On the way towards a generalized entropy maximization procedure

We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Rényi and Tsallis entropies. The generalized entropy maximization procedure for Rényi entropies results in the exponential stationary distribution asymptotically for q∈(0,1] in contrast to the stationary distribution of the inverse power law obtained through the ordinary entropy maximization procedure. Another result of the generalized entropy maximization procedure is that one can naturally obtain all the possible stationary distributions associated with the Tsallis entropies by employing either ordinary or q-generalized Fourier transforms in the averaging procedure.     

Phosphorus-nitrogen compounds. Part 13. Syntheses, crystal structures, spectroscopic, stereogenic, and anisochronic properties of novel spiro-ansa-spiro-, spiro-bino-spiro-, and spiro-crypta phosphazene derivatives

The condensation reactions of N2Ox (x = 2, 3) donor-type aminopodand (4) and dibenzo-diaza-crown ethers (5, 6, and 9) with hexachlorocyclotriphosphazatriene, N3P3Cl6, produce two kinds of partially substituted novel phosphazene derivatives, namely, spiro-bino-spiro- (19) and spiro-crypta (21, 22, and 25) phosphazenes. The partially substituted spiro-ansa-spiro-phosphazene (11) reacted with pyrrolidine and 1,4-dioxa-8-azaspiro[4,5]decane (DASD) give the corresponding new fully substituted phosphazenes (14 and 16). Unexpectedly, the reactions of 23 and 24 with pyrrolidine result in only geminal crypta phosphazenes (26 and 27). The solid-state structures of 16 and 22 have been determined by X-ray diffraction techniques. The relative inner hole-size of the macrocycle in the radii of 22 is 1.27 A. The relationship between the exocyclic NPN (alpha') and endocyclic (alpha) bond angles for spiro-crypta phosphazenes and exocyclic OPN (alpha') bond angles for spiro-ansa-spiro- and spiro-bino-spiro-phosphazenes with 31P NMR chemical shifts of NPN and OPN phosphorus atoms, respectively, have been investigated. The structures of 10, 14, 16, 19, 21, 22, and 25-27 have also been examined by FTIR, 1H, 13C, and 31P NMR, HETCOR, MS, and elemental analyses. The 31P NMR spectra of 10, 21, 22, and 25 indicate that the compounds have anisochrony. In compounds 16 and 22, the spirocyclic nitrogen atoms have pyramidal geometries resulting in stereogenic properties.     

On Two Equivalent Dilation Theorems in VH-Spaces

We prove that a generalized version, essentially obtained by R.M. Loynes, of the B. Sz.-Nagy??s Dilation Theorem for ${\mathcal{B}^*(\mathcal{H})}$ -valued (here ${\mathcal{H}}$ is a VH-space in the sense of Loynes) positive semidefinite maps on *-semigroups is equivalent with a generalized version of the W.F. Stinespring??s Dilation Theorem for ${\mathcal{B}^*(\mathcal{H})}$ -valued completely positive linear maps on B ^*-algebras. This equivalence result is a generalization of a theorem of F.H. Szafraniec, originally proved for the case of operator valued maps (that is, when ${\mathcal{H}}$ is a Hilbert space).     

Minimizing Constant Mean Curvature Hypersurfaces in Hyperbolic Space

We study the constant mean curvature (CMC) hypersurfaces in whose asymptotic boundaries are closed codimension-1 submanifolds in . We consider CMC hypersurfaces as generalizations of minimal hypersurfaces. We naturally generalize some notions of minimal hypersurfaces like being area-minimizing, convex hull property, exchange roundoff trick to CMC hypersurface context. We also give a generic uniqueness result for CMC hypersurfaces in hyperbolic space.     

[1,2,5]thiadiazolo[3,4‐g]quinoxaline acceptor‐based donor–acceptor–donor‐type polymers: Effect of strength and size of donors on the band gap

Electrochromic polymers based on [1,2,5]thiadiazolo[3,4‐g]quinoxaline acceptor and thiophene, 3,4‐ethylenedioxythiophene and 3,3‐didecyl‐3,4‐proylenedioxythiophene donors, namely poly(6,7‐diphenyl‐4,9‐di(thiophen‐2‐yl)‐[1,2,5]thiadiazolo[3,4‐g]quinoxaline) ( P1 ), poly(4‐(2,3‐dihydrothieno[3,4‐b][1,4]dioxin‐5‐yl)‐9‐(2,3‐dihydrothieno[3,4‐b][1,4]dioxin‐7‐yl)‐6,7‐diphenyl‐[1,2,5]thiadiazolo[3,4‐g]quinoxaline) ( P2 ), and poly(4‐(3,3‐didecyl‐3,4‐dihydro‐2H‐thieno[3,4‐b][1,4]dioxepin‐6‐yl)‐9‐(3,3‐didecyl‐3,4‐dihydro‐2H‐thieno[3,4‐b][1,4]dioxepin‐8‐yl)‐6,7‐diphenyl‐[1,2,5]thiadiazolo[3,4‐g]quinoxaline) ( P3 ), respectively, were electrochemically and/or chemically synthesized and characterized. Electrochemical and optical properties of the polymers were then investigated. The results, which were obtained electrochemically and optically, indicate that the polymers bearing the same acceptor and different donor units have a band gap range of 0.59–1.24 eV depending on the strength and size of the donor units and band gap determination method. A significant finding in this study was the phenomenon that when the acceptor is physically huge, the general rule that a weak donor would have a high band gap whereas a strong donor would have low band gap can be broken due to the torsional angles/steric hindrances involved with physically large donor molecules. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3483–3493     

Low‐Fouling Fluoropolymers for Bioconjugation and In Vivo Tracking

The conjugation of hydrophilic low‐fouling polymers to therapeutic molecules and particles is an effective approach to improving their aqueous stability, solubility, and pharmacokinetics. Recent concerns over the immunogenicity of poly(ethylene glycol) has highlighted the importance of identifying alternative low fouling polymers. Now, a new class of synthetic water‐soluble homo‐fluoropolymers are reported with a sulfoxide side‐chain structure. The incorporation of fluorine enables direct imaging of the homopolymer by ¹⁹F MRI, negating the need for additional synthetic steps to attach an imaging moiety. These self‐reporting fluoropolymers show outstanding imaging sensitivity and remarkable hydrophilicity, and as such are a new class of low‐fouling polymer for bioconjugation and in vivo tracking.