Some Lower Bounds in the B. and M. Shapiro Conjecture for Flag Varieties

The B. and M. Shapiro conjecture stated that all solutions of the Schubert Calculus problems associated with real points on the rational normal curve should be real. For Grassmannians, it was proved by Mukhin, Tarasov, and Varchenko. For flag varieties, Sottile found a counterexample and suggested that all solutions should be real under certain monotonicity conditions. In this paper, we compute lower bounds on the number of real solutions for some special cases of the B. and M. Shapiro conjecture for flag varieties, when Sottile’s monotonicity conditions are not satisfied.     

Ultrasensitive separation of methylprednisolone acetate using a photoresponsive molecularly imprinted polymer incorporated polyester dendrimer based on magnetic nanoparticles

We developed an approach for the use of polyester dendrimer during the imprinting process to raise the number of recognized sites in the polymer matrix and improve its identification ability. Photoresponsive molecularly imprinted polymers were synthesized on modified magnetic nanoparticles involving polyester dendrimer which uses the reactivity between allyl glycidyl ether and acrylic acid for the high‐yielding assembly by surface polymerization. The photoresponsive molecularly imprinted polymers were constructed using methylprednisoloneacetate as the template, water‐soluble azobenzene involving 5‐[(4, 3‐(methacryloyloxy) phenyl) diazenyl] dihydroxy aniline as the novel functional monomer, and ethylene glycol dimethacrylate as the cross‐linker. Through the evaluation of a series of features of spectroscopic and nano‐structural, this sorbent showed excellent selective adsorption, recognition for the template, and provided a highly selective and sensitive strategy for determining the methylprednisoloneacetate in real and pharmaceutical samples. In addition, this sorbent according to good photo‐responsive features and specific affinity to methylprednisoloneacetate with high recognition ability, represented higher binding capacity, a more extensive specific area, and faster mass transfer rate than its corresponding surface molecularly imprinted polymer.     

Singlet oxygen chemistry in water: a porous vycor glass-supported photosensitizer

Singlet molecular oxygen [1O2 (1Deltag)] is generated cleanly in aqueous solution upon irradiation of a heterogeneous complex, meso-tetra(N-methyl-4-pyridyl)porphine (1) adsorbed onto porous Vycor glass (PVG). The cationic photosensitizer 1 tightly binds onto PVG and gives a stable material, which does not dissociate 1 into the surrounding aqueous phase. The production of 1O2 was measured by monitoring the time-resolved 1O2 (1Deltag) phosphorescence at 1270 nm. Indirect analysis of 1O2 generation was also carried out with the photooxidation of trans-2-methyl-2-pentenoate anion, which afforded the corresponding hydroperoxide. Sensitizer-1-impregnated PVG gives rise to a new singlet oxygen generator but more importantly provides a heterogeneous system for use in water.     

Numerical simulation of secondary vortex chamber effect on the cooling capacity enhancement of vortex tube

A vortex tube with additional chamber is investigated by computational fluid mechanics techniques to realize the effects of additional chamber in Ranque–Hilsch vortex tube and to understand optimal length for placing the second chamber in order to have maximum cooling effect. Results show that by increasing the distance between two chambers, both minimum cold and maximum hot temperatures increase and maximum cooling effect occurs at Z/L = 0.047 (dimensionless distance).     

Constrained supersymmetric flipped SU(5) GUT phenomenology

We explore the phenomenology of the minimal supersymmetric flipped SU(5) GUT model (CFSU(5)), whose soft supersymmetry-breaking (SSB) mass parameters are constrained to be universal at some input scale, M _in , above the GUT scale, M _GUT. We analyze the parameter space of CFSU(5) assuming that the lightest supersymmetric particle (LSP) provides the cosmological cold dark matter, paying careful attention to the matching of parameters at the GUT scale. We first display some specific examples of the evolutions of the SSB parameters that exhibit some generic features. Specifically, we note that the relationship between the masses of the lightest neutralino χ and the lighter stau [(t)tilde]₁{tilde{tau}_{1}} is sensitive to M _in , as is the relationship between m _χ and the masses of the heavier Higgs bosons A,H. For these reasons, prominent features in generic (m _1/2,m ₀) planes such as coannihilation strips and rapid-annihilation funnels are also sensitive to M _in , as we illustrate for several cases with tan β=10 and 55. However, these features do not necessarily disappear at large M _in , unlike the case in the minimal conventional SU(5) GUT. Our results are relatively insensitive to neutrino masses.