Restrictions on arrangements of ovals of projective algebraic curves of odd degree

This paper investigates the first part of Hilbert's 16th problem which asks about topology of the real projective algebraic curves. Using the Rokhlin-Viro-Fiedler method of complex orientation, we obtain new restrictions on the arrangements of ovals of projective algebraic curves of odd degree , , with nests of depth .

     

Reaction of ortho-palladated dimethylbenzylamine with styrene: Unexpected salt effect

Treatment of ortho-palladated complex $\text{I}$ with styrene in benzene - acetic acid mixture gives complex $\text{IV}$. The reaction is strongly accelerated in the presence of NaClO₄ or LiClO₄.     

New Multifunctional Agents Based on Conjugates of 4-Amino-2,3-polymethylenequinoline and Butylated Hydroxytoluene for Alzheimer’s Disease Treatment

New hybrids of 4-amino-2,3-polymethylenequinoline with different sizes of the aliphatic ring linked to butylated hydroxytoluene (BHT) by enaminoalkyl (7) or aminoalkyl (8) spacers were synthesized as potential multifunctional agents for Alzheimer’s disease (AD) treatment. All compounds were potent inhibitors of acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) with selectivity toward BChE. Lead compound 8c, 2,6-di-tert-butyl-4-{[2-(7,8,9,10- tetrahydro-6H-cyclohepta[b]quinolin-11-ylamino)-ethylimino]-methyl}-phenol exhibited an IC₅₀(AChE) = 1.90 ± 0.16 µM, IC₅₀(BChE) = 0.084 ± 0.008 µM, and 13.6 ± 1.2% propidium displacement at 20 μM. Compounds possessed low activity against carboxylesterase, indicating likely absence of clinically unwanted drug-drug interactions. Kinetics were consistent with mixed-type reversible inhibition of both cholinesterases. Docking indicated binding to catalytic and peripheral AChE sites; peripheral site binding along with propidium displacement suggest the potential of the hybrids to block AChE-induced β-amyloid aggregation, a disease-modifying effect. Compounds demonstrated high antioxidant activity in ABTS and FRAP assays as well as inhibition of luminol chemiluminescence and lipid peroxidation in mouse brain homogenates. Conjugates 8 with amine-containing spacers were better antioxidants than those with enamine spacers 7. Computational ADMET profiles for all compounds predicted good blood-brain barrier distribution (permeability), good intestinal absorption, and medium cardiac toxicity risk. Overall, based on their favorable pharmacological and ADMET profiles, conjugates 8 appear promising as candidates for AD therapeutics.     

Electrochemically induced multicomponent ‘one-pot’ assembling benzaldehydes,N,N′-dimethylbarbituric acid,and kojic acid

Monatshefte für Chemie - Chemical Monthly - The new electrochemically induced multicomponent assembling was found: the electrocatalytic transformation of benzaldehydes,...     

Bulk plasmon‐polaritons in hyperbolic nanorod metamaterial waveguides

Hyperbolic metamaterials comprised of an array of plasmonic nanorods provide a unique platform for designing optical sensors and integrating nonlinear and active nanophotonic functionalities. In this work, the waveguiding properties and mode structure of planar anisotropic metamaterial waveguides are characterized experimentally and theoretically. While ordinary modes are the typical guided modes of the highly anisotropic waveguides, extraordinary modes, below the effective plasma frequency, exist in a hyperbolic metamaterial slab in the form of bulk plasmon‐polaritons, in analogy to planar‐cavity exciton‐polaritons in semiconductors. They may have very low or negative group velocity with high effective refractive indices (up to 10) and have an unusual cut‐off from the high‐frequency side, providing deep‐subwavelength (λ₀/6–λ₀/8 waveguide thickness) single‐mode guiding. These properties, dictated by the hyperbolic anisotropy of the metamaterial, may be tuned by altering the geometrical parameters of the nanorod composite.

     

Spontaneous emission from cylindrical atomic cloud: Collective eigenstates and non-local effects

We consider collective emission of a single photon stored in a cloud of N two-level atoms (with energy ?ω) confined inside an infinite cylinder and discuss eigenstates of this system, their decay rates and collective frequency shifts. We found that states with wave number k_z ≥ ω/c do not decay and analogous to guiding modes in dielectric waveguides. Evolution of such states is qualitatively different in local (Markovian) and non-local regimes. We found that in the Markovian regime there is no photon emission. In contrast, non-local (memory) effects result in emission and reabsorption of the photon so that probability to find atoms excited oscillates with a collective Rabi frequency. Cross-over between local and non-local behavior can be observed by increasing radius of the cylinder or wave number k_z of the excited atomic state. Similar behavior can also be observed in slab geometry and tested in synchrotron experiments on collective excitation of solid-state samples by increasing thickness of the nuclear layer.     

The Nd–Mn exchange interaction,low temperature specific heat and magnetism of Nd2/3Ca1/3MnO3

The low temperature specific heat and magnetic characteristics of Nd_2/3Ca_1/3MnO₃ perovskite are studied in a wide range of magnetic fields (up to 9 T). Temperature dependent specific heat data show a broadened Schottky-like anomaly below 20 K caused by splitting of the Nd³⁺ ions ground-state doublet in the effective molecular field H_ex, determined by exchange interaction between Nd and Mn spin systems supplemented by an applied external magnetic field. Existence of the splitting at zero magnetic field and expressed field dependence is the evidence of a strong exchange coupling between Nd and Mn magnetic subsystems. The Nd-ions magnetic ordering leads to an additional contribution to the magnetic moment of the system below 30 K, producing anomalies of the magnetic loss and field-cooled and zero-field-cooled magnetizations. The observed broadened Schottky-like anomalies are fitted for each applied magnetic field by the sum of three Schottky functions. Applied magnetic field extends the anomaly region and shifts it to higher temperatures. Splitting of the higher crystal field Kramers doublets gives an additional contribution to the heat capacity in magnetic fields. The ground state doublet g-factors g_|| and g_⊥ were estimated to be 3.4 and 2.2, respectively, and H_ex was estimated to be 9 T. The Nd³⁺ ions magnetic moment estimated from the magnetization data agrees with the value obtained from the specific heat data.     

Spontaneous symmetry breaking on a mutiple-channel hollow cylinder

This Letter investigates coupled asymmetric exclusion processes with two types of particles on multiple parallel channels of a hollow cylinder. The model is inspired by the structure of microtubules, along which motor proteins such as kinesins and dyneins move in opposite directions. Interactions between two-species particles are assumed to take place only on the left and right boundaries where a rule of narrow entrances is applied. Narrow entrances mean that a particle cannot enter the system if either of two nearest-neighbor sites on the neighboring channels is occupied by a particle of the other species. This rule is similar to, but different from, that in [E. Pronina, A.B. Kolomeisky, J. Phys. A 40 (2007) 2275] since the narrow entrance rule in our model involves two neighbors. The phase diagram of our model is studied theoretically and via Monte Carlo simulations. The spontaneous symmetry breaking (SSB) is observed in the system. There are four possible phases in the system and with SSB occurring in two of them: high/low density and asymmetric low/low density. Bulk density and particle currents are also computed. Theoretical calculations deviate from Monte Carlo simulation results due to the neglecting of correlations in particles dynamics in mean-field analysis.     

Physics of protein-DNA interactions: mechanisms of facilitated target search

One of the most critical aspects of protein-DNA interactions is the ability of protein molecules to quickly find and recognize specific target sequences on DNA. Experimental measurements indicate that the corresponding association rates to few specific sites among large number of non-specific sites are typically large. For some proteins they might be even larger than maximal allowed three-dimensional diffusion rates. Although significant progress in understanding protein search and recognition of targets on DNA has been achieved, detailed mechanisms of these processes are still strongly debated. Here we present a critical review of current theoretical approaches and some experimental observations in this area. Specifically, the role of lowering dimensionality, non-specific interactions, diffusion along the DNA molecules, protein and target sites concentrations, and electrostatic effects are critically analyzed. Possible future directions and outstanding problems are also presented and discussed.