Elliptic solutions for a family of fifth order nonlinear evolution equations

The family of fifth order nonlinear evolution equations is studied. Some traveling wave elliptic solutions are found. The classification of these exact solutions is given.     

Octonions and Singular Solutions of Hessian Elliptic Equations

Algebra of Octonions is used to construct singular viscosity solutions of fully nonlinear Hessian elliptic equations. These equations are written in the form of an Isaacs equation.     

Mathematical modeling of respiratory viral infection and applications to SARS-CoV-2 progression

Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It is shown that progression of viral infection can be characterized by the viral replication number, time-dependent viral load, and the speed of infection spreading. These three characteristics are determined through the original model parameters including the rates of cell infection and of virus production in the infected cells. The clinical manifestations of viral infection, depending on tissue damage, correlate with the speed of infection spreading, while the infectivity of a respiratory infection depends on the viral load in the upper respiratory tract. Parameter determination from the experiments on Delta and Omicron variants allows the estimation of the infection spreading speed and viral load. Different variants of the SARS-CoV-2 infection are compared confirming that Omicron is more infectious and has less severe symptoms than Delta variant. Within the same variant, spreading speed (symptoms) correlates with viral load allowing prognosis of disease progression.     

Tris(pentafluoroethyl)difluorophosphorane: A Versatile Fluoride Acceptor for Transition Metal Chemistry

Fluoride abstraction from different types of transition metal fluoride complexes [L_nMF] (M=Ti, Ni, Cu) by the Lewis acid tris(pentafluoroethyl)difluorophosphorane (C₂F₅)₃PF₂ to yield cationic transition metal complexes with the tris(pentafluoroethyl)trifluorophosphate counterion ( FAP anion, [(C₂F₅)₃PF₃]⁻) is reported. (C₂F₅)₃PF₂ reacted with trans-[Ni(iPr₂Im)₂(Ar^F)F] (iPr₂Im=1,3-diisopropylimidazolin-2-ylidene; Ar^F=C₆F₅, 1 a ; 4-CF₃-C₆F₄, 1 b ; 4-C₆F₅-C₆F₄, 1 c ) through fluoride transfer to form the complex salts trans-[Ni(iPr₂Im)₂(solv)(Ar^F)] FAP ( 2 a - c[solv] ; solv=Et₂O, CH₂Cl₂, THF) depending on the reaction medium. In the presence of stronger Lewis bases such as carbenes or PPh₃, solvent coordination was suppressed and the complexes trans-[Ni(iPr₂Im)₂(PPh₃)(C₆F₅)] FAP ( trans -2 a[PPh₃] ) and cis-[Ni(iPr₂Im)₂(Dipp₂Im)(C₆F₅)] FAP ( cis -2 a[Dipp₂Im] ) (Dipp₂Im=1,3-bis(2,6-diisopropylphenyl)imidazolin-2-ylidene) were isolated. Fluoride abstraction from [(Dipp₂Im)CuF] ( 3 ) in CH₂Cl₂ or 1,2-difluorobenzene led to the isolation of [{(Dipp₂Im)Cu}₂]²⁺2 FAP⁻ ( 4 ). Subsequent reaction of 4 with PPh₃ and different carbenes resulted in the complexes [(Dipp₂Im)Cu(LB)] FAP ( 5 a – e , LB=Lewis base). In the presence of C₆Me₆, fluoride transfer afforded [(Dipp₂Im)Cu(C₆Me₆)] FAP ( 5 f ), which serves as a source of [(Dipp₂Im)Cu)]⁺. Fluoride abstraction of [Cp₂TiF₂] ( 7 ) resulted in the formation of dinuclear [FCp₂Ti(μ-F)TiCp₂F] FAP ( 8 ) (Cp=η⁵-C₅H₅) with one terminal fluoride ligand at each titanium atom and an additional bridging fluoride ligand.     

A new method of one-pot synthesis of dicarboxylic acid derivatives and diketones containing quaternary carbon atom and remote functional groups from linear acyl halides

The one-pot, regioselective synthesis of branched diacid derivatives – diesters, dithioesters, diamides [YC(O)O(CH₂)_mC(Me)₂OC(O)Y] and diketones of aromatic and heteroaromatic series, [ArCO(CH₂)_mC(Me)₂C(O)Ar,) from available linear acyl halides, C_nH_2 n+1COCl (n = 7–9), CO (1 at) and various nucleophiles (YH = EtOH, CF₃CH₂OH, H(CF₂)₂CH₂OH, thiophene, anisole, Et₂NH, aniline, and morpholine) in the presence of the superelectrophilic complex, CBr₄·2AlBr₃ has been performed for the first time. This method provides access to new and promising groups of dicarboxylic acid derivatives and diketones containing quaternary carbon atom and remote functional groups.