Jordan operator algebras revisited

Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particular, surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras.     

Reasoning about proof and knowledge

In previous work [15], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from Gödel's interpretation of IPC in S4, our modal systems contain IPC in the way established in [13]. The modal operator can be viewed as a predicate for intuitionistic truth, i.e. proof. Epistemic principles are partially adopted from Intuitionistic Epistemic Logic IEL [4]. In the present paper, we show that the S5-style systems of our hierarchy correspond to an extended Brouwer–Heyting–Kolmogorov interpretation and are complete w.r.t. a relational semantics based on intuitionistic general frames. In this sense, our S5-style logics are adequate and complete systems for the reasoning about proof combined with belief or knowledge. The proposed relational semantics is a uniform framework in which also IEL can be modeled. Verification-based intuitionistic knowledge formalized in IEL turns out to be a special case of the kind of knowledge described by our S5-style systems.     

Room temperature suzuki cross‐coupling polymerizations of aryl dihalides and aryldiboronic acid/acid esters with t‐Bu3P‐coordinated 2‐phenylaniline‐based palladacycle complex as the precatalyst

Room temperature Suzuki cross‐coupling polymerization of aryl dibromides/diiodides with aryldiboronic acids/acid esters with t‐Bu₃P‐coordinated 2‐phenylaniline‐based palladacycle complex, [2′‐(amino‐kN)[1,1′‐biphenyl]‐2‐yl‐kC]chloro(tri‐t‐butylphosphine)palladium, as a general precatalyst is described. Such room temperature Suzuki cross‐coupling polymerization is achieved by employing six equivalents or more of the base and affords polymers within an hour, with the yields and the molecular weights in general comparable to or higher than reported results that required higher reaction temperature and/or longer polymerization time. Our study provides a general catalyst system for the room temperature Suzuki cross‐coupling polymerization of aryl dibromides/diiodides with aryldiboronic acids/acid esters and paves the road for the investigation of employing other monodentate ligand‐coordinated palladacycle complexes including other electron‐rich monophosphine‐coordinated ones for room temperature cross‐coupling polymerizations. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1606–1611     

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.     

On nonlinear boundary value problem corresponding to N-dimensional inverse spectral problem

We establish a relationship between an inverse optimization spectral problem for the N-dimensional Schrödinger equation $?\mathrm{\Delta }?+q(x)?=\lambda ?$ and a solution of the nonlinear boundary value problem $?\mathrm{\Delta }u+q(x)u=\lambda u?u^{\gamma ?1},u>0,u{|}_{?\mathrm{\Omega }}=0$. Using this relationship, we find an exact solution for the inverse optimization spectral problem, investigate its stability and obtain new results on the existence and uniqueness of the solution for the nonlinear boundary value problem.     

Tensor products of n-complete algebras

If A and B are n- and m-representation finite k-algebras, then their tensor product $\mathrm{\Lambda }=A{?}_{k}B$ is not in general $(n+m)$-representation finite. However, we prove that if A and B are acyclic and satisfy the weaker assumption of n- and m-completeness, then Λ is $(n+m)$-complete. This mirrors the fact that taking higher Auslander algebra does not preserve d-representation finiteness in general, but it does preserve d-completeness. As a corollary, we get the necessary condition for Λ to be $(n+m)$-representation finite which was found by Herschend and Iyama by using a certain twisted fractionally Calabi–Yau property.     

On the radius of spatial analyticity for the modified Kawahara equation on the line

First, by using linear and trilinear estimates in Bourgain type analytic and Gevrey spaces, the local well‐posedness of the Cauchy problem for the modified Kawahara equation on the line is established for analytic initial data that can be extended as holomorphic functions in a strip around the x‐axis. Next we use this local result and a Gevrey approximate conservation law to prove that global solutions exist. Furthermore, we obtain explicit lower bounds for the radius of spatial analyticity given by , where can be taken arbitrarily small and c is a positive constant.     

Preparation of free‐standing silicone particles in aqueous heterogeneous system

To prepare cross‐linked silicone (silicone rubber) particles in an aqueous medium, we investigated two synthesis methods involving a miniemulsion system. The first method was based on cationic ring‐opening polymerization of cyclic siloxane, which is a common synthetic route for linear silicone oil and uses octamethylcyclotetrasiloxane (D₄) as the monomer and dimeric D₄ (bis‐D₄) as the cross‐linker. Although this method produces silicone particles, the particles do not remain in the particulate state after drying because of low cross‐linking density. The polymerization mechanism of this method was also investigated, which proceeds under the ring‐opening reaction of D₄ in monomer droplets and upon polycondensation of hydrolyzed D₄, which occurs in the water phase (ie, outside the monomer droplets). This mechanism implied that introducing the cross‐linking structure into particles is difficult because of the low solubility of bis‐D₄ in water. To overcome these difficulties, we demonstrated a second method of preparing silicone particles based on the thiol‐Michael addition reaction between thiol‐terminated silicone oil and triacrylate in miniemulsion systems. Transmission electron microscopy images indicated that the silicone particles obtained in the particulate state upon drying and the aggregates of these particles showed elasticity.     

Novel palladium nanoparticles supported on β‐cyclodextrin@graphene oxide as magnetically recyclable catalyst for Suzuki–Miyaura cross‐coupling reaction with two different approaches in bio‐based solvents

A novel nanocatalyst was designed and prepared. Initially, the surface of magnetic graphene oxide (M‐GO) was modified using thionyl chloride, tris(hydroxymethyl)aminomethane and acryloyl chloride as linkers which provide reactive C═C bonds for the polymerization of vinylic monomers. Separately, β‐cyclodextrin (β‐CD) was treated with acryloyl chloride to provide a modified β‐CD. Then, in the presence methylenebisacrylamide as a cross‐linker, monomers of modified β‐CD and acrylamide were polymerized on the surface of the pre‐prepared M‐GO. Finally, palladium acetate and sodium borohydride were added to this composite to afford supported palladium nanoparticles. This fabricated nanocomposite was fully characterized using various techniques. The efficiency of this easily separable and reusable heterogeneous catalyst was successfully examined in Suzuki–Miyaura cross‐coupling reactions of aryl halides and boronic acid as well as in modified Suzuki–Miyaura cross‐coupling reactions of N‐acylsuccinimides and boronic acid in green media. The results showed that the nanocatalyst was efficient in coupling reactions for direct formation of the corresponding biphenyl as well as benzophenone derivatives in green media based on bio‐based solvents. In addition, the nanocatalyst was easily separable, using an external magnet, and could be reused several times without significant loss of activity under the optimum reaction conditions.