Large free sets in powers of universal algebras

We prove that for each universal algebra ${(A, \mathcal{A})}$ of cardinality ${|A| \geq 2}$ and infinite set X of cardinality ${|X| \geq | \mathcal{A}|}$ , the X-th power ${(A^{X}, \mathcal{A}^{X})}$ of the algebra ${(A, \mathcal{A})}$ contains a free subset ${\mathcal{F} \subset A^{X}}$ of cardinality ${|\mathcal{F}| = 2^{|X|}}$ . This generalizes the classical Fichtenholtz–Kantorovitch–Hausdorff result on the existence of an independent family ${\mathcal{I} \subset \mathcal{P}(X)}$ of cardinality ${|\mathcal{I}| = |\mathcal{P}(X)|}$ in the Boolean algebra ${\mathcal{P}(X)}$ of subsets of an infinite set X.     

Experimental quantum cloning with prior partial information

When prior partial information about a state to be cloned is available, it can be cloned with a fidelity higher than that of universal quantum cloning. We experimentally verify this intriguing relationship between the cloning fidelity and the prior information by reporting the first experimental optimal quantum state-dependent cloner, using nuclear magnetic resonance techniques. Our experiments may further cast important implications into many quantum information processing protocols.     

Entanglement interferometry for precision measurement of atomic scattering properties

We report on a matter wave interferometer realized with entangled pairs of trapped 87Rb atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin superposition of the two atoms and then tuning the interstate scattering length via a Feshbach resonance. The selective change of the interstate scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic interaction parameters. Furthermore, the interferometer allows us to separate lattice sites with one or two atoms in a nondestructive way.     

Mirror inversion of quantum states in linear registers

Transfer of data in linear quantum registers can be significantly simplified with preengineered but not dynamically controlled interqubit couplings. We show how to implement a mirror inversion of the state of the register in each excitation subspace with respect to the center of the register. Our construction is especially appealing as it requires no dynamical control over individual interqubit interactions. If, however, individual control of the interactions is available then the mirror inversion operation can be performed on any substring of qubits in the register. In this case, a sequence of mirror inversions can generate any permutation of a quantum state of the involved qubits.     

Phenol adsorption on closed carbon nanotubes

We present the results of systematic studies of phenol adsorption on closed commercially available, unmodified carbon nanotubes. Phenol adsorption is determined by the value of tube-specific surface area, the presence of small amount of surface groups influence adsorption only in very small amount. Phenol can be applied as a probe molecule for comparative analysis of tube surface areas. Tube curvature influences adsorption from solution, i.e., we observe increasing adsorption energy (and slower desorption process) with the decrease in tube curvature. This is in full accordance with molecular simulation results.     

Synthesis of porphyrin indolin-2-one conjugates via palladium-catalyzed amination reactions

New porphyrin indolin-2-one conjugates were synthesized via palladium-catalyzed amination reactions of iodinated and dibrominated indolin-2-one derivatives with (2-amino-5,10,15,20-tetraphenylporphyrinato)nickel(II). The combination of palladium catalysts and the phosphine ligand dicyclohexylphosphino-2′,4′,6′-triisopropylbiphenyl (XPhos) is an effective methodology for catalyzing the coupling of 5-iodo-, 5,7-dibromo- and 4,6-dibromo-1,3,3-trimethylindolin-2-one with 2-aminoporphyrin to give the corresponding mono-(2-aminoporphyrinyl)- and di-(2-aminoporphyrinyl)-substituted indolin-2-ones in satisfactory yields under mild conditions. The mono brominated porphyrinic derivatives also underwent cross-coupling reactions under similar catalytic conditions. The studies also demonstrated that the course of the coupling process depends on factors, such as the catalytic system, number and position of the halogen substituents and the heating condition. Insights into the reactivity trends of the 5-iodo; 4,6- and 5,7-dibrominated indolin-2-one derivatives was carried out using theoretical calculations performed using density-functional theory with the B3LYP functional.     

Reaction of N-(Benzyloxycarbonyl)aminobenzyl-phosphonous Acid with Ethyl Orthoformate

Reaction of N-(benzyloxycarbonyl)aminobenzylphosphonous acid with ethyl orthoformate afforded two major products diethyl N-(benzyloxycarbonyl)aminobenzylphosphhite and ethyl (diethoxymethyl)[N-(benzyloxy-carbonyl)aminobenzyl]phosphmate, a product of addition of phosphonous acid to orthoformate.     

Transport properties of alkyltrimethylammonium bromide surfactants in aqueous solutions

Differential mutual diffusion coefficients of n-alkyltrimethylammonium bromides [CH₃(CH₂)_n–1N(CH₃)₃Br, C_nTAB] (n=10, 12, 14, 16) have been measured in aqueous solutions at 298.15 K using a conductimetric cell and an automatic apparatus to follow diffusion. The cell is based on an open-ended capillary, and the technique follows the diffusion process by measuring the resistance of a solution inside the capillaries at various times. The electrical conductances of those solutions have also been measured to calculate the critical micellar concentration (cmc). Thermodynamic analysis of the data suggests that the free ion concentration decreases at concentrations above the cmc, in agreement with theoretical predictions. The obtained values of the micellization parameters were used to model the mutual diffusion coefficients of C_nTAB aqueous solutions.