Cross-coupling reactions towards the synthesis of natural products

Molecular Diversity - Cross-coupling reactions are powerful synthetic tools for the formation of remarkable building blocks of many naturally occurring molecules, polymers and biologically active...     

New fermions at the LHC and mass of the Higgs boson

Unification at MGUT∼3×¹⁰¹⁶ GeV$M_{\mathrm{GUT}}\sim 3\times {10}^{16}\text{GeV}$ of the three Standard Model (SM) gauge couplings can be achieved by postulating the existence of a pair of vectorlike fermions carrying SM charges and masses of order 300 GeV–1 TeV. The presence of these fermions significantly modifies the vacuum stability and perturbativity bounds on the mass of the SM Higgs boson. The new vacuum stability bound in this extended SM is estimated to be 117 GeV, to be compared with the SM prediction of about 128 GeV. An upper bound of 190 GeV is obtained based on perturbativity arguments. The impact on these predictions of type I seesaw physics is also discussed. The discovery of a relatively ‘light’ Higgs boson with mass ∼117 GeV$\sim 117\text{GeV}$ could signal the presence of new vectorlike fermions within reach of the LHC.     

On the Unital C*-Algebras Generated by Certain Subnormal Tuples

We consider an important class of subnormal operator m-tuples M _p (p = m,m + 1, . . .) that is associated with a class of reproducing kernel Hilbert spaces H_p{{\mathcal H}_p} (with M _m being the multiplication tuple on the Hardy space of the open unit ball \mathbb B^2m{{\mathbb B}^{2m}} in \mathbb C^m{{\mathbb C}^m} and M _m+1 being the multiplication tuple on the Bergman space of \mathbb B^2m{{\mathbb B}^{2m}}). Given any two C*-algebras A{\mathcal A} and B{\mathcal B} from the collection {C^*(M_p), C^*([(M)\tilde]_p): p 3 m}{\{C^*({M}_p), C^*({\tilde M}_p): p \geq m\}} , where C*(M _p ) is the unital C*-algebra generated by M _p and C^*([(M)\tilde]_p){C^*({\tilde M}_p)} the unital C*-algebra generated by the dual [(M)\tilde]_p{{\tilde M}_p} of M _p , we verify that A{\mathcal A} and B{\mathcal B} are either *-isomorphic or that there is no homotopy equivalence between A{\mathcal A} and B{\mathcal B} . For example, while C*(M _m ) and C*(M _m+1) are well-known to be *-isomorphic, we find that C^*([(M)\tilde]_m){C^*({\tilde M}_m)} and C^*([(M)\tilde]_m+1){C^*({\tilde M}_{m+1})} are not even homotopy equivalent; on the other hand, C*(M _m ) and C^*([(M)\tilde]_m){C^*({\tilde M}_{m})} are indeed *-isomorphic. Our arguments rely on the BDF-theory and K-theory.     

More results on Hermite-Hadamard type inequality through} $( \alpha ,m)$-preinvexity

We establish various inequalities for n-times differentiable mappings that are connected with illustrious Hermite-Hadamard integral inequality for mapping whose absolute values of derivatives are $\left( {\alpha ,m} \right)$-preinvex function. The new integral inequalities are then applied to some special means     

Completely Hyperexpansive Operator Tuples

The notion of a completely hyperexpansive operator on a Hilbert space is generalized to that of a completely hyperexpansive operator tuple, which in some sense turns out to be antithetical to the notion of a subnormal operator tuple with contractive coordinates. The countably many negativity conditions characterizing a completely hyperexpansive operator tuple are closely related to the Levy–Khinchin representation in the theory of harmonic analysis on semigroups. The interplay between the theories of positive and negative definite functions on semigroups forces interesting connections between the classes of subnormal and completely hyperexpansive operator tuples. Further, the several–variable generalization allows for a stimulating interaction with the multiparameter spectral theory.     

Identification and profiling of targeted oxidized linoleic acid metabolites in rat plasma by quadrupole time‐of‐flight mass spectrometry

Linoleic acid (LA) and LA‐esters are the precursors of LA hydroperoxides, which are readily converted to 9‐ and 13‐hydroxy‐?octadecadienoic acid (HODE) and 9‐ and 13‐oxo‐?octadecadienoic acid (oxo ODE) metabolites in vivo. These four oxidized LA metabolites (OXLAMs) have been implicated in a variety of pathological conditions. Therefore, their accurate measurement may provide mechanistic insights into disease pathogenesis. Here we present a novel quadrupole time‐of‐flight mass spectrometry (Q‐TOFMS) method for quantitation and identification of target OXLAMs in rat plasma. In this method, the esterified OXLAMs were base‐hydrolyzed and followed by liquid–liquid extraction. Quantitative analyses were based on one‐point standard addition with isotope dilution. The Q‐TOFMS data of target metabolites were acquired and multiple reaction monitoring extracted‐ion chromatograms were generated post‐acquisition with a 10 ppm extraction window. The limit of quantitation was 9.7–35.9 nmol/L depending on the metabolite. The method was reproducible with a coefficient of variation of <18.5%. Mean concentrations of target metabolites in rat plasma were 57.8, 123.2, 218.1 and 57.8 nmol/L for 9‐HODE, 13‐HODE, 9‐oxoODE and 13‐oxoODE, respectively. Plasma levels of total OXLAMs were 456.9 nmol/L, which correlated well with published concentrations obtained by gas chromatography/mass spectrometry (GC/MS). The concentrations were also obtained utilizing a standard addition curve approach. The calibration curves were linear with correlation coefficients of >0.991. Concentrations of 9‐HODE, 13‐HODE, 9‐oxoODE and 13‐oxoODE were 84.0, 138.6, 263.0 and 69.5 nmol/L, respectively, which were consistent with the results obtained from one‐point standard addition. Target metabolites were simultaneously characterized based on the accurate Q‐TOFMS data. This is the first study of secondary LA metabolites using Q‐TOFMS. Published 2012. This article is a U.S. Government work and is in the public domain in the USA.     

On the local stability analysis of the approximate harmonic balance solutions

Periodic response of nonlinear oscillators is usually determined by approximate methods. In the "steady state" type methods, first an approximate solution for the steady state periodic response is determined, and then the local stability of this solution is determined by analyzing the equation of motion linearized about this predicted "solution". An exact stability analysis of this linear variational equation can provide erroneous stability type information about the approximate solutions. It is shown that a consistent stability type information about these solutions can be obtained only when the linearized variational equation is analyzed by approximate methods, and the level of accuracy of this analysis is consistent with that of the approximate solutions. It is demonstrated that these consistent stability results do not imply that the approximate solution is qualitatively correct. It is also shown that the difference between an approximate and the next higher order stability analysis can be used to "guess" the role of higher harmonics in the periodic response. This trial and error procedure can be used to ensure the qualitatively correct and numerically accurate nature of the approximate solutions and the corresponding stability analysis.     

Radiation properties of a uniaxial chiral quadratic inhomogeneous slab under oblique incidence

In this paper, the focussing of the transmitted electromagnetic field through a quadric inhomogeneous slab of lossless uniaxial chiral medium is derived using transmission coefficient under oblique incidence. The inhomogeneity in the uniaxial chiral slab has been incorporated through permittivity parameter. Asymptotic ray theory provides valid field everywhere except at focal point where it gives infinite value. Singularity of the field at focal point is addressed using Maslov's method. The derived analytical field expressions at caustic or focal point of uniaxial quadratic inhomogeneous slab have been solved numerically using MATHEMATICA. The effects of chirality parameter, axial permittivity, transvers permittivity, angle of incidence on the refracted field are discussed and the effects of Brewster angle on the focussed field are also discussed. The results obtained using Maslov's method are compared with Huygens–Kirchhoff's integral which are in good agreement.     

Democratic approach to atmospheric and solar neutrino oscillations

Working with a flavor symmetry, we show how the hierarchical structure in the charged fermion sector and a democratic approach for neutrinos that yields large solar and atmospheric neutrino mixings can be simultaneously realized in the MSSM framework. However, in SU(5) due to the unified multiplets we encounter difficulties. Namely, democracy for the neutrinos leads to a wrong hierarchical pattern for charged fermion masses and mixings. We discuss how this is overcome in flipped SU(5).