Distribution of eigenvalues for the discontinuous boundary-value problem with functional-manypoint conditions

In this study, we investigate the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also a point of discontinuity, a finite number of internal points and abstract linear functionals. So our problem is not a pure boundary-value one. We single out a class of linear functionals and find simple algebraic conditions on the coefficients which guarantee the existence of an infinite number of eigenvalues. Also, the asymptotic formulas for the eigenvalues are found. The results obtained in this paper are new, even in the case of boundary conditions either without internal points or without linear functionals.     

Human Serum Albumin−Gold Nanoparticle Based Impedimetric Sensor for Sensitive Detection of miRNA-200c

Here, human serum albumin conjugated gold nanoparticles (HSA−AuNPs) were synthesized by a simple route to develop an impedimetric sensor for miRNA-200c detection based on a selective oligo-hybridization process without any labeling. The synthetic DNA capture probe for miRNA-200c was decorated onto the HSA−AuNPs modified pencil graphite electrodes. Impedimetric signals were monitored after the hybridization process between the DNA probe and target miRNA-200c. HSA−AuNPs adsorption time, incubation time of the capture probe and hybridization time-temperature were optimized. The proposed miRNA-200c biosensor demonstrated proper sensitivity and selectivity, low detection limit (1.13 fM), good reproducibility and simple direct detection of miRNA-200c in serum.     

Regular boundary value problems with a discontinuous coefficient,functional-multipoint conditions,and a linear spectral parameter

We consider a linear differential equation which includes a linear abstract operator, with a piecewise constant coefficient at the principal differential term, together with multipoint boundary-transmission conditions, including linear functionals. The spectral parameter appears linearly in the equation and may appear also linearly in the boundary-transmission conditions. We prove an isomorphism and coerciveness of the problem with respect to the spectral parameter and the space variable.     

Two-particle Wigner functions in a one-dimensional Calogero-Sutherland potential

We calculate the Wigner distribution function for the Calogero-Sutherland system which consists of harmonic and inverse-square interactions. The Wigner distribution function is separated out into two parts corresponding to the relative and center-of-mass motions. A general expression for the relative Wigner function is obtained in terms of the Laguerre polynomials by introducing a new identity between Hermite and Laguerre polynomials.     

Antioxidant,Antidiabetic, Anticholinergic,and Antiglaucoma Effects of Magnofluorine

Magnofluorine, a secondary metabolite commonly found in various plants, has pharmacological potential; however, its antioxidant and enzyme inhibition effects have not been investigated. We investigated the antioxidant potential of Magnofluorine using bioanalytical assays with 2,2-azinobis (3-ethylbenzothiazoline-6-sulfonic acid) (ABTS^•+), N,N-dimethyl-p-phenylenediamine dihydrochloride (DMPD^•+), and 1,1-diphenyl-2-picrylhydrazyl (DPPH^•) scavenging abilities and K₃[Fe(CN)₆] and Cu²⁺ reduction abilities. Further, we compared the effects of Magnofluorine and butylated hydroxytoluene (BHT), butylated hydroxyanisole (BHA), α-Tocopherol, and Trolox as positive antioxidant controls. According to the analysis results, Magnofluorine removed 1,1-diphenyl-2-picrylhydrazyl (DPPH) radicals with an IC₅₀ value of 10.58 μg/mL. The IC₅₀ values of BHA, BHT, Trolox, and α-Tocopherol were 10.10 μg/mL, 25.95 μg/mL, 7.059 μg/mL, and 11.31 μg/mL, respectively. Our results indicated that the DPPH· scavenging effect of Magnofluorine was similar to that of BHA, close to that of Trolox, and better than that of BHT and α-tocopherol. The inhibition effect of Magnofluorine was examined against enzymes, such as acetylcholinesterase (AChE), α-glycosidase, butyrylcholinesterase (BChE), and human carbonic anhydrase II (hCA II), which are linked to global disorders, such as diabetes, Alzheimer’s disease (AD), and glaucoma. Magnofluorine inhibited these metabolic enzymes with Ki values of 10.251.94, 5.991.79, 25.411.10, and 30.563.36 nM, respectively. Thus, Magnofluorine, which has been proven to be an antioxidant, antidiabetic, and anticholinergic in our study, can treat glaucoma. In addition, molecular docking was performed to understand the interactions between Magnofluorine and target enzymes BChE (D: 6T9P), hCA II (A:3HS4), AChE (B:4EY7), and α-glycosidase (C:5NN8). The results suggest that Magnofluorine may be an important compound in the transition from natural sources to industrial applications, especially new drugs.     

ASYMPTOTIC BEHAVIOUR OF EIGENVALUES FOR THE DISCONTINUOUS BOUNDARY-VALUE PROBLEM WITH FUNCTIONAL-TRANSMISSION CONDITIONS

In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of innnit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.     

Synthesis,photophysical and antioxidant properties of carbazole-based bis-thiosemicarbazones

Research on Chemical Intermediates - Utilizing Schiff base condensation of the 9-ethylcarbazole-3,6-dicarbaldehyde and thiosemicarbazides, four new N-ethylcarbazole-based bis-thiosemicarbazone...     

Sahlep (Dactylorhiza osmanica): Phytochemical Analyses by LC-HRMS,Molecular Docking,Antioxidant Activity,and Enzyme Inhibition Profiles

Studies have shown an inverse correlation among age-related illnesses like coronary heart disease and cancer and intake of fruit and vegetable. Given the probable health benefits of natural antioxidants from plants, research on them has increased. Dactylorhiza osmanica is consumed as a food and traditional medicine plant in some regions of Turkey, so evaluation of the biological ability of this species is important. In this study, the amount of phenolic content (LC-HRMS), antioxidant activities and enzyme inhibitory properties of an endemic plant, D. osmanica, were investigated. The antioxidant capacities of an ethanol extract of D. osmanica aerial parts (EDOA) and roots (EDOR) were evaluated with various antioxidant methods. Additionally, the enzyme inhibitory effects of EDOA and EDOR were examined against acetylcholinesterase (AChE), α-glycosidase, and α-amylase enzymes, which are associated with common and global Alzheimer’s disease and diabetes mellitus. The IC₅₀ values of EDOA against the enzymes were found to be 1.809, 1.098, and 0.726 mg/mL, respectively; and the IC₅₀ values of EDOR against the enzymes were found to be 2.466, 0.442, and 0.415 mg/mL, respectively. Additionally, LC-HRMS analyses revealed p-Coumaric acid as the most plentiful phenolic in both EDOA (541.49 mg/g) and EDOR (559.22 mg/g). Furthermore, the molecular docking interaction of p-coumaric acid, quercitrin, and vanillic acid, which are the most plentiful phenolic compounds in the extracts, with AChE, α-glucosidase, and α-amylase, were evaluated using AutoDock Vina software. The rich phenolic content and the effective antioxidant ability and enzyme inhibition potentials of EDOA and EDOR may support the plant’s widespread food and traditional medicinal uses.     

Evaluation of the Antioxidant and Antiradical Properties of Some Phyto and Mammalian Lignans

In this study, the antioxidant and antiradical properties of some phyto lignans (nordihydroguaiaretic acid, secoisolariciresinol, secoisolariciresinol diglycoside, and α-(-)-conidendrin) and mammalian lignans (enterodiol and enterolactone) were examined by different antioxidant assays. For this purpose, radical scavenging activities of phyto and mammalian lignans were realized by 2,2′-azino-bis (3-ethylbenzothiazoline-6-sulphonic acid) radical (ABTS^•+) scavenging assay and 1,1-diphenyl-2-picrylhydrazyl radical (DPPH) scavenging assay. Additionally, the reducing ability of phyto and mammalian lignans were evaluated by cupric ions (Cu²⁺) reducing (CUPRAC) ability, and ferric ions (Fe³⁺) and [Fe³⁺-(TPTZ)2]³⁺ complex reducing (FRAP) abilities. Also, half maximal inhibitory concentration (IC₅₀) values were determined and reported for DPPH^• and ABTS^•+ scavenging influences of all of the lignan molecules. The absorbances of the lignans were found in the range of 0.150–2.320 for Fe³⁺ reducing, in the range of 0.040–2.090 for Cu²⁺ reducing, and in the range of 0.360–1.810 for the FRAP assay. On the other hand, the IC₅₀ values of phyto and mammalian lignans were determined in the ranges of 6.601–932.167 µg/mL for DPPH^• scavenging and 13.007–27.829 µg/mL for ABTS^•+ scavenging. In all of the used bioanalytical methods, phyto lignans, as secondary metabolites in plants, demonstrated considerably higher antioxidant activity compared to that of mammalian lignans. In addition, it was observed that enterodiol and enterolactone exhibited relatively weaker antioxidant activities when compared to phyto lignans or standard antioxidants, including butylated hydroxytoluene (BHT), butylated hydroxyanisole (BHA), Trolox, and α-tocopherol.     

Screening of Carbonic Anhydrase,Acetylcholinesterase, Butyrylcholinesterase,and α-Glycosidase Enzyme Inhibition Effects and Antioxidant Activity of Coumestrol

Coumestrol (3,9-dihydroxy-6-benzofuran [3,2-c] chromenone) as a phytoestrogen and polyphenolic compound is a member of the Coumestans family and is quite common in plants. In this study, antiglaucoma, antidiabetic, anticholinergic, and antioxidant effects of Coumestrol were evaluated and compared with standards. To determine the antioxidant activity of coumestrol, several methods—namely N,N-dimethyl-p-phenylenediamine dihydrochloride radical (DMPD^•+)-scavenging activity, 2,2′-azinobis-(3-ethylbenzothiazoline-6-sulphonate) radical (ABTS^•+)-scavenging activity, 1,1-diphenyl-2-picrylhydrazyl radical (DPPH^•)-scavenging activity, potassium ferric cyanide reduction ability, and cupric ion (Cu²⁺)-reducing activity—were performed. Butylated hydroxyanisole (BHA), Trolox, α-Tocopherol, and butylated hydroxytoluene (BHT) were used as the reference antioxidants for comparison. Coumestrol scavenged the DPPH radical with an IC₅₀ value of 25.95 μg/mL (r²: 0.9005) while BHA, BHT, Trolox, and α-Tocopherol demonstrated IC₅₀ values of 10.10, 25.95, 7.059, and 11.31 μg/mL, respectively. When these results evaluated, Coumestrol had similar DPPH^•-scavenging effect to BHT and lower better than Trolox, BHA and α-tocopherol. In addition, the inhibition effects of Coumestrol were tested against the metabolic enzymes acetylcholinesterase (AChE), butyrylcholinesterase (BChE), carbonic anhydrase II (CA II), and α-glycosidase, which are associated with some global diseases such as Alzheimer’s disease (AD), glaucoma, and diabetes. Coumestrol exhibited K_i values of 10.25 ± 1.94, 5.99 ± 1.79, 25.41 ± 1.10, and 30.56 ± 3.36 nM towards these enzymes, respectively.