Synthesis and rheological properties of star-shaped polydimethylsiloxanes based on carbosilane dendrimers

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Progress toward the total synthesis of 9β-hydroxyvertine: Construction of an advanced quinolizidine intermediate

Progress toward the total synthesis of 9β-hydroxyvertine 2 is described. Our approach involves a Petasis borono-Mannich reaction to assemble a key intermediate A, securing the correct configuration at H-9 and H-10 in the final targeted molecule. Subsequent formation of the quinolizidine framework B allowed the synthesis of an advanced intermediate containing all but the lactone moiety of 2. Our unsuccessful attempts at introducing this lactone feature are also described.     

Synthetic studies toward swinhoeisterol A,a novel steroid with an unusual carbon skeleton

Swinhoeisterol A is a novel steroid with unusual 6/6/5/7 tetracyclic skeleton. The model compound with BCD rings is constructed by Friedel–Crafts acylation and an oxidative dearomatization as key steps.     

Gaussian unitary ensembles with two jump discontinuities,PDEs, and the coupled Painlevé II and IV systems

We consider the Hankel determinant generated by the Gaussian weight with two jump discontinuities. Utilizing the results of Min and Chen [Math. Methods Appl Sci. 2019;42:301‐321] where a second‐order partial differential equation (PDE) was deduced for the log derivative of the Hankel determinant by using the ladder operators adapted to orthogonal polynomials, we derive the coupled Painlevé IV system which was established in Wu and Xu [arXiv: 2002.11240v2] by a study of the Riemann‐Hilbert problem for orthogonal polynomials. Under double scaling, we show that, as , the log derivative of the Hankel determinant in the scaled variables tends to the Hamiltonian of a coupled Painlevé II system and it satisfies a second‐order PDE. In addition, we obtain the asymptotics for the recurrence coefficients of orthogonal polynomials, which are connected with the solutions of the coupled Painlevé II system.     

Closed‐form approximations for spread options in Lévy markets

We provide new closed‐form approximations for the pricing of spread options in three specific instances of exponential Lévy markets, ie, when log‐returns are modeled as Brownian motions (Black‐Scholes model), variance gamma processes (VG model), or normal inverse Gaussian processes (NIG model). For the specific case of exchange options (spread options with zero strike), we generalize the well‐known Margrabe formula (1978) that is valid in a Black‐Scholes model to the VG model under a homogeneity assumption.     

Structure of 5-methyl-7-methoxy-isoflavone

The structure of 5-methyl-7-methoxy-isoflavone was determined by X-ray diffraction. The compound crystallizes in the monoclinic space group P2₁/c, with cell dimensions of a = 10.321(3) Å; b = 11.290(5) Å; c = 11.979(8) Å; = 107.00(5)°; V = 1334.9(11) ų and D_calc. = 1.325 Mg/m³ for Z = 4. The structure was solved by direct methods and refined to an R value of 0.0409. As expected ring A and ring B in 5-methyl-7-methoxy-isoflavone are coplanar, while ring C is rotated to a dihedral angle of 59.42 (7)°. Intermolecular C–HO hydrogen bonds link molecules related by the screw axis and glide-planes to form a loosely connected layer structure.     

Monasnicotinic acid,a novel pyridine alkaloid of the fungus Aspergillus cavernicola: isolation and structure elucidation

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Synthesis of tritium-labeled PAM-43

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Synthesis and electrochemical study of 2-carbamoyl-4,5-dihydro-1,3,4-thiadiazole-containing ligands and their complexes with Cuii, Coii and Niii

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