Fuzzy turnover rate chance constraints portfolio model

One concern of many investors is to own the assets which can be liquidated easily. Thus, in this paper, we incorporate portfolio liquidity in our proposed model. Liquidity is measured by an index called turnover rate. Since the return of an asset is uncertain, we present it as a trapezoidal fuzzy number and its turnover rate is measured by fuzzy credibility theory. The desired portfolio turnover rate is controlled through a fuzzy chance constraint. Furthermore, to manage the portfolios with asymmetric investment return, other than mean and variance, we also utilize the third central moment, the skewness of portfolio return. In fact, we propose a fuzzy portfolio mean–variance–skewness model with cardinality constraint which combines assets limitations with liquidity requirement. To solve the model, we also develop a hybrid algorithm which is the combination of cardinality constraint, genetic algorithm, and fuzzy simulation, called FCTPM.     

Divergent trajectories and ℚ-rank

The author proves a conjecture of the author: IfG is a semisimple real algebraic defined over ℚ, Γ is an arithmetic subgroup (with respect to the given ℚ-structure) andA is a diagonalizable subgroup admitting a divergent trajectory inG/Γ, then dimA≤ rank_ℚ G.     

Signal Amplification Technologies for the Detection of Nucleic Acids: from Cell-Free Analysis to Live-Cell Imaging

Due to their unique properties, such as programmability, ligand-binding capability, and flexibility, nucleic acids can serve as analytes and/or recognition elements for biosensing. To improve the sensitivity of nucleic acid-based biosensing and hence the detection of a few copies of target molecule, different modern amplification methodologies, namely target-and-signal-based amplification strategies, have already been developed. These recent signal amplification technologies, which are capable of amplifying the signal intensity without changing the targets’ copy number, have resulted in fast, reliable, and sensitive methods for nucleic acid detection. Working in cell-free settings, researchers have been able to optimize a variety of complex and quantitative methods suitable for deploying in live-cell conditions. In this study, a comprehensive review of the signal amplification technologies for the detection of nucleic acids is provided. We classify the signal amplification methodologies into enzymatic and non-enzymatic strategies with a primary focus on the methods that enable us to shift away from in vitro detecting to in vivo imaging. Finally, the future challenges and limitations of detection for cellular conditions are discussed.     

Supramolecular Translation of Enzymatically Triggered Disassembly of Micelles into Tunable Fluorescent Responses

The need for advanced fluorescent imaging and delivery platforms has motivated the development of smart probes that change their fluorescence in response to external stimuli. Here a new molecular design of fluorescently labeled PEG–dendron hybrids that self‐assemble into enzyme‐responsive micelles with tunable fluorescent responses is reported. In the assembled state, the fluorescence of the dyes is quenched or shifted due to intermolecular interactions. Upon enzymatic cleavage of the hydrophobic end‐groups, the labeled polymeric hybrids become hydrophilic, and the micelles disassemble. This supramolecular change is translated into a spectral response as the dye–dye interactions are eliminated and the intrinsic fluorescence is regained. We demonstrate the utilization of this molecular design to generate both Turn‐On and spectral shift responses by adjusting the type of the labeling dye. This approach enables transformation of non‐responsive labeling dyes into smart fluorescent probes.     

Green and Straightforward Modification of Graphite Electrode via In Situ Synthesis of Graphene Nanosheets for Quantifying Prazosin Hydrochloride in Urine Samples and Pharmaceutical Formulations

A sensitive electrochemical sensor based on in situ modification of graphite electrode via graphene nanosheets (GNs) was developed as a green method for prazosin hydrochloride (PRA) analyses. In this study, GNs were electrochemically synthesized on the surface of graphite electrode via in situ approach and used for the analyses. The proposed sensor showed several advantages such as high sensitivity, low LOD, and excellent repeatability. The oxidation peak current at the optimum analytical conditions using a GNs/graphite electrode at pH 6.0 was linearly dependent on PRA concentration in the range of 0.09–100 µM. A LOD of 0.02 µM and RSD of 3.8 % for 10 µM solution of PRA with a great recovery were obtained.     

Conducting polyfurans by electropolymerization of oligofurans

Polyfurans have never been established as useful conjugated polymers, as previously they were considered to be inherently unstable and poorly conductive. Here, we show the preparation of stable and conducting polyfuran films by electropolymerization of a series of oligofurans of different chain lengths substituted with alkyl groups. The polyfuran films show good conductivity in the order of 1 S cm^–1, good environmental and electrochemical stabilities, very smooth morphologies (roughness 1–5 nm), long effective conjugation lengths, well-defined spectroelectrochemistry and electro-optical switching (in the Vis-NIR region), and have optical band-gaps in the range of 2.2–2.3 eV. A low oxidation potential needed for polymerization of oligofurans (compared to furan) is a key factor in achievement of improved properties of polyfurans reported in this work. DFT calculations and experiments show that polyfurans are much more rigid than polythiophenes, and alkyl substitution does not disturb backbone planarity and conjugation. The obtained properties of polyfuran films are similar or superior to the properties of electrochemically prepared poly(oligothiophene)s under similar conditions.     

Double Bonds in Fused Hexacyclic Systems

If a hexacyclic graph, G, represents a benzenoid, a perfect matching corresponds to the location of double bonds (pi-bonds). We present an algorithm for counting the number of configurations of double bonds for various benzenoids.     

Bilayered cyclofusene

Multiply-connected monolayered cyclofusene (MMC) is a fused hexacyclic system with at least two interior empty regions called holes. Multiply-connected bilayered cyclofusene (MBC) is a structure derived from an MMC by replacing each layer of hexacycles by two layers. Various properties of the equitability of these bipartite graphs are examined.     

Finite dimensional representations and subgroup actions on homogeneous spaces

LetH be an ℝ-subgroup of a ℚ-algebraic groupG. We study the connection between the dynamics of the subgroup action ofH onG/G _ℤ and the representation-theoretic properties ofH being observable and epimorphic inG. We show that ifH is a ℚ-subgroup thenH is observable inG if and only if a certainH orbit is closed inG/G _ℤ; that ifH is epimorphic inG then the action ofH onG/G _ℤ is minimal, and that the converse holds whenH is a ℚ-subgroup ofG; and that ifH is a ℚ-subgroup ofG then the closure of the orbit underH of the identity coset image inG/G _ℤ is the orbit of the same point under the observable envelope ofH inG. Thus in subgroup actions on homogeneous spaces, closures of ‘rational orbits’ (orbits in which everything which can be defined over ℚ, is defined over ℚ) are always submanifolds.