Direct Proof of Determinant Representation for Scalar Products of the XXZ Gaudin Model with Generic Non-Diagonal Boundary Terms

After constructing the Bethe state of the XXZ Gaudin model with generic non-diagonal boundary terms,we analyze the properties of this state and obtain the determinant representations of the scalar products for this XXZ Gaudin model.     

Engyodontochones,Antibiotic Polyketides from the Marine Fungus Engyodontium album Strain LF069

Six new ( 2 , 4 – 8 ) and two known polyketides with a basic structure of an anthraquinone‐xanthone were isolated from mycelia and culture broth of the fungus Engyodontium album strain LF069. The structures and relative configurations of these compounds were established by spectroscopic means, and their absolute configurations were defined mainly by comparison of quantum chemical TDDFT calculated and experimental ECD spectra. Compounds 2 and 4 – 8 were given the trivial names engyodontochone A ( 2 ) and B–F ( 4 – 8 ). Compounds 5 – 8 represent the first example of a 23,28 seco‐beticolin carbon skeleton. The relative and absolute configurations of two known substances JBIR‐97/98 ( 1 ) and JBIR‐99 ( 3 ) were determined for the first time. All isolated compounds were subjected to bioactivity assays. Compounds 1 – 4 exhibited inhibitory activity against methicillin‐resistant Staphylococcus aureus (MRSA) that was 10‐fold stronger than chloramphenicol.     

Stereodivergent Synthesis and Stereochemical Reassignment of the C79–C104 Fragment of Symbiodinolide

We have synthesized eight possible diastereoisomers 3 a – h of the C79–C97 fragment of symbiodinolide ( 1 ) in a stereodivergent manner by utilizing a dithiane addition to the aldehyde as a key step. Comparison of the ¹³C NMR chemical shifts of the natural product 1 and the synthetic products 3 a – h indicated that the relative stereostructure of this fragment in symbiodinolide ( 1 ) is that represented in 3 a or f . We have stereodivergently synthesized eight possible diastereoisomers of the C94–C104 fragment 4 a – h , and we have compared their ¹³C NMR chemical shifts with those of the natural product, which established the relative stereochemistry of this fragment to be that described in diastereoisomers 4 a or e . By combining the stereostructural outcomes of the C79–C97 and C94–C104 fragments, we have proposed four candidate compounds of the C79–C104 fragment 2 a – d . We also synthesized diastereoisomers 2 a and b ( 2 a in the preceding article; Chem. Eur. J. 2015 , DOI: 10.1002/chem.201503880) by a Julia–Kocienski olefination and diastereoisomers 2 c and d by a Wittig reaction. By comparing the ¹³C NMR chemical shifts of natural symbiodinolide ( 1 ) with those of the synthetic products 2 a – d , we have reassigned the stereostructure of the C79–C104 fragment of natural product 1 to be that depicted in diastereoisomer 2 b .     

A Straightforward Synthesis of Polyketides via Ester Dienolate Matteson Homologation

Application of ester dienolates as nucleophiles in Matteson homologations allows for the stereoselective synthesis of highly substituted α,β-unsaturated δ-hydroxy carboxyl acids, structural motifs widespread found in polyketide natural products. The protocol is rather flexible and permits the introduction of substituents and functionalities also at those positions which are not accessible by the commonly used aldol reaction. Therefore, this ester dienolate Matteson approach is an interesting alternative to the “classical” polyketide syntheses.     

Study of the circumstance influence on the elemental distribution in ancient animal bone using μ-XRF

Elemental analysis of archaeological bone plays an important role in the study of the dietary habits of ancient animals. The elemental characteristic of diagenetic skeletons depends on the surrounding circum-stance. The study of environmental influence on the elemental concentration of ancient bone is significant. In this paper, the diagenetic influence on archaeological skeletons is analyzed by microbeam X-ray fluorescence (μ-XRF). The results show that the enamel is an excellent barrier to the diagenesis and the element Sr in bone isn’t susceptible to contamination from the buried environment.     

Unified,Efficient, and Scalable Synthesis of Halichondrins: Zirconium/Nickel‐Mediated One‐Pot Ketone Synthesis as the Final Coupling Reaction

Unified, efficient, and scalable syntheses of the halichondrin natural products are reported. A newly developed Zr/Ni‐mediated one‐pot ketone synthesis was used to couple the two halves of the final product at a late stage in the synthesis. With the use of a slight excess of the left halves, the desired ketones were isolated in yields of 80–90 %. The halichondrins were obtained from these ketones in two steps, namely desilylation and [5,5]‐spiroketal formation. The new synthetic route was effective for the total synthesis of all members in the homohalichondrin subgroup. The scalability of this process was demonstrated with halichondrin B; 150 mg of halichondrin B (68 % overall yield) were obtained from 200 mg of the right‐half precursor.     

乘积图的Fractional控制

Let G =(V,E) be a simple graph.For any real function g :V-→ R and a subset S V,we write g(S) =∑v∈Sg(v).A function f :V-→ [0,1] is said to be a fractional dominating function(F DF) of G if f(N [v]) ≥ 1 holds for every vertex v ∈ V(G).The fractional domination number γf(G) of G is defined as γf(G) = min{f(V)|f is an F DF of G }.The fractional total dominating function f is defined just as the fractional dominating function,the difference being that f(N(v)) ≥ 1 instead of f(N [v]) ≥ 1.The fractional total domination number γ0f(G) of G is analogous.In this note we give the exact values ofγf(Cm × Pn) and γ0f(Cm × Pn) for all integers m ≥ 3 and n ≥ 2.