FFT-based homogenization on periodic anisotropic translation invariant spaces

In this paper we derive a discretisation of the equation of quasi-static elasticity in homogenization in form of a variational formulation and the so-called Lippmann–Schwinger equation, in anisotropic spaces of translates of periodic functions. We unify and extend the truncated Fourier series approach, the constant finite element ansatz and the anisotropic lattice derivation. The resulting formulation of the Lippmann–Schwinger equation in anisotropic translation invariant spaces unifies and analyses for the first time both the Fourier methods and finite element approaches in a common mathematical framework. We further define and characterize the resulting periodised Green operator. This operator coincides in case of a Dirichlet kernel corresponding to a diagonal matrix with the operator derived for the Galerkin projection stemming from the truncated Fourier series approach and to the anisotropic lattice derivation for all other Dirichlet kernels. Additionally, we proof the boundedness of the periodised Green operator. The operator further constitutes a projection if and only if the space of translates is generated by a Dirichlet kernel. Numerical examples for both de la Vallée Poussin means and Box splines illustrate the flexibility of this framework.     

Single-molecule FRET studies on interactions between elongation factor 4 (LepA) and ribosomes

Elongation factor 4 interacts with both PRE- and POST- translocation ribosomal complexes and modulates sub-steps of elongation in different manners to fulfill its functions.     

Non-Newtonian pseudoplastic fluids: Analytical results and exact solutions

A one layer model of laminar non-Newtonian fluids (Ostwald-de Waele model) past a semi-infinite flat plate is revisited. The stretching and the suction/injection velocities are assumed to be proportional to x^1/(1−2n) and x⁻¹, respectively, where n is the power-law index which is taken in the interval . It is shown that the boundary-layer equations display both similarity and pseudosimilarity reductions according to a parameter γ, which can be identified as suction/injection velocity. Interestingly, it is found that there is a unique similarity solution, which is given in a closed form, if and only if γ=0 (impermeable surface). For γ≠0 (permeable surface) we obtain a unique pseudosimilarity solution for any 0≠γ≥−((n+1)/3n(1−2n))^n/(n+1). Moreover, we explicitly show that any pseudosimilarity solution exhibits similarity behavior and it is, in fact, similarity solution to a modified boundary-layer problem for an impermeable surface. In addition, the exact similarity solution of the original boundary-layer problem is used, via suitable transverse translations, to construct new explicit solutions describing boundary-layer flows induced by permeable surfaces.     

Translation map in quantum principal bundles

The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle E((B, V, A) associated to a quantum principal bundle P (B, A) are in bijective correspondence with equivariant maps V → P, and that a quantum principal bundle is trivial if it admits a cross section which is an algebra map. The vertical automorphisms and gauge transformations of a quantum principal bundle are discussed. In particular it is shown that vertical automorphisms are in bijective correspondence with Ad_R-covariant maps A → P.     

直线上带平移的奇异积分方程的解

该文讨论了直线上带实平移或复平移的奇异积分方程的解，获得了方程的可解条件，证明了方程解的唯一性，给出了方程有解的情况下解的积分或级数表达式。     

分形曲面的构造

本文利用图自相似的性质研究构造分形平移曲面，是［２］有关讨论的推广     

Ribosome kinetics and aa-tRNA competition determine rate and fidelity of peptide synthesis

It is generally accepted that the translation rate depends on the availability of cognate aa-tRNAs. In this study it is shown that the key factor that determines translation rate is the competition between near-cognate and cognate aa-tRNAs. The transport mechanism in the cytoplasm is diffusion, thus the competition between cognate, near-cognate and non-cognate aa-tRNAs to bind to the ribosome is a stochastic process. Two competition measures are introduced; C(i) and R(i) (i = 1, 64) are quotients of the arrival frequencies of near-cognates vs. cognates and non-cognates vs. cognates, respectively. Furthermore, the reaction rates of bound cognates differ from those of bound near-cognates. If a near-cognate aa-tRNA binds to the A site of the ribosome, it may be rejected at the anti-codon recognition step or proofreading step or it may be accepted. Regardless of its fate, the near-cognates and non-cognates have caused delays of varying duration to the observed rate of translation. Rate constants have been measured at a temperature of 20 °C by (Gromadski, K.B., Rodnina, M.V., 2004. Kinetic determinants of high-fidelity tRNA discrimination on the ribosome. Mol. Cell 13, 191–200). These rate constants have been re-evaluated at 37 °C, using experimental data at 24.5 °C and 37 °C (Varenne, S., et al., 1984. Translation in a non-uniform process: effect of tRNA availability on the rate of elongation of nascent polypeptide chains. J. Mol. Biol. 180, 549–576). The key results of the study are: (i) the average time (at 37 °C) to add an amino acid, as defined by the ith codon, to the nascent peptide chain is: τ(i) = 9.06 + 1.445 × [10.48C(i) + 0.5R(i)] (in ms); (ii) the misreading frequency is directly proportional to the near-cognate competition, E(i) = 0.0009C(i); (iii) the competition from near-cognates, and not the availability of cognate aa-tRNAs, is the most important factor that determines the translation rate – the four codons with highest near-cognate competition (in the case of E. coli) are [GCC] > [CGG] > [AGG] > [GGA], which overlap only partially with the rarest codons: [AGG] < [CCA] < [GCC] < [CAC]; (iv) based on the kinetic rates at 37 °C, the average time to insert a cognate amino acid is 9.06 ms and the average delay to process a near-cognate aa-tRNA is 10.45 ms and (vii) the model also provides estimates of the vacancy times of the A site of the ribosome – an important factor in frameshifting.