Mixed micellization between natural and synthetic block copolymers: β-casein and Lutrol F-127

Amphiphilic block copolymers and mixtures of amphiphiles find broad applications in numerous technologies, including pharma, food, cosmetic and detergency. Here we report on the interactions between a biological charged diblock copolymer, β-casein, and a synthetic uncharged triblock copolymer, Lutrol F-127 (EO(101)PO(56)EO(101)), on their mixed micellization characteristics and the micelles' structure and morphology. Isothermal titration calorimetry (ITC) experiments indicate that mixed micelles form when Lutrol is added to monomeric as well as to assembled β-casein. The main driving force for the mixed micellization is the hydrophobic interactions. Above β-casein CMC, strong perturbations caused by penetration of the hydrophobic oxypropylene sections of Lutrol into the protein micellar core lead to disintegration of the micelles and reformation of mixed Lutrol/β-casein micelles. The negative enthalpy of micelle formation (ΔH) and cooperativity increase with raising β-casein concentration in solution. ζ-potential measurements show that Lutrol interacts with the protein micelles to form mixed micelles even below its critical micellization temperature (CMT). They further indicate that Lutrol effectively masks the protein charges, probably by forming a coating layer of the ethyleneoxide rich chains. Small-angle X-ray scattering (SAXS) and cryogenic-transmission electron microscopy (cryo-TEM) indicate relatively small changes in the oblate micellar shape, but do show swelling along the small axis of β-casein micelles in the presence of Lutrol, thereby confirming the formation of mixed micelles.     

Bias-controlled selective excitation of vibrational modes in molecular junctions: a route towards mode-selective chemistry

We show that individual vibrational modes in single-molecule junctions with asymmetric molecule-lead coupling can be selectively excited by applying an external bias voltage. Thereby, a non-statistical distribution of vibrational energy can be generated, that is, a mode with a higher frequency can be stronger excited than a mode with a lower frequency. This is of particular interest in the context of mode-selective chemistry, where one aims to break specific (not necessarily the weakest) chemical bond in a molecule. Such mode-selective vibrational excitation is demonstrated for two generic model systems representing asymmetric molecular junctions and/or scanning tunneling microscopy experiments. To this end, we employ two complementary theoretical approaches, a nonequilibrium Green's function approach and a master equation approach. The comparison of both methods reveals good agreement in describing resonant electron transport through a single-molecule contact, where differences between the approaches highlight the role of non-resonant transport processes, in particular co-tunneling and off-resonant electron-hole pair creation processes.     

Diophantine Approximations on Fractals

We exploit dynamical properties of diagonal actions to derive results in Diophantine approximations. In particular, we prove that the continued fraction expansion of almost any point on the middle third Cantor set (with respect to the natural measure) contains all finite patterns (hence is well approximable). Similarly, we show that for a variety of fractals in [0, 1]², possessing some symmetry, almost any point is not Dirichlet improvable (hence is well approximable) and has property C (after Cassels). We then settle by similar methods a conjecture of M. Boshernitzan saying that there are no irrational numbers x in the unit interval such that the continued fraction expansions of {nx mod 1}_{n ? \mathbb N}{\{nx\,{\rm mod}\,1\}_{n \in {\mathbb N}}} are uniformly eventually bounded.     

Wave propagation in parallel-plate waveguides filled with nonlinear left-handed material

A theoretical investigation of field components for transverse electric mode in the parallel-plate waveguides has been studied. In this analysis two different types of waveguide structures have been discussed, i.e., (a) normal good/perfect conducting parallel-plate waveguide filled with nonlinear left-handed material and (b) high-temperature-superconducting parallel-plate waveguide filled with nonlinear left-handed material. The dispersion relations of transverse electric mode have also been discussed for these two types of waveguide structures.     

Jumps of computably enumerable equivalence relations

We study computably enumerable equivalence relations (or, ceers), under computable reducibility ≤, and the halting jump operation on ceers. We show that every jump is uniform join-irreducible, and thus join-irreducible. Therefore, the uniform join of two incomparable ceers is not equivalent to any jump. On the other hand there exist ceers that are not equivalent to jumps, but are uniform join-irreducible: in fact above any non-universal ceer there is a ceer which is not equivalent to a jump, and is uniform join-irreducible. We also study transfinite iterations of the jump operation. If a is an ordinal notation, and E is a ceer, then let $E^{(a)}$ denote the ceer obtained by transfinitely iterating the jump on E along the path of ordinal notations up to a. In contrast with what happens for the Turing jump and Turing reducibility, where if a set X is an upper bound for the A-arithmetical sets then $X^{(2)}$ computes $A^{(\omega )}$, we show that there is a ceer R such that $R\ge {\mathrm{Id}}^{(n)}$, for every finite ordinal n, but, for all k, $R^{(k)}?{\mathrm{Id}}^{(\omega )}$ (here Id is the identity equivalence relation). We show that if $a,b$ are notations of the same ordinal less than ${\omega }^2$, then $E^{(a)}\equiv E^{(b)}$, but there are notations $a,b$ of ${\omega }^2$ such that ${\mathrm{Id}}^{(a)}$ and ${\mathrm{Id}}^{(b)}$ are incomparable. Moreover, there is no non-universal ceer which is an upper bound for all the ceers of the form ${\mathrm{Id}}^{(a)}$ where a is a notation for ${\omega }^2$.     

Molecular shift register and its utilization as an autonomous DNA synthesizer

A novel algorithmic approach to the synthesis of fairly long DNA molecules with nonrecurring sequences is demonstrated. The scheme exploits chemical embodiment of shift registers (SR) to execute algorithms similar to those used to generate pseudorandom numbers on a computer. Single stranded DNA molecules guide the synthesis of double stranded DNA according to the SR truth table. The SR logic facilitates an exponentially smaller synthesis effort compared with all other strategies. A redundancy based scheme, similar to those used in communication, is utilized to suppress synthesis errors.     

On the relation between finitely and infinitely repeated games with incomplete information

For a class of repeated two-person zero-sum games with incomplete information it was proved byAumann andMaschler that \(\mathop {\lim }\limits_{n \to \infty } v_n\) exists,Ν _n being the value of the game withn repetitions. As for the speed of convergenceAumann andMaschler showed that the error termδ _n=¦Ν _n?limΝ _n¦ is bounded from above byc/√n for some positive constantc. Both results have been generalized byMertens andZamir. It is shown in this paper that the above mentioned theorem about the speed of convergence is sharp in the sense that there are games in whichδ _n≥c′/√n for some positive constantc′. However there are games for which δ_n is of a lower order of magnitude, for instancec′(logn)/n≤δ _n≤c (logn)/n orc′/n≤δ _n≤c/n. Sufficient conditions are given here for games to belong to one of these categories as well as examples of games from each category.     

Attempted synthesis of 2,4- and 1,3-benzodiazepinones

The cyclodehydration reaction performed upon α-acylamino carboxamides is known to constitute a facile synthetic approach to five-membered heterocyclic systems. Attempts to prepare 2,4- and 1,3-benzodiazepinone derivatives (VI, XIX) of potential C.N.S. Activity using such methods, proved unsuccessful. A new triazine system (X) which was prepared did not exhibit any C.N.S. activity.