Relative entropy maximization and directed diffusion equations

Motivated by the concept of maximum entropy methods in signal and image processing, we introduce and discuss a class of ‘directed diffusion equations’ with suitable boundary conditions. The paradigmatic ‘directed diffusion equation’ is The relative entropy $ Sb[f](t): = - \int_\Omega {f(t,x)} \;\ln \;(f(t,x)/b(x))dx $ is rapidly increasing along solution trajectories of (i). This suggests that solving (i) will yield efficient procedures for entropy maximization. We also discuss the asymptotic behavior of solutions of (i)—this is readily done because (i) has a large family of Ljapunov functionals.     

Neue anorganische Ringsysteme. 34. Derivate eines Cyclo-1-thiaIV- und eines Cyclo-1-thiaIV- 3,4-disila-2,5-diazans

Novel Inorganic Ring Systems. 34. Derivatives of the Cyclo-1-thia^IV- and of the Cyclo-1-thia ^VI-3,4-disila-2,5-diazane Variations of fivemembered “hetero” cyclosilazanes of the type Si₂N₂El could be enlarged to the systems with El = SO and SO₂. They are obtained by the formation principles 4 + 1 and 2 + 3 respectively, according to the equation (1), (4) and (5). The prepared compound are described in their properties and confirmed in their structure (Tables 1–2).     

Synthetically attractive indolization processes and newer methods for the preparation of selectively substituted indoles

The synthetically interesting processes available for indolization reactions are discussed and illustrated in tabular form and particular emphasis is placed on the more recent methods.     

A case study in conformation design: learning by doing

Efforts are described to design simple, fully flexible but conformationally preorganised omega-hydroxy-nonanoic acids that could serve as the conformation controlling unit in analogues of the potent protein-kinase C activator aplysiatoxin. Such analogues are macrodilactones incorporating the designed omega-hydroxy-nonanoic acid and 3,4-dihydroxy-pentanoic acid, which contains the pharmacophoric groups. The design process (replacement of CH(2) groups by an oxygen atom, annelation of a six-membered ring and placement of alkyl substituents) of the omega-hydroxy-nonanoic acids was monitored by force-field calculations. In the end of this process simple analogues of aplysiatoxin are proposed in which the proper disposition of the pharmacophoric groups is secured by a conformationally flexible but preorganised template structure as part of the macrodilactone ring.     

Time-dependent close coupling for vibrational excitation in three dimensions: Application to H+ - H2

Impact parameter calculations for the non-reactive H⁺ + H₂ (n_i = 0) → H⁺ + H₂ (n_f) collision are reported for energies 10 eV ? E_cm ? 200 eV describing the rotational motion of the molecule in the sudden limit. The time-dependent Schrödinger equation for the vibrational motion has been solved by close coupling techniques expanding the vibrational wavefunction into both harmonic and numerically exact H₂ bound states. The convergence in vibrational basis sets, where up to six vibrational levels are considered, becomes worse with decreasing energy and increasing inelasticity. Furthermore, the harmonic wavefunctions are not suitable over a large range of energies to calculate proper cross sections. The various integral and differential cross sections have been compared with the classical results of Giese and Gentry.     

3D H-bonding networks self-assembly from pyridinium derivatives and bis(maleonitriledithiolato)zincate(II)

The two ion-pair complexes, [pyH]₂[Zn(mnt)₂] (1) and [4,4′-bipyH₂]-[Zn(mnt)₂] (2), were synthesized, where mnt²⁻ denotes maleonitriledithiolate, and [pyH]⁺, [4,4′-bipyH₂]²⁺ represent pyridinium and diprotonated 4,4′-bipyridinium, respectively. Their single crystal structures show that there are strong bifurcated H-bonding interactions between the cations of the pyridinium derivative and the [Zn(mnt)₂]²⁻ anions in both 1 and 2. The bifurcated H-bonding interactions between the N–H of the pyridiniums and the CN groups of the mnt²⁻ ligands give rise to a 2D layered H-bonding network, the adjacent layers come together in such way as mutual embrace to give a tight pack, thus 2D hydrogen-bonding sheets further develop into 3D H-bonding networks through weak C–HS and ππ stacking interactions in 1. As for 2, the cations and anions connect into several types of H-bonding macrorings ([2+2], [3+3] and [4+4]), these H-bonding macrorings fuse to extend into 2D layered structure, the interpenetration between [3+3] and [4+4] type H-bonding macrorings in the adjacent layers give further rise to novel 3D extended H-bonding networks, in which there are clearly parallel stacks of cations and the chelate rings of anions.     

Intramolecular charge transfer with the planarized 4-aminobenzonitrile 1-tert-butyl-6-cyano-1,2,3,4-tetrahydroquinoline (NTC6)

Fast and efficient intramolecular charge transfer (ICT) and dual fluorescence is observed with the planarized aminobenzonitrile 1-tert-butyl-6-cyano-1,2,3,4-tetrahydroquinoline (NTC6) in a series of solvents from n-hexane to acetonitrile and methanol. Such a reaction does not take place for the related molecules with 1-isopropyl (NIC6) and 1-methyl (NMC6) groups, nor with the 1-alkyl-5-cyanoindolines with methyl (NMC5), isopropyl (NIC5), or tert-butyl (NTC5) substituents. For these molecules, a single fluorescence band from a locally excited (LE) state is found. The charge transfer reaction of NTC6 is favored by its relatively small energy gap DeltaE(S(1),S(2)), in accordance with the PICT model for ICT in aminobenzonitriles. For the ICT state of NTC6, a dipole moment of around 19 D is obtained from solvatochromic measurements, similar to micro(e)(ICT) = 17 D of 4-(dimethylamino)benzonitrile (DMABN). For NMC5, NIC5, NTC5, NMC6, and NIC6, a dipole moment of around 10 D is determined by solvatochromic analysis, the same as that of the LE state of DMABN. For NTC6 in diethyl ether at -70 degrees C, the forward ICT rate constant (1.3 x 10(11) s(-1)) is much smaller than that of the back reaction (5.9 x 10(9) s(-1)), showing that the equilibrium is on the ICT side. The results presented here make clear that ICT can very well take place with a planarized molecule such as NTC6, when DeltaE(S(1),S(2)) is sufficiently small, indicating that a perpendicular twist of the amino group relative to the rest of the molecule is not necessary for reaching an ICT state with a large dipole moment. The six-membered alicyclic ring in NMC6, for example, prevents ICT by increasing DeltaE(S(1),S(2)) relative to that of DMABN.     

Low distortion recording of transient low- light-level phenomena

Two types of low-light-level image sensors have been investigated for use in low distortion recording: an SIT-vidicon (Silicon-Intensifier Target), and a sensor consisting of a newvicon and two stage proxifier. The results are compared and discussed. In addition, a triggerable video frame store is described.