Isolated singularities of polyharmonic operator in even dimension

We consider the equation Delta(2)u = g(x, u) >= 0 in the sense of distribution in Omega' = Omega\textbackslash {0} where u and -Delta u >= 0. Then it is known that u solves Delta(2)u = g(x, u) + alpha delta(0) - beta Delta delta(0), for some nonnegative constants alpha and beta. In this paper, we study the existence of singular solutions to Delta(2)u = a(x) f (u) + alpha delta(0) - beta Delta delta(0) in a domain Omega subset of R-4, a is a nonnegative measurable function in some Lebesgue space. If Delta(2)u = a(x) f (u) in Omega', then we find the growth of the nonlinearity f that determines alpha and beta to be 0. In case when alpha = beta = 0, we will establish regularity results when f (t) <= Ce-gamma t, for some C, gamma > 0. This paper extends the work of Soranzo (1997) where the author finds the barrier function in higher dimensions (N >= 5) with a specific weight function a(x) = |x|(sigma). Later, we discuss its analogous generalization for the polyharmonic operator.

Prediction of electronically nonadiabatic decomposition mechanisms of isolated gas phase nitrogen-rich energetic salt: Guanidium-triazolate

Electronically nonadiabatic decomposition pathways of guanidium triazolate are explored theoretically. Nonadiabatically coupled potential energy surfaces are explored at the complete active space self-consistent field (CASSCF) level of theory. For better estimation of energies complete active space second order perturbation theories (CASPT2 and CASMP2) are also employed. Density functional theory (DFT) with B3LYP functional and MP2 level of theory are used to explore subsequent ground state decomposition pathways. In comparison with all possible stable decomposition products (such as, N-2, NH3, HNC, HCN, NH2CN and CH3NC), only NH3 (with NH2CN) and N-2 are predicted to be energetically most accessible initial decomposition products. Furthermore, different conical intersections between the S-1 and S-0 surfaces, which are computed at the CASSCF(14,10)/6-31G(d) level of theory, are found to play an essential role in the excited state deactivation process of guanidium triazolate. This is the first report on the electronically nonadiabatic decomposition mechanisms of isolated guanidium triazolate salt. (C) 2015 Elsevier B.V. All rights reserved.

An Endophytic Fungus, Talaromyces radicus, Isolated from Catharanthus roseus, Produces Vincristine and Vinblastine, Which Induce Apoptotic Cell Death

Endophytic fungi isolated from Catharanthus roseus were screened for the production of vincristine and vinblastine. Twenty-two endophytic fungi isolated from various tissues of C. roseus were characterized taxonomically by sequence analysis of the internal transcribed spacer (ITS) region of rDNA and grouped into 10 genera: Alternaria, Aspergillus, Chaetomium, Colletotrichum, Dothideomycetes, Eutypella, Eutypa, Flavodon, Fusarium and Talaromyces. The antiproliferative activity of these fungi was assayed in HeLa cells using the MTT assay. The fungal isolates Eutypella sp-CrP14, obtained from stem tissues, and Talaromyces radicus-CrP20, obtained from leaf tissues, showed the strongest antiproliferative activity, with IC50 values of 13.5 mu g/ml and 20 mu g/ml, respectively. All 22 endophytic fungi were screened for the presence of the gene encoding tryptophan decarboxylase (TDC), the key enzyme in the terpenoid indole alkaloid biosynthetic pathway, though this gene could only be amplified from T. radicus-CrP20 (NCBI GenBank accession number KC920846). The production of vincristine and vinblastine by T. radicus-CrP20 was confirmed and optimized in nine different liquid media. Good yields of vincristine (670 mu g/l) in modified M2 medium and of vinblastine (70 mu g/l) in potato dextrose broth medium were obtained. The cytotoxic activity of partially purified fungal vincristine was evaluated in different human cancer cell lines, with HeLa cells showing maximum susceptibility. The apoptosis-inducing activity of vincristine derived from this fungus was established through cell cycle analysis, loss of mitochondrial membrane potential and DNA fragmentation patterns.