A Divergent Approach to the Marine Diterpenoids (+)‐Dictyoxetane and (+)‐Dolabellane V

We present a full account of the development of a strategy that culminated in the first total syntheses of the unique oxetane‐containing natural product (+)‐dictyoxetane and the macrocyclic diterpene (+)‐dolabellane V. Our retrosynthetic planning was guided by both classical and nonconventional strategies to construct the oxetane, which is embedded in an unprecedented 2,7‐dioxatricyclo[4.2.1.0^3,8]nonane ring system. Highlights of the successful approach include highly diastereoselective carbonyl addition reactions to assemble the full carbon skeleton, a Grob fragmentation to construct the 11‐membered macrocycle of (+)‐dolabellane V, and a bioinspired 4‐exo‐tet, 5‐exo‐trig cyclization sequence to form the complex dioxatricyclic framework of (+)‐dictyoxetane. Furthermore, an unprecedented strain‐releasing type I dyotropic rearrangement of an epoxide‐oxetane substrate was developed.     

Synthesis and characterization of a new red-emitting Ca2+ indicator, calcium ruby

Calcium Ruby m-Cl (X = H, Y = Cl) is a visible-light excited red-emitting calcium concentration ([Ca2+]) indicator dye (579/598 nm peak excitation/emission) with a side arm for conjugation via EDC or click chemistry. Its large molar extinction and high quantum yield rank it among the brightest long-wavelength Ca2+ indicators. Calcium Ruby is a promising alternative to existing dyes for imaging [Ca2+] in multicolor fluorescence applications or in the presence of yellow-green cellular autofluorescence.     

Positive curvature effects and interparticle capillary condensation during nitrogen adsorption in particulate porous materials

The adsorption of nitrogen in a collection of spheres that touch or merge in a sintering-like manner is modeled using a Derjaguin-Broeckhof-de Boer approach. The proposed model accounts for both positive curvature effects and for capillary condensation at the contact between two spheres. A methodology is proposed to fit the P/P(0)>0.4 adsorption region with the coordination number of the spheres as the only adjustable parameter. The use of the model is illustrated on a series of silica aerogels. The suitability of various standard isotherms needed for the modeling is also discussed.     

Time-Resolved Fluorescence and Transient Spectroscopy in Determining Photochemical and Photophysical Channels in Reacting Systems in Solutions and Microheterogeneous Media

Abstract— Characterization of short-lived intermediates in homogeneous and microheterogeneous systems has been carried out using time-resolved spectroscopic techniques. The data obtained from these techniques have been analyzed in a relatively unconventional manner to elucidate complex transient behavior for two reactive systems. The highly nonexponential fluorescence decay for a series of fraws-stilbene-derivatized amphiphiles that readily form bilayer systems in aqueous media has been analyzed using a distribution of lifetimes analysis (DLA). The utility of DLA for quantitative studies was first determined by simulation of artificial decay data. Despite some limitations in DLA, qualitative conclusions as to the nature of the fluorescing species may be drawn when supplementary information such as steady-state spectroscopic data are also considered. The results indicate that the observed fluorescence originates from different types of excited-state species that consist of two or more trans-stilbene units; one of the emissions is attributed to the excited state of a ground-state aggregate while the other is assigned to an excimer that may arise from a 'defect'in the bilayer. The nonexponential nature of the decays is attributed to distributions of environments experienced by the fluorescing species. Electron transfer (ET) reactions between several excited pinacols and carbon tetrachloride in solution have been found to yield products with quantum yields that are higher than unity in the presence of oxygen, suggesting a chain mechanism for product formation. In these systems both the donor and the acceptor undergo bond fragmentation following the initial ET step. The individual steps involved in the proposed mechanism for these systems have been investigated in part using different steady-state and time-resolved laser spectroscopic techniques. However, it was also necessary to utilize pulse radiolysis in order to confirm the involvement of certain radical intermediates that were not observable by the usual flash photolysis techniques.     

qNMR for profiling the production of fungal secondary metabolites

Analysis of complex mixtures is a common challenge in natural products research. Quantitative nuclear magnetic resonance spectroscopy offers analysis of complex mixtures at early stages and with benefits that are orthogonal to more common methods of quantitation, including ultraviolet absorption spectroscopy and mass spectrometry. Several experiments were conducted to construct a methodology for use in analysis of extracts of fungal cultures. A broadly applicable method was sought for analysis of both pure and complex samples through use of an externally calibrated method. This method has the benefit of not contaminating valuable samples with the calibrant, and it passed scrutiny for line fitting and reproducibility. The method was implemented to measure the yield of griseofulvin and dechlorogriseofulvin from three fungal isolates. An isolate of Xylaria cubensis (coded MSX48662) was found to biosynthesize griseofulvin in the greatest yield, 149 ± 8 mg per fermentation, and was selected for further supply experiments. Copyright © 2016 John Wiley & Sons, Ltd.     

An improvement on Marotto’s theorem and its applications to chaotification of switching systems

The controversy surrounding the correctness of Marotto’s theorem continues over the last two decades, with many researchers claiming to have found an error in the proof. In this paper, we show that Marotto’s theorem is indeed correct for analyzing the existence of chaos in the sense of Li-Yorke even after relaxing certain assumptions in the proof. In addition, we extend the theory to derive the conditions for the existence of chaos in the sense of Devaney. We show that these results can be applied to study the chaotification of linear switching systems.     

一种新的求解带约束的有限极大极小问题的精确罚函数

提出了一种新的精确光滑罚函数求解带约束的极大极小问题．仅仅添加一个额外的变量,利用这个精确光滑罚函数,将带约束的极大极小问题转化为无约束优化问题． 证明了在合理的假设条件下,当罚参数充分大,罚问题的极小值点就是原问题的极小值点．进一步,研究了局部精确性质．数值结果表明这种罚函数算法是求解带约束有限极大极小问题的一种有效算法．     

Random Skew Plane Partitions with a Piecewise Periodic Back Wall

Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work, we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise linear curve with non-lattice slopes, describing the limit shape and the local fluctuations in various regions. This analysis is fairly similar to that in Okounkov and Reshetikhin (Commun Math Phys 269:571–609, 2007), but we do find some new behavior. For instance, the boundary of the limit shape is now a single smooth (not algebraic) curve, whereas the boundary in Okounkov and Reshetikhin (Commun Math Phys 269:571–609, 2007) is singular. We also observe the bead process introduced in Boutillier (Ann Probab 37(1):107–142, 2009) appearing in the asymptotics at the top of the limit shape.     

Tenth Peregrine breather solution to the NLS equation

In this paper we construct a particularly important solution to the focusing NLS equation, namely a Peregrine breather of the rank 10 which we call, P₁₀$P_{10}$ breather. The related explicit formula is given by the ratio of two polynomials of degree 110 with integer coefficients times trivial exponential factor. This formula drastically simplifies for the “initial values” namely for t=0$t=0$ or x=0$x=0$. This formula confirms a general conjecture saying that between all quasi-rational solutions of the rank N$N$ fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at the point (x=0,t=0)$(x=0,t=0)$, the P_N$P_N$ breather is distinguished by the fact that P_N(0,0)=2N+1$P_N(0,0)=2N+1$ and, in the aforementioned class of quasi-rational solutions, it is an absolute maximum. At the end we also make a few remarks concerning the rational deformations of P₁₀$P_{10}$ breather involving 2N−2$2N-2$ free real parameters chosen in a way that P_N$P_N$ breather itself corresponds to the zero values of these parameters although we have no intention to discuss the properties of these deformations here.