Organophosphine bearing multiple hydrogen-bond donors for asymmetric Michael addition reaction of 1-oxoindane-2-carboxylic acid ester via dual-reagent catalysis

Multiple hydrogen bonds containing nucleophilic phosphines derived from dipeptide dual-reagents catalyzed asymmetric Michael addition reactions between indene esters and activated olefins in high yields and good to excellent enantioselectivities under mild reaction conditions. The success of current highly selective reactions should provide inspiration for expansion to other reactions and would open up new paradigms for the synthesis of indanone derivatives bearing chiral quaternary carbon centers.     

Mechanical wave momentum from the first principles

Axial momentum carried by waves in a uniform waveguide is considered based on the conservation laws and a kind of the causality principle. Specifically, we examine (without resorting to constitutive data) steady-state waves of an arbitrary shape, periodic waves which speed differs from the speed of its form and binary waves carrying self-equilibrated momentum. The approach allows us to represent momentum as a product of the wave mass and the wave speed. The propagating wave mass, positive or negative, is the excess of that in the wave over its initial value. This general representation is valid for mechanical waves of arbitrary nature and intensity. The finite-amplitude longitudinal and periodic transverse waves are examined in more detail. It is shown in particular, that the transverse excitation of a string or an elastic beam results in the binary wave. The closed-form expressions for the drift in these waves functionally reduce to the Stokes’ drift in surface water waves (a half the latter by the value). Besides, based on the general representation an energy–momentum relation is discussed and the physical meaning of the so-called “wave momentum” is clarified.     

Three qubits in a symmetric environment: Dissipatively generated asymptotic entanglement

We study the asymptotic entanglement of three identical qubits under the action of a Markovian open system dynamics that does not distinguish them. We show that by adding a completely depolarized qubit to a special class of two-qubit states, by letting them reach the asymptotic state and by finally eliminating the added qubit, can provide more entanglement than by direct immersion of the two qubits within the same environment.     

Cation−π interactions in high resolution protein−RNA complex crystal structures

In this work, we have analyzed the influence of cation–π interactions to the stability of 59 high resolution protein–RNA complex crystal structures. The total number of Lys and Arg are similar in the dataset as well as the number of their interactions. On the other hand, the aromatic chains of purines are exhibiting more cation–π interactions than pyrimidines. 35% of the total interactions in the dataset are involved in the formation of multiple cation–π interactions. The multiple cation–π interactions have been conserved more than the single interactions. The analysis of the geometry of the cation–π interactions has revealed that the average distance (d) value falls into distinct ranges corresponding to the multiple (4.28 Å) and single (5.50 Å) cation–π interactions. The G–Arg pair has the strongest interaction energy of −3.68 kcal mol⁻¹ among all the possible pairs of amino acids and bases. Further, we found that the cation–π interactions due to five-membered rings of A and G are stronger than that with the atoms in six-membered rings. 8.7% stabilizing residues are involved in building cation–π interactions with the nucleic bases. There are three types of structural motifs significantly over-represented in protein–RNA interfaces: beta-turn-ir, niche-4r and st-staple. Tetraloops and kink-turns are the most abundant RNA motifs in protein–RNA interfaces. Amino acids deployed in the protein–RNA interfaces are deposited in helices, sheets and coils. Arg and Lys, involved in cation–π interactions, prefer to be in the solvent exposed surface. The results from this study might be used for structure–based prediction and as scaffolds for future protein–RNA complex design.     

An asymptotic Reissner–Mindlin plate model

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.     

Boundary Behavior of Semigroups of Holomorphic Mappings on the Unit Ball in C n

We study the asymptotic behavior of semigroups generated by holomorphic mappings by using an infinitesimal version of the boundary Schwarz-Wolff Lemma. In particular, the best rate of exponential convergence is obtained. In addition, we establish a geometrical version of the implicit function theorem.     

Resource augmentation for online bounded space bin packing

We study online bounded space bin packing in the resource augmentation model of competitive analysis. In this model, the online bounded space packing algorithm has to pack a list L of items in (0,1] into a small number of bins of size b1. Its performance is measured by comparing the produced packing against the optimal offline packing of the list L into bins of size 1.We present a complete solution to this problem: For every bin size b1, we design online bounded space bin packing algorithms whose worst case ratio in this model comes arbitrarily close to a certain bound ρ(b). Moreover, we prove that no online bounded space algorithm can perform better than ρ(b) in the worst case.     

On a Delay Reaction-Diffusion Difference Equation of Neutral Type

In this paper, we first consider a delay difference equation of neutral type of the form: Δ(y _n + py _n−k + q _n y _n−l = 0 for n∈ℤ⁺(0) (1*) and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241–248) to guarantee that every non-oscillatory solution of (1*) with p = 1 tends to zero as n→∞. Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form: Δ₁(u _n,m + pu _n−k,m ) + q _n,m u _n−l,m = a ²Δ² ₂ u _{n +1, m−1} for (n,m) ∈ℤ⁺ (0) ×Ω, (2*) study various cases of p in the neutral term and obtain that if p≥−1 then every non-oscillatory solution of (2*) tends uniformly in m∈Ω to zero as n→∞; if p = −1 then every solution of (2*) oscillates and if p < −1 then every non-oscillatory solution of (2*) goes uniformly in m∈Ω to infinity or minus infinity as n→∞ under some hypotheses. Received July 14, 1999, Revised August 10, 2000, Accepted September 30, 2000     

Absorption Spectra of Excited Ruby Crystals

We have investigated the absorption spectra of excited laser single crystals of ruby. The longlived increase in absorption depending on the degree of excitation is observed in optically excited crystals of ruby in a wide spectral range. Moreover, in the absorption spectrum of a postexcited ruby we discovered the excitationinduced longlived kinetic instability, namely, the noiselike quasiline component variable in time and over the spectrum and imposed on the smooth spectral curve.