Search results for "Valence"
showing 10 items of 2732 documents
Skeleta of affine hypersurfaces
2014
A smooth affine hypersurface Z of complex dimension n is homotopy equivalent to an n-dimensional cell complex. Given a defining polynomial f for Z as well as a regular triangulation of its Newton polytope, we provide a purely combinatorial construction of a compact topological space S as a union of components of real dimension n, and prove that S embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S.
Equivalence of viscosity and weak solutions for the $p(x)$-Laplacian
2010
We consider different notions of solutions to the $p(x)$-Laplace equation $-\div(\abs{Du(x)}^{p(x)-2}Du(x))=0$ with $ 1<p(x)<\infty$. We show by proving a comparison principle that viscosity supersolutions and $p(x)$-superharmonic functions of nonlinear potential theory coincide. This implies that weak and viscosity solutions are the same class of functions, and that viscosity solutions to Dirichlet problems are unique. As an application, we prove a Rad\'o type removability theorem.
Some Common Fixed Point Results in Cone Metric Spaces
2009
We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results.
Molecular chaperones and mirnas in epilepsy: Pathogenic implications and therapeutic prospects
2021
Epilepsy is a pathologic condition with high prevalence and devastating consequences for the patient and its entourage. Means for accurate diagnosis of type, patient monitoring for predicting seizures and follow up, and efficacious treatment are desperately needed. To improve this adverse outcome, miRNAs and the chaperone system (CS) are promising targets to understand pathogenic mechanisms and for developing theranostics applications. miRNAs implicated in conditions known or suspected to favor seizures such as neuroinflammation, to promote epileptic tolerance and neuronal survival, to regulate seizures, and others showing variations in expression levels related to seizures are promising ca…
Evaluation of the Physicochemical Properties of the Iron Nanoparticle Drug Products: Brand and Generic Sodium Ferric Gluconate
2021
Complex iron nanoparticle-based drugs are one of the oldest and most frequently administered classes of nanomedicines. In the US, there are seven FDA-approved iron nanoparticle reference drug products, of which one also has an approved generic drug product (i.e., sodium ferric gluconate (SFG)). These products are indicated for the treatment of iron deficiency anemia and are administered intravenously. On the molecular level, iron nanomedicines are colloids composed of an iron oxide core with a carbohydrate coating. This formulation makes nanomedicines more complex than conventional small molecule drugs. As such, these products are often referred to as nonbiological complex drugs (e.g., by t…
The Transoid, Ortho, and Gauche Conformers of Decamethyl-n-tetrasilane, n-Si4Me10: Electronic Transitions in the Multistate Complete Active Space Se…
2003
Multistate complete active space second-order perturbation theory (MS-CASPT2) is used to improve earlier descriptions of the low-energy valence excited states of the transoid, ortho, and gauche conformers of decamethyl-n-tetrasilane, n-Si4Me10, using a generally contracted basis set of atomic natural orbitals (ANOs) at a ground-state geometry optimized in the second-order Moller−Plesset perturbation theory (MP2) approximation with Dunning's correlation consistent triple-ζ basis set (cc-pVTZ) on the silicon atoms and the 6-31G* and 6-31G basis sets on the carbon and hydrogen atoms, respectively. Relative energies, relative free energies, and mole fractions of the transoid, ortho, and gauche …
On the temperature dependence of the electrical conductivity in hot quenched lattice QCD
2011
Extending our recent work, we report on a calculation of the vector current correlation function for light valence quarks in the deconfined phase of quenched QCD in the temperature range 1.16Tc<T<2.98Tc. After performing a systematic analysis of the in fluence of cut-off effects on light quark meson correlators using clover improved Wilson fermions, we discuss resulting constraints on the electrical conductivity in a quark gluon plasma.
Lifetime measurements of excited states in $^{169,171,173}$Os: Persistence of anomalous $B(E2)$ ratios in transitional rare earth nuclei in the prese…
2021
International audience; Lifetimes of low-lying excited states in the νi13/2+ bands of the neutron-deficient osmium isotopes 169,171,173Os have been measured for the first time using the recoil-distance Doppler shift and recoil-isomer tagging techniques. An unusually low value is observed for the ratio B(E2;21/2+→17/2+)/B(E2;17/2+→13/2+) in 169Os, similar to the “anomalously” low values of the ratio B(E2;41+→21+)/B(E2;21+→0gs+) previously observed in several transitional rare-earth nuclides with even numbers of neutrons and protons, including the neighbouring 168,170Os. Furthermore, the evolution of B(E2;21/2+→17/2+)/B(E2;17/2+→13/2+) with increasing neutron number in the odd-mass isotopic c…
Orbital dimerization inNaTiSi2O6:An orbital analogue of the spin-Peierls phase transition
2004
We measure the Raman scattering spectra of NaTiSi2O6, analyze the vibrational properties, and study the origin of the phase transition in this compound. In this quasi-one-dimensional S = 1/2 system we observe anomalous high-temperature phonon broadenings, and large changes of the phonon energies and line-widths across the phase transition temperature of 210 K. These results, combined with theoretical considerations, indicate that the phonon anomalies originate from an orbital order-disorder type of phase transition. We find that the high temperature dynamical Jahn-Teller phase of NaTiSi2O6 exhibits a spontaneous breaking of translational symmetry into a dimerized, Jahn-Teller distorted, orb…
Spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the star lattice: Competing valence-bond-solid phases studied by means of tensor networks
2018
Using the infinite Projected Entangled Pair States (iPEPS) algorithm, we study the ground-state properties of the spin-$1/2$ quantum Heisenberg antiferromagnet on the star lattice in the thermodynamic limit. By analyzing the ground-state energy of the two inequivalent bonds of the lattice in different unit-cell structures, we identify two competing Valence-Bond-Solid (VBS) phases for different antiferromagnetic Heisenberg exchange couplings. More precisely, we observe (i) a VBS state which respects the full symmetries of the Hamiltonian, and (ii) a resonating VBS state which, in contrast to previous predictions, has a six-site unit-cell order and breaks $C_3$ symmetry. We also studied the g…