Microwave‐associate synthesis of Co3O4 nanoparticles as an effcient nanocatalyst for the synthesis of arylidene barbituric and Meldrum's acid derivatives in green media

In this study, Co₃O₄ nanocatalysts were constructed in environmentally appropriate conditions using controlled, effective, and facile microwave method. The final nanostructures were characterized by SEM, XRD, and TEM analyses. The products had a small size distribution, homogeneous morphology, and crystallographic structures associated with the formation of Co₃O₄ nanostructures. Moreover, EDS mapping analysis confirmed the existence of Co and O elements in the final structure, and the magnetic properties of the samples were investigated by VSM. The application of this nanostructure in a catalytic process was further examined, and the results suggested that it could be used as a novel candidate for the synthesis of arylidene barbituric and Meldrum^,s acid through Knoevenagel condensation of aldehydes by barbituric and Meldrum^,s acid in aqueous media. The high yield of these nanocatalysts would be justified by the nature of the nanostructure as well as the experimental procedure developed in this study, which affected the physicochemical features of the products.     

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.     

C‐S cross‐coupling reaction using novel and green synthesized CuO nanoparticles assisted by Euphorbia maculata extract

In the present study, biosynthesis of CuO nanoparticles using a rapid, eco‐friendly, cost‐effective and efficient method has been reported employing aqueous Euphorbia maculata extract as mild, renewable and non‐toxic reducing and capping agents without adding any surfactants. The biogenic and green method has some benefits compared to conventional physical and chemical methods. It is simple, cheap and environmentally friendly. The biosynthesized CuO NP displayed a color change pattern (from sky blue to black) on preparation and presented its respective broad peak at 365 nm, which was analyzed by UV–Vis spectroscopy. Using the FT‐IR analysis, biomolecules in E. maculata extract which are responsible for bioreduction activity and synthesize of CuO NP, were identified. The XRD, EDX and FESEM results confirmed the successful synthesis of CuO nanoparticles of 18 nm sizes, with spherical and sponge crystal structure. The catalytic activity of biosynthesized CuO NPs was studied in C‐S cross‐coupling reaction. This method has the advantages of high yields, easy work‐up, and simple reusability. The recovered CuO NP can be reused four times without any considerable loss of its catalytic activity.     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach

Let e_?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory.     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

A concise synthesis of 3-substituted-7-amino-6-carboxyl-8-azachromones

We report on an approach to truncate the tricyclic 5H-chromeno[2,3-b]pyridin-5-one core of amlexanox, an approved drug under investigation for the treatment of obesity, to the bicyclic 4H-pyrano[2,3-b]pyridin-4-one (8-azachromone) core. A short, concise synthesis generates a key intermediate with requisite functionality on the pyridyl A-ring and iodo functionality on the 4-pyrone B-ring upon which palladium-catalyzed cross-coupling and subsequent reactions generate representative analogues. One of these shows a 14.2-fold increase in aqueous solubility over amlexanox.     

Palladium catalyzed domino C-H activation strategy: An access to 9- fluorenones

Palladium catalyzed domino C-H functionalization reaction of arylaldehyde with dihaloarene has been developed to access 9-flourenone molecules. Bidentate ligand assisted strategy, single step reaction, high yield and excellent functional group tolerance make this method concise and effective for the synthesis of 9-flourenone. In addition, proposed method has been successfully employed to synthesise Tilorone in gram scale.     

Trisaminomethane–cobalt complex supported on Fe3O4 magnetic nanoparticles as an efficient recoverable nanocatalyst for oxidation of sulfides and C–S coupling reactions

In this work, trisaminomethane–cobalt complex immobilized onto the surface of Fe₃O₄ magnetic nanoparticles was successfully prepared via a simple and inexpensive procedure. The prepared nanocatalyst was considered a robust and clean nanoreactor catalyst for the oxidation and synthesis of sulfides under green conditions. This ecofriendly heterogeneous catalyst was characterized by Fourier transform infrared spectroscopy, X-ray diffractometry, energy-dispersive X-ray spectroscopy, inductively coupled plasma-atomic emission spectroscopy, thermogravimetric analysis, vibrating sample magnetometry, X-ray mapping, scanning electron microscopy, and transmission electron microscopy techniques. Use of green medium, easy separation and workup, excellent reusability of the nanocatalyst, and short reaction time are some outstanding advantages of this method.