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Search results for: fractional derivatives and integrals
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Comments on “Closed Form Variable Fractional Time Delay Using FFT”
PublicationIn this letter drawbacks of the aforementioned paper are pointed out. The proposed approach is improved with minor modifications of the discrete frequency response. This allows for design of fractional delay filters which are close to optimal and can be efficiently implemented in the frequency domain using the sliding DFT based structure. Alternatively, the derived equivalent closed form formulae for offset windows can be used...
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Fractional Order Circuit Elements Derived from Electromagnetism
PublicationIn this paper, derivations of fractional-order (FO) circuit-element equations from electromagnetism are presented. Whilst many papers are devoted to FO modelling of electrical circuits, there are no strong foundations for such an approach. Therefore, we investigate relations between the FO electromagnetism and the FO circuit theory. Our derivations start from quasi-static (QS) approximations of Maxwell's equations in media with...
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Fractional neutron point kinetics equations for nuclear reactor dynamics – Numerical solution investigations
PublicationThis paper presents results concerning numerical solutions to a fractional neutron point kinetics model for a nuclear reactor. The paper discusses and expands on results presented in (Espinosa-Paredes et al., 2011). The fractional neutron point kinetics model with six groups of delayed neutron precursors was developed and a numerical solution using the Edwards’ method was proposed (Edwards et al., 2002). The mathematical model...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublicationThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublicationThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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Advancement of Non-Newtonian Fluid with Hybrid Nanoparticles in a Convective Channel and Prabhakar’s Fractional Derivative—Analytical Solution
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On possible applications of media described by fractional-order models in electromagnetic cloaking
PublicationThe purpose of this paper is to open a scientific discussion on possible applications of media described by fractional-order (FO) models (FOMs) in electromagnetic cloaking. A 2-D cloak based on active sources and the surface equivalence theorem is simulated. It employs a medium described by FOM in communication with sources cancelling the scattered field. A perfect electromagnetic active cloak is thereby demonstrated with the use...
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Signal propagation in electromagnetic media described by fractional-order models
PublicationIn this paper, signal propagation is analysed in electromagnetic media described by fractional-order (FO) models (FOMs). Maxwell’s equations with FO constitutive relations are introduced in the time domain. Then, their phasor representation is derived for one-dimensional case of the plane wave propagation. With the use of the Fourier transformation, the algorithm for simulation of the non-monochromatic wave propagation is introduced....
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Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (-1,1)
PublicationZaprezentowano metode obliczenia dwóch całek oznaczonych zawierających wielomiany Gegenbauera. Wynik wykorzystano do znalezienia sum czterech szeregów o wyrazach zawierających wielomiany Gegenbauera oraz funkcje Legendre'a (pierwszego lub drugiego rodzaju) na odcinku (-1,1).
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Evaluating the antibacterial activity of muramyl dipeptide derivatives, retro-tuftsin derivatives, and anthraquinone oligopeptides against a range of pathogenic bacteria
PublicationSearch for new and efficient antibiotic is crucial because of microbial drug resistance and problems with side effects of the administered medication. In this study, we evaluate the in vitro microbiological activity of muramyl dipeptide derivatives, retro-tuftsin derivatives (i.e., tuftsin with reversed amino acid sequences), and combinations of retro-tuftsin derivatives with substituted anthraquinones. The potency of the investigated...
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Catalytic Asymmetric Synthesis of Isochroman Derivatives
PublicationThe isochroman scaffold constitutes an important structural unit, which is present in various bioactive natural products and synthetic pharmaceutical compounds exhibiting wide arrays of biological properties. Hence the synthesis of this class of heterocyclic compounds in a stereoselective fashion is highly significant and desirable. In the last decade, a substantial advancement has been witnessed ln the catalytic asymmetric...
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MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION
PublicationThe purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic...
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Recurrent Neural Network Based Adaptive Variable-Order Fractional PID Controller for Small Modular Reactor Thermal Power Control
PublicationThis paper presents the synthesis of an adaptive PID type controller in which the variable-order fractional operators are used. Due to the implementation difficulties of fractional order operators, both with a fixed and variable order, on digital control platforms caused by the requirement of infinite memory resources, the fractional operators that are part of the discussed controller were approximated by recurrent neural networks...
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Hedging with derivatives - Case of Polish market
PublicationThis paper attempts to show the ways of reaching the competitive advantage by hedging with derivatives in Poland. It shows the results of investigation of 50 Polish companies and comparison to the situation in high developed countries. Through broad review of relevant literature, the authors presented the correlation between hedging and competitive advantage. Moreover, paper shows the reasons, of differences between Poland and...
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Fuzzy Multi-Regional Fractional PID controller for Pressurized Water nuclear Reactor
PublicationThe paper presents the methodology for the synthesis of a Fuzzy Multi-Regional Fractional Order PID controller (FMR-FOPID) used to control the average thermal power of a PWR nuclear reactor in the load following mode. The controller utilizes a set of FOPID controllers and the fuzzy logic Takagi-Sugeno reasoning system. The proposed methodology is based on two optimization parts. The first part is devoted to finding the optimal...
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Successive Iterative Method for Higher-Order Fractional Differential Equations Involving Stieltjes Integral Boundary Conditions
PublicationIn this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.
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A Nyquist filter of fractional delay
PublicationIn the paper a novel discrete-time FIR fractonal delay specjal filter is investigated. This is a Nyquist filter which, besides the traditional its attribute (interymbol interference (ISI) free property), has the ability to compensate for subsample transmission delay involved, for example, in multipath propagation channel. The performance of the filter is analysed and illustrated.
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Studies on the influence of β-cyclodextrin derivatives on the physical stability of famotidine
PublicationThe usage of Fourier transform infrared spectroscopy, near infrared spectroscopy, differential scanning calorimetry and microscopy is presented in this work focused on the exploration of the effect of CD on the physical stability of famotidine (FAM). The most significant information was achieved by analysis of the second derivatives ofnear infrared (NIR) spectra recorded. Changes in the shape of spectra derivatives allow...
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Anticancer Properties of Amino Acid and Peptide Derivatives of Mycophenolic Acid
PublicationBackground: Although Mycophenolic Acid (MPA) is applied as prodrugs in clinic as an immunosuppressant, it also possesses anticancer activity. MPA acts as Inosine-5’-Monophosphate Dehydrogenase (IMPDH) inhibitor, where the carboxylic group at the end of the side chain interacts with Ser 276 of the enzyme via hydrogen bonds. Therefore, MPA derivatives with other polar groups indicated high inhibition too. On the other hand, potent...
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Synthesis and crystal structure of ferrocenyl benzothiazole derivatives
PublicationNovel ferrocenyl-containing benzothiazole derivatives were synthesised in moderate yields by one-pot α-amidoalkylation of ferrocene. The reaction conditions were critically evaluated and the crystal structure of one of the amidoalkylated ferrocenes was resolved. Oxidation of the obtained compounds led to known fully aromatic 2-ferrocenylbenzothiazole in 81 % yield, which represents a convenient alternative to earlier methods utilizing...
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Rhodotorulic Acid and its Derivatives: Synthesis, Properties, and Applications
PublicationSiderophores are low molecular weight compounds produced by microorganisms to scavenge iron in iron-deficient environments. Rhodotorulic acid (RA), a natural hydroxamate siderophore, plays a vital role in iron acquisition for fungi and bacteria. As the simplest natural hydroxamate siderophore, RA exhibits a high affinity for ferric ions, enabling it to form stable complexes that facilitate iron uptake and transport within microorganisms....
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Indirect Measurement of Motor Current Derivatives in PMSM Sensorless Drives
PublicationMotor current derivatives contain useful information for control algorithms, especially in sensorless electric drives. The measurement of motor current derivatives in electric motors supplied by voltage source inverter can be performed using di/dt transducers. However, in such a solution additional sensors have to be installed, e.g. Rogowski coils. Another approach is to measure current derivatives indirectly – by oversampling...
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Rhodotorulic Acid and its Derivatives: Synthesis, Properties, and Applications
PublicationSiderophores are low molecular weight compounds produced by microorganisms to scavenge iron in iron-deficient environments. Rhodotorulic acid, a natural hydroxamate siderophore, plays a vital role in iron acquisition for fungi and bacteria. As the simplest natural hydroxamate siderophore, it exhibits a high affinity for ferric ions, enabling it to form stable complexes that facilitate iron uptake and transport within microorganisms....
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Therapeutic Potential of Carnosine and Its Derivatives in the Treatment of Human Diseases
PublicationDespite significant progress in the pathogenesis, diagnosis, treatment, and prevention of cancer and neurodegenerative diseases, their occurrence and mortality are still high around theworld. The resistance of cancer cells to the drugs remains a significant problem in oncology today,while in the case of neuro-degenerative diseases, therapies reversing the process are still yet to be found. Furthermore, it is important to seek new...
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Stability analysis of interconnected discrete-time fractional-order LTI state-space systems
PublicationIn this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained...
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New Chalcones Derivatives With Potent Antitumor Activity And Their Metabolism In Vitro
PublicationChalcone derivatives exhibit a broad range of biological activities, with antioxidant and cytotoxic properties among the most studied. Despite numerous reports on chalcones as cytotoxic, and potentially anticancer agents, very little is know on their actual mechanism of activity. Generally, chalcones are considered as antimitotic agents, which interfere with tubulin assembly.We have recently developed a new class of chalcones with...
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Fractional differential equations with deviating arguments
PublicationDla równań różniczkowych typu ułamkowego, zostały podane warunki dostateczne na istnienie jednego rozwiązania lub rozwiazań ekstremalnych. Nierówności różniczkowe są też doskutowane.
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Some applications of fractional order calculus
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Fractional Order Models of Dynamic Systems
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Optimal Control for Discrete Fractional Systems
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Immunosuppressive properties of amino acid and peptide derivatives of mycophenolic acid
PublicationMycophenolic acid (MPA) was coupled with amino acids and biologically active peptides including derivatives of tuftsin to modify its immunosuppressive properties. Both amino acid unit in the case of simple MPA amides and modifications within peptide moiety of MPA - tuftsin conjugates influenced the observed activity. Antiproliferative potential of the obtained conjugates was investigated in vitro and MPA amides with threonine methyl...
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Acyl Meldrum's acid derivatives: application in organic synthesis
PublicationThis review is focused on one of the most important classes of Meldrum's acid derivatives commonly known as acyl Meldrum's acids. The preparation methods of these compounds are considered including the recently proposed and rather rarely used ones. The chemical properties of acyl Meldrum's acids are described in detail, including thermal stability and reactions with various nucleiophiles. The possible mechanisms of these transformations...
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Metal dusting phenomena of 501 AISI furnace tubes in refinery fractional distillation unit
PublicationThe purpose of this investigation was to conduct the failure analysis of 501 AISI furnace tubes places before distillation column in fractional distillation unit. The investigated furnace tubes were planned to work for ten years however after just two years of exploitation <30% of the material left. The observed corrosion process had the intense and complex character. The well-adhered shiny black deposits and deep, round pits were...
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Synthesis and antimicrobial activity of amino acid and peptide derivatives of mycophenolic acid
PublicationThe series of 16 novel amino acid and peptide mycophenolic acid (MPA) derivatives was obtained as potential antibacterial agents. Coupling of MPA with respective amines was optimized with condensing reagents such as EDCI/DMAP and T3P/TEA. Amino acid analogs were received both as methyl esters and also with the free carboxylic group. The biological activity of the products was tested on five references bacterial strains: Klebsiella...
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Improving the regulation of the derivatives market as an objective prerequisite for sustainable development of the global financial system
PublicationThe development of financial markets is characterized by the emergence of new financial instruments, in particular derivatives, the risk level analysis of which is complicated. Counterparties are not always fully aware of and do not adequately assess the potential risks of derivatives, which may lead to large financial losses and sometimes bankruptcies. The purpose of the study is to generalize approaches to regulating derivative...
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Therapeutic Potential of Multifunctional Derivatives of Cholinesterase Inhibitors
PublicationThe aim of this work is review of tacrine analogues from the last three years, which were not included in the latest review work, donepezil and galantamine hybrids from 2015 and rivastigmine derivatives from 2014. In this account we summarize the efforts toward the development and characterization of non-toxic inhibitors of cholinesterases based on mentioned drugs with various interesting additional properties such as antioxidant,...
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Thermodynamics aspects of interactions between acridine derivatives and DNA
PublicationDNA is a molecular target for many anticancer and antiviral drugs. Therefore, a clear understanding of the interaction of small molecules with DNA is important in the rational design of ligands that can bind to DNA with high affinity and selectivity. There are several methods to investigate interactions between drug and DNA. Some of them measure changing into DNA structures, such as lengthening and untwisting of helix of DNA. Other...
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Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals
PublicationIn this paper, the buckling of rectangular functionally graded (FG) porous nanoplates based on threedimensional elasticity is investigated. Since, similar researches have been done in two-dimensional analyses in which only large deflections with constant thickness were studied by using various plate theories; therefore, discussion of large deformations and change in thickness of plates after deflection in this study is examined....
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Design and synthesis of new analogues of batracylin linked to tuftsin and retro-tuftsin derivatives
PublicationThe synthesis of derivatives of batracylin with several peptides was elaborated followed by their cytotoxic activity investigation.
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Influence of a lipid bilayer on the conformational behavior of amphotericin B derivatives - A molecular dynamics study.
PublicationAmphotericin B (AmB) is an effective but very toxic antifungal antibiotic. In our laboratory a series of AmB derivatives of improved selectivity of action was synthesized and tested. To understand molecular basis of this improvement, comparative conformational studies of amphotericin B and its two more selectivederivatives were carried out in an aqueous solution and in a lipid membrane. These molecular simulation studies revealed...
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Two-Rate Based Low-Complexity Variable Fractional-Delay FIR Filter Structures
PublicationThis paper considers two-rate based structures for variable fractional-delay (VFD) finite-length impulse response (FIR) filters. They are single-rate structures but derived through a two-rate approach. The basic structure considered hitherto utilizes a regular half-band (HB) linear-phase filter and the Farrow structure with linear-phase subfilters. Especially for wide-band specifications, this structure is computationally efficient...
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Diaryl Sulfide Derivatives as Potential Iron Corrosion Inhibitors: A Computational Study
PublicationThe present work aimed to assess six diaryl sulfide derivatives as potential corrosion inhibitors. These derivatives were compared with dapsone (4,4′-diaminodiphenyl sulfone), a common leprosy antibiotic that has been shown to resist the corrosion of mild steel in acidic media with a corrosion efficiency exceeding 90%. Since all the studied compounds possess a common molecular backbone (diphenyl sulfide), dapsone was taken as the...
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Investigations on the immunosuppressive activity of derivatives of mycophenolic acid in immature dendritic cell
PublicationThe main activity of mycophenolic acid (MPA) and its analogs is the inhibition of proliferation of T cells. Here, we hypothesized that MPA and its conjugates inhibits also the activity of antigen-presenting cells (APC) including dendritic cells (DCs). We tested the effect of novel amino acid derivatives of MPA and conjugates of MPA with acridines/acridones on DCs by flow cytometry, ELISA and MLR assay. Both acridines/acridone derivatives...
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Novel amides of mycophenolic acid and some heterocyclic derivatives as immunosuppressive agents
PublicationThe group of new amide derivatives of mycophenolic acid (MPA) and selected heterocyclic amines was synthesised as potential immunosuppressive agents functioning as inosine-5'-monophosphate dehydrogenase (IMPDH) uncompetitive inhibitors. The synthesis employed uronium-type activating system (TBTU/HOBt/DIPEA) while or phosphonic acid anhydride method (T3P/Py) facilitating amides to be obtained in moderate to excellent yields without...
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NUMERICAL ESTIMATION OF HULL HYDRODYNAMIC DERIVATIVES IN SHIP MANOUVERING PREDICTION
PublicationOperating in crowded waterways pose a risk of accidents and disasters due to maneuvering limitations of the ship. In order to predict ship’s maneuvering characteristics at the design stage, model tests are often executed as the most accurate prediction tool. Two approaches can be distinguished here: free running model tests and numerical simulations based on planar motion model with the use of hydrodynamic derivatives obtained...
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Synthesis and biological activity of mycophenolic acid-amino acid derivatives
PublicationIn search of new immunosuppressants, mycophenolic acid (MPA) was coupled with amino acid methyl esters followed by hydrolysis to analogs bearing free carboxylic groups. The obtained compunds were tested in vitro as growth inhibitors of lymphoid cell line (Jurkat) and human peripheral blood mononuclear cells (PBMC) from healthy donors. According to obtained results recovering of free carboxylic group increased their activity. Additionally,...
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Amphotericin B and Its New Derivatives - Mode of Action
PublicationAmphotericin B (AmB) is a well known antifungal and antiprotozoal antibiotic used in the clinic for several decades. Clinicalapplications of AmB, however, are limited by its nephrotoxicity and many other acute side effects which are not acceptable by patientswhen their life is not threaten. In order to improve the therapeutic index of this drug, lipid formulations have been introduced and manyefforts have been made to obtain less...
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N-Alkyl Derivatives of L-Glutamine As Inhibitors of Glutamine - Utilizing Enzymes
PublicationA general facile method to synthesize the N-gamma-alkyl and N-gamma,N-gamma-dialkyl derivatives of L-glutamine (1a-d) from L-glutamic acid as a starting substrate is presented. The obtained compounds are shown to inhibit three diferent glutamine-utilizing enzymes, namely: glutaminase, gamma-glutamyl transpeptidase, and glucosamine-6-phosphate synthase, with inhibitory constants within the milimolar range.
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Synthesis of bicoumarin thiophosphate derivatives as steroid sulfatase inhibitors
PublicationBased on the frameworks of 7-hydroxy-2,3-dihydro-1H-cyclopenta[c]chromen-4-one, 3-hydroxy- 7,8,9,10-tetrahydro-6H-benzo[c]chromen-6-one and 3-hydroxy-8,9,10,11-tetrahydro-7H-cyclohepta[c] chromen-6-one, a series of bicoumarin thiophosphate analogs have been synthesized and biologically evaluated. Additionally, their binding modes have been modeled using docking techniques. The inhibitory properties of the synthesized compounds...
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General, Mild, and Metal-Free Functionalization of Indole and Its Derivatives Through Direct C3-Selenylation
PublicationA very mild method for the introduction of functionalized alkylselenyl group at C-3 position of the indole ring was developed. The proposed procedure consists of an electrophilic substitution of indole and its derivatives with bis(O,O-diisopropoxyphosphorothioyl) diselenide and subsequent cleavage of the P–Se bond with tetrabutylammonium fluoride in the presence of various electrophilic reagents. This method can be successfully...