Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.     

A New Cohomology Theory of Orbifold

Based on the orbifold string theory model in physics, we construct a new cohomology ring for any almost complex orbifold. The key theorem is the associativity of this new ring. Some examples are computed.Both authors partially supported by the National Science Foundation     

DIFFUSION-DRIVEN INSTABILITY IN THE GIERER-MEINHARDT MODEL OF MORPHOGENESIS

In this paper, we consider the Gierer-Meinhardt model of morphogenesis. It is shown that the homogeneous equilibrium solution and the homogeneous periodic solution become diffusively unstable if the diffusion coefficients of the two substances are chosen suitably.     

Description of proton-calcium scattering using the α-particle model

The theoretical proton-⁴⁰Ca optical potential is constructed based on theα-particle model of the nucleus. With this potential, the differential cross section, analysing power and the spin rotation function for 200 MeV proton-⁴⁰Ca elastic scattering are calculated. The results are in good agreement with the experimental data.     

Noncollinear optical parametric amplification in lithium triborate seeded by a cw Ti:sapphire laser

Experimental investigations of a type-I noncollinear phase-matched optical parametric amplification based on lithium triborate, which was pumped by a 5-ns second-harmonic pulses from a Q-switched Nd:YAG, seeded by a cw Ti:sapphire laser at 800 nm, was presented. The experiments generated 2-ns signal output pulses at 800 nm, the maximum signal output pulse energy reached 19 μJ, the corresponding parametric gain was 44 dB. Furthermore, the experiments demonstrate that the 65 nm-FWHM parametric fluorescence gain spectrum could also be observed. A quantitative account of the ultrabroadband parametric fluorescence gain spectrum was given with our theory. The experimental measurements are in agreement with theoretical calculations.     

Zig‐Zag Diphosphene Oligomers Linked by Silver(I) Cation

The coordination of silver cation to diphosphene Mes*P=PMes* ( 1 , Mes* = ^tBu₃C₆H₂) was investigated in detail. The reaction of 1 with Ag[Al(OR_F)₄] (OR_F = OC(CF₃)₃) in the ratios of 2 : 1, 3 : 2 and 1 : 2 led to the formation of the first cationic silver linked diphosphene complexes 2 — 4 . Complexes 2 and 3 contain two and three diphosphene molecules linked by the linear Ag(I) cation, respectively, and they feature unusual zig‐zag topologies. Complex 4 is a dinuclear silver complex, and each Ag(I) center features a tetrahedral geometry, coordinated by one phosphorus atom of diphosphene 1 and three chloro atoms of two CH₂Cl₂ molecules.     

Composite alignment media for the measurement of independent sets of NMR residual dipolar couplings

The measurement of independent sets of NMR residual dipolar couplings (RDCs) in multiple alignment media can provide a detailed view of biomolecular structure and dynamics, yet remains experimentally challenging. It is demonstrated here that independent sets of RDCs can be measured for ubiquitin using just a single alignment medium composed of aligned bacteriophage Pf1 particles embedded in a strained polyacrylamide gel matrix. Using this composite medium, molecular alignment can be modulated by varying the angle between the directors of ordering for the Pf1 and strained gel matrix, or by varying the ionic strength or concentration of the Pf1 particles. This approach offers significant advantages in that greater experimental control can be exercised over the acquisition of multi-alignment RDC data while a homogeneous chemical environment is maintained across all of the measured RDC data.     

MoO3、NiO、ZnO在小表面金红石上的分散行为

Dispersion of MoO3, NiO, ZnO on rutile TiO2 with low specific surface area was studied with Mercury Porosimeter, SEM, XPS and Ammonia Extraction method. The dispersion thresholds of MoO3, NiO, ZnO on three rutile TiO2 carriers were obtained with XPS, and com-pared with those on anatase TiO2 with high specific surf are area. Ammonia Extraction method was used to identify the surface oxide species interarting with support surface in different strength and it was found that the proportions of oxides that can not be extracted by ammonia extraction are different for MoO3, NiO and ZnO which are supported on rutile TiO2.     

Carbohydrate-binding module O-mannosylation alters binding selectivity to cellulose and lignin

Improved understanding of the effect of protein glycosylation is expected to provide the foundation for the design of protein glycoengineering strategies. In this study, we examine the impact of O-glycosylation on the binding selectivity of a model Family 1 carbohydrate-binding module (CBM), which has been shown to be one of the primary sub-domains responsible for non-productive lignin binding in multi-modular cellulases. Specifically, we examine the relationship between glycan structure and the binding specificity of the CBM to cellulose and lignin substrates. We find that the glycosylation pattern of the CBM exhibits a strong influence on the binding affinity and the selectivity between both cellulose and lignin. In addition, the large set of binding data collected allows us to examine the relationship between binding affinity and the correlation in motion between pairs of glycosylation sites. Our results suggest that glycoforms displaying highly correlated motion in their glycosylation sites tend to bind cellulose with high affinity and lignin with low affinity. Taken together, this work helps lay the groundwork for future exploitation of glycoengineering as a tool to improve the performance of industrial enzymes.

Improved understanding of the effect of protein glycosylation is expected to provide the foundation for the design of protein glycoengineering strategies.

The cell walls of terrestrial plants primarily comprise the polysaccharides cellulose, hemicellulose, and pectin, as well as the heterogeneous aromatic polymer, lignin. In nature, carbohydrates derived from plant polysaccharides provide a massive carbon and energy source for biomass-degrading fungi, bacteria, and archaea, which together are the primary organisms that recycle plant matter and are a critical component of the global carbon cycle. Across the various environments in which these microbes break down lignocellulose, a few known enzymatic and chemical systems have evolved to deconstruct polysaccharides to soluble sugars.^1–6 These natural systems are, in several cases, being evaluated for industrial use to produce sugars for further conversion into renewable biofuels and chemicals.From an industrial perspective, overcoming biomass recalcitrance to cost-effectively produce soluble intermediates, including sugars for further upgrading remains the main challenge in biomass conversion. Lignin, the evolution of which in planta provided a significant advantage for terrestrial plants to mitigate microbial attack, is now widely recognized as a primary cause of biomass recalcitrance.⁷ Chemical and/or biological processing scenarios of lignocellulose have been evaluated⁸ and several approaches have been scaled to industrial biorefineries to date. Many biomass conversion technologies overcome recalcitrance by partially or wholly removing lignin from biomass using thermochemical pretreatment or fractionation. This approach enables easier polysaccharide access for carbohydrate-active enzymes and/or microbes. There are however, several biomass deconstruction approaches that employ enzymes or microbes with whole, unpretreated biomass.^9,10 In most realistic biomass conversion scenarios wherein enzymes or microbes are used to depolymerize polysaccharides, native or residual lignin remains.^11,12 It is important to note that lignin can bind and sequester carbohydrate-active enzymes, which in turn can affect conversion performance.¹³Therefore, efforts aimed at improving cellulose binding selectivity relative to lignin have emerged as major thrusts in cellulase studies.^14–25 Multiple reports in the past a few years have made exciting new contributions to our collective understanding of how fungal glycoside hydrolases, which are among the most well-characterized cellulolytic enzymes given their importance to cellulosic biofuels production, bind to lignin from various pretreatments.^15,17 Taken together, these studies have demonstrated that the Family 1 carbohydrate-binding modules (CBMs) often found in fungal cellulases are the most relevant sub-domains for non-productive binding to lignin,^15,17,20,26 likely due to the hydrophobic face of these CBMs that is known to be also responsible for cellulose binding (Fig. 1).²⁷Open in a separate windowFig. 1Model of glycosylated CBM binding the surface of a cellulose crystal. Glycans are shown in green with oxygen atoms in red, tyrosines known to be critical to binding shown in purple, and disulfide bonds Cys8–Cys25 and Cys19–Cys35 in yellow.Furthermore, several studies have been published recently using protein engineering of Family 1 CBMs to improve CBM binding selectivity to cellulose with respect to lignin. Of particular note, Strobel et al. screened a large library of point mutations in both the Family 1 CBM and the linker connecting the catalytic domain (CD) and CBM.^21,22 These studies demonstrated that several mutations in the CBM and one in the linker led to improved cellulose binding selectivity compared to lignin. The emerging picture is that the CBM-cellulose interaction, which occurs mainly as a result of stacking between the flat, hydrophobic CBM face (which is decorated with aromatic residues) and the hydrophobic crystal face of cellulose I, is also likely the main driving force in the CBM-lignin interaction given the strong potential for aromatic–aromatic and hydrophobic interactions.Alongside amino acid changes, modification of O-glycosylation has recently emerged as a potential tool in engineering fungal CBMs, which Harrison et al. demonstrated to be O-glycosylated.^28–31 In particular, we have revealed that the O-mannosylation of a Family 1 CBM of Trichoderma reesei cellobiohydrolase I (TrCel7A) can lead to significant enhancements in the binding affinity towards bacterial microcrystalline cellulose (BMCC).^30,32,33 This observation, together with the fact that glycans have the potential to form both hydrophilic and hydrophobic interactions with other molecules, led us to hypothesize that glycosylation may have a unique role in the binding selectivity of Family 1 CBMs to cellulose relative to lignin and as such, glycoengineering may be exploited to improve the industrial performance of these enzymes. To test this hypothesis, in the present study, we systematically probed the effects of glycosylation on CBM binding affinity for a variety of lignocellulose-derived cellulose and lignin substrates and investigated routes to computationally predict the binding properties of different glycosylated CBMs.