of cyanogen (NC-CN) with MN(3) (M=Na, K) in liquid SO(2) leads to the formation of the 5-cyanotetrazolate anion as the monohemihydrate sodium (1·1.5 H(2)O) and potassium (2) salts, respectively. Both 1·1.5 H(2)O and 2 were used as starting materials for the synthesis of a new family of nitrogen-rich salts containing the 5-cyanotetrazolate anion and nitrogen-rich cations, namely ammonium (3), hydrazinium (4), semicarbazidium (5), guanidinium (6), aminoguanidinium (7), diaminoguanidinium (8), and triaminoguanidinium (9). Compounds 1-9 were synthesised in good yields and characterised by using analytical and spectroscopic methods. In addition, the crystal structures of 1·1.5 H(2)O, 2, 3, 5, 6, and 9·H(2)O were determined by using low-temperature single-crystal X-ray diffraction. An insight into the hydrogen bonding in the solid state is described in terms of graph-set analysis. Differential scanning calorimetry and sensitivity tests were used to assess the thermal stability and sensitivity against impact and friction of the materials, respectively. For the assessment of the energetic character of the nitrogen-rich salts 3-9, quantum chemical methods were used to determine the constant volume energies of combustion, and these values were used to calculate the detonation velocity and pressure of the salts using the EXPLO5 computer code. Additionally, the performances of formulations of the new compounds with ammonium nitrate and ammonium dinitramide were also predicted. Lastly, the ICT code was used to determine the gases and heats of explosion released upon decomposition of the 5-cyanotetrazolate salts.     

The preparation and characterization of guanylurea nitrate and perchlorate salts

Guanylurea nitrate (GUN) and guanylurea perchlorate (GUP) were prepared from cyanoguanidine (CG) and concentrated nitric or perchloric acid, respectively. Both compounds were fully characterized by analytical and spectroscopic methods. Crystals of GUP were grown from water, and its crystal structure was determined by single‐crystal X‐ray diffraction. GUP crystallizes in the monoclinic space group P2₁/c with four molecules in the unit cell; different unit cell parameters are a = 8.0115(2) Å, b = 9.7328(2) Å c = 9.5770(2) Å and β = 105.89(1)°. The heats of combustion of both compounds were determined using oxygen bomb calori‐metry. Finally, the EXPLO5 computer code was used to determine the detonation velocity (D = 5734 m s⁻¹) and pressure (P = 10.6 GPa) of GUN as well as those of formulations with ammonium nitrate and dinitramide. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:301–306, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20419     

Detection of Cheaters in Vector Space Secret Sharing Schemes

A perfect secret sharing scheme is a method of distributing shares of a secret among a set P of participants in such a way that only qualified subsets of P can reconstruct the secret from their shares and non-qualified subsets have absolutely no information on the value of the secret. In a secret sharing scheme, some participants could lie about the value of their shares in order to obtain some illicit benefit. Therefore, the security against cheating is an important issue in the implementation of secret sharing schemes. Two new secret sharing schemes in which cheaters are detected with high probability are presented in this paper. The first one has information rate equal to 1/2 and can be implemented not only in threshold structures, but in a more general family of access structures. We prove that the information rate of this scheme is almost optimal among all schemes with the same security requirements. The second scheme we propose is a threshold scheme in which cheaters are detected with high probability even if they know the secret. The information rate is in this case 1/3 In both schemes, the probability of cheating successfully is a fixed value that is determined by the size of the secret.     

Bicyclic Guanidine Promoted Mechanistically Divergent Depolymerization and Recycling of a Biobased Polycarbonate

We here report the organocatalytic and temperature-controlled depolymerization of biobased poly(limonene carbonate) providing access to its trans-configured cyclic carbonate as the major product. The base TBD (1,5,7-triazabicyclo[4.4.0]dec-5-ene) offers a unique opportunity to break down polycarbonates via end-group activation or main chain scission pathways as supported by various controls and computational analysis. These energetically competitive processes represent an unprecedented divergent approach to polycarbonate recycling. The trans limonene carbonate can be converted back to its polycarbonate via ring-opening polymerization using the same organocatalyst in the presence of an alcohol initiator, offering thus a potential circular and practical route for polycarbonate recycling.