Vector Hulls of Affine Spaces and Affine Bundles

Every affine space A can be canonically immersed as a hyperplane into a vector space  , which is called the vector hull of A. This immersion satisfies a universal property for affine functions defined on A. In the same way, every affine map between affine spaces has a linear prolongation to their vector hulls. Though not much known, this construction is greatly clarifying, both for affine geometry and for its applications. The goal of this paper is to perform a thorough study of the vector hull functor and to describe its counterpart in the framework of affine bundles. With this respect, it is shown that the vector hull of some interesting affine bundles, and more specifically some jet bundles, can be identified with certain vector bundles.      

Initial density fluctuations effects on the microphase separation in ramified polymer mixture

Our study focuses on the initial density fluctuations effects on microphase separation in ramified polymer mixture. For this purpose, we introduce a screening length κ   by considering the condition that the scattered intensity should not be changed by cross-linking. We recover that κ²∼C/(χ−χi)${\kappa }^2\sim C/(\chi -{\chi }_i)$, where C is the rigidity constant of the network and χ the Flory parameter. Three regimes versus the temperature of the mixture are discussed. The kinetics of the microphase separation is also studied through the relaxation rate. The derived relaxation rate evolution relative to ramified polymers mixture must be compared to that relative to a linear polymer mixture. Finally, we discuss the solvent effect on the microphase separation and we show that the initial fluctuations have little importance because of the excluded volume interaction.     

Synthesis and evaluation of hexitol nucleoside congeners as ambiguous nucleosides

A series of anhydrohexitol nucleoside congeners was synthesized as ambiguous or so-called universal nucleosides and was evaluated for their hybridization potential and discrimination properties. The 1,5-anhydro-2,3-dideoxy-2-(5-nitroindazol-1-yl)-d-arabino-hexitol 4e showed the lower spread in T_m values upon hybridization to the natural bases, with minimal destabilization, and therefore behaved as a true ambiguous nucleoside.     

Classical kinetic energy,quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson’s stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsäcker term and an (N?1)-electron kinetic correlation term. We further show that the Weizsäcker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. We then write the N-electron classical kinetic energy as the sum of the (one-electron) classical kinetic energy and another (N?1)-electron kinetic correlation term. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsäcker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase, and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases. Finally, we underline that, although our aim in this paper is conceptual rather than practical, our results are potentially useful for the construction of improved kinetic-energy functionals.     

Coarse-grained force field for the nucleosome from self-consistent multiscaling

A coarse-grained simulation model for the nucleosome is developed, using a methodology modified from previous work on the ribosome. Protein residues and DNA nucleotides are represented as beads, interacting through harmonic (for neighboring) or Morse (for nonbonded) potentials. Force-field parameters were estimated by Boltzmann inversion of the corresponding radial distribution functions obtained from a 5-ns all-atom molecular dynamics (MD) simulation, and were refined to produce agreement with the all-atom MD simulation. This self-consistent multiscale approach yields a coarse-grained model that is capable of reproducing equilibrium structural properties calculated from a 50-ns all-atom MD simulation. This coarse-grained model speeds up nucleosome simulations by a factor of 10(3) and is expected to be useful in examining biologically relevant dynamical nucleosome phenomena on the microsecond timescale and beyond.     

Gamma-ray irradiation and characterization of synthesized bidentate and tetradentate Schiff base ligands and their complexes with some transition metal ions

Salen ligands are essential for coordinating a diverse group of metals in their respective oxidation states. This creates significant complexes of salen metals that are used in different fields. Condensation of ehylenediamine (en) with p-methoxybenzaldehyde (L¹) or o-hydroxyacetophenone (L²) with a ratio 1: 2 (en: p-methoxybenzaldehyde or o-hydroxyacetophenone) or by the interaction of o-phenylenediamine (phen) with o-hydroxybenzaldehyde (L³) or p-hydroxybenzaldehyde (L⁴) with a ratio 1: 2 (phen: o-hydroxybenzaldehyde or p-hydroxybenzaldehyde) has been used to prepare four symmetrical Schiff bases (L¹-L⁴). The UV–vis spectroscopy has been used to investigate the diverse electronic transitions associated with the Schiff bases molecules as well as how these transitions are impacted by diverse polarities of solvents. Elemental analysis, FT-IR, UV–vis spectra, molar conductivity, and ¹H NMR have been used to characterise all the compounds obtained in this process. The continuous variation applied alongside molar ratio spectral methods showed the formation of different complexes arising from the reaction of the ligand (L^1-L⁴) with the metal ions Mn(II), Fe(III) and Cu(II) is 1: 1 and/ or 1: 2 (M: L). A series of universal buffer solutions (20 % ethanol v/v) with varying pH values were used in spectrophotometry to determine the acid dissociation constants of the L² and L⁴ ligands. Gamma radiation was applied to examine the compounds’ irradiation stability. Additionally, the absorptions of the main functional groups were screened using FT-IR spectra before and after Gamma irradiation. The results show that all the compounds are stable after irradiation process; therefore, it could be used as enhancing agents in cancer therapy.     

Thermal Ripples in Model Molybdenum Disulfide Monolayers

Molybdenum disulfide (MoS₂) monolayers have the potential to revolutionize nanotechnology. To reach this potential, it will be necessary to understand the behavior of this two‐dimensional (2D) material on large length scales and under thermal conditions. Herein, we use molecular dynamics (MD) simulations to investigate the nature of the rippling induced by thermal fluctuations in monolayers of the 2H and 1T phases of MoS₂. The 1T phase is found to be more rigid than the 2H phase. Both monolayer phases are predicted to follow long wavelength scaling behavior typical of systems with anharmonic coupling between vibrational modes as predicted by classic theories of membrane‐like systems.     

Coupling a universal DNA circuit with graphene sheets/polyaniline/AuNPs nanocomposites for the detection of BCR/ABL fusion gene

This article described a novel method by coupling a universal DNA circuit with graphene sheets/polyaniline/AuNPs nanocomposites (GS/PANI/AuNPs) for highly sensitive and specific detection of BCR/ABL fusion gene (bcr/abl) in chronic myeloid leukemia (CML). DNA circuit known as catalyzed hairpin assembly (CHA) is enzyme-free and can be simply operated to achieve exponential amplification, which has been widely employed in biosensing. However, application of CHA has been hindered by the need of specially redesigned sequences for each single-stranded DNA input. Herein, a transducer hairpin (HP) was designed to obtain a universal DNA circuit with favorable signal-to-background ratio. To further improve signal amplification, GS/PANI/AuNPs with excellent conductivity and enlarged effective area were introduced into this DNA circuit. Consequently, by combining the advantages of CHA and GS/PANI/AuNPs, bcr/abl could be detected in a linear range from 10 pM to 20 nM with a detection limit of 1.05 pM. Moreover, this protocol showed excellent specificity, good stability and was successfully applied for the detection of real sample, which demonstrated its great potential in clinical application.     

研究随机有热场中扩散行为标度律的一种自洽方法

本介绍了一种研究随机有势场中扩散问题标度律的自洽方法,并综述性介绍了该方法在计算聚合物的Flory指数、研究随机介质中无规行走的长时间下的渐近行为、研究均匀各向同性湍充场中粒子的相对扩散、研究Kuramoto-Sivashinsky方程的奇异扩散行为以及研究微乳浊液中热脉动对化学反应的影响等方面的应用。     

非理想强度差起伏量子非破坏性测量的实验方案

提出了一种强度差起伏量子非破坏性（QND）测量的实验方案,该方案通过一个非简并光学参量放大腔实现。推导了在非理想状态下该系统的传输系数和量子态制备能力的关系式,分别讨论了探针输入噪声谱和探测系统测量效率对其测量的影响。结果表明：探针输入噪声越小,测量效率越高,则其测量质量就越好,且对测量效率越敏感。