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Search results for: SECOND DERIVATIVE
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On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces
PublicationIn this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c(x, A) = |A[x]2 |. We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable...
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Positive solutions to second-order differential equations with dependence on the first-order derivative and nonlocal boundary conditions
PublicationIn this paper, we consider the existence of positive solutions for second-order differential equations with deviating arguments and nonlocal boundary conditions. By the fixed point theorem due to Avery and Peterson, we provide sufficient conditions under which such boundary value problems have at least three positive solutions. We discuss our problem both for delayed and advanced arguments α and also in the case when α(t)=t, t∈[0,1]....
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On the derivative of associated Le.gendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
PublicationW pracy podano szereg zamkniętych wyrażeń dla pochodnej stowarzyszonej funkcji Legendre'a o stopniu (dolnym indeksie) całkowitym względem jej rzędu (górnego indeksu). Wyniki zastosowano do wyprowadzenia kilku nowych reprezentacji, w tym typu Rodriguesa, stowarzyszonych funkcji Legendre'a drugiego rodzaju z całkowityni indeksani.
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On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree (with applications to the construction of the associated Legendre function of the second kind of integer degree and order).
PublicationWyprowadzono szereg zamkniętych wyrażeń dla pochodnych stowarzyszonej funkcji Legendre'a pierwszego rodzaju względem jej dolnego indeksu w przypadku, gdy górny indeks jest liczbą całkowitą. Wyniki zastosowano do znalezienia pewnych nowych reprezentacji (w tym typu Rodriguesa) stowarzyszonych funkcji Legendre'a drugiego rodzaju o indeksach całkowitych.
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Numerical Investigation of Nuclear Reactor Kinetic and Heat Transfer Fractional Model with Temperature Feedback
PublicationAbstract—In the paper, the numerical results concerning the kinetics and proposed heat exchange models in nuclear reactor based on fractional calculus are presented for typical inputs. Two fractional models are proposed and compared with the model based on ordinary derivative. The first fractional model is based on one of the generalized Cattaneo equations. The second one is based on replacing the ordinary to fractional order of...
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Solvent-Free Synthesis of Phosphonic Graphene Derivative and Its Application in Mercury Ions Adsorption
PublicationFunctionalized graphene was efficiently prepared through ball-milling of graphite in the presence of dry ice. In this way, oxygen functional groups were introduced into material. The material was further chemically functionalized to produce graphene derivative with phosphonic groups. The obtained materials were characterized by spectroscopic and microscopic methods, along with thermogravimetric analysis. The newly developed material...
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Modeling and control of a redundantly actuated variable mass 3RRR planar manipulator controlled by a model-based feedforward and a model-based-proportional-derivative feedforward–feedback controller
PublicationIn the paper, dynamics of a complex mechatronics system is considered. A redundantly actuated planar manipulator is the base of the mechanical part of it. It is a 3RRR 1 platform based parallel manipulator. To control its trajectory, a model-based feedforward controller is employed. Three aspects are fundamental in the presented investigations. The first focus is on development of an accurate numerical model used to solve the inverse...
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Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor
PublicationThe paper presents the neutron point kinetics and heat exchange models for the nuclear reactor. The models consist of a nonlinear system of fractional ordinary differential and algebraic equations. Two numerical algorithms are used to solve them. The first algorithm is application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. The second involves building an analog scheme in the FOMCON Toolbox...
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Numerical solution of fractional neutron point kinetics in nuclear reactor
PublicationThis paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme...
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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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Chalcogen bonding interactions in a series of aromatic selenocyanates
PublicationSelenium atoms in aromatic selenocyanates are characterized by the occurrence of two σ-holes, a stronger one in the prolongation of the NC–Se bond and a weaker one in the prolongation of the Ar–Se bond. The crystal structures of several bis(selenocyanato) derivatives, prepared by a method originally developed for ortho bis-substituted derivatives, illustrate very well this difference, with a short NC–Se⋯NC ChB interaction organizing...
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Electronic States of Tris(bipyridine) Ruthenium(II) Complexes in Neat Solid Films Investigated by Electroabsorption Spectroscopy
PublicationWe present the electric field-induced absorption (electroabsorption, EA) spectra of the solid neat films of tris(bipyridine) Ru(II) complexes, which were recently functionalized in our group as photosensitizers in dye-sensitized solar cells, and we compare them with the results obtained for an archetypal [Ru(bpy)3]2+ ion (RBY). We argue that it is difficult to establish a unique set of molecular parameter values by discrete parametrization...
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The absorption and fluorescence spectra of C-1305 derivatives (IKE1-IKE8), potential antifungal agents
Open Research DataOptical measurements of C-1305 derivatives (IKE1-IKE8). The absorption spectra were recorded at 300 - 800 nm for solutions with 16 μg / mL derivative concentration. The fluorescence emission spectra were determined at 420-800 nm with the excitation wavelengths 360 or 415 nm for solutions with 1 μg / mL derivative concentration. All measurements were...
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Fe3–xInSnxO6 (x = 0, 0.25, or 0.5): A Family of Corundum Derivatives with Sn-Induced Polarization and Above Room Temperature Antiferromagnetic Ordering
PublicationThree new double corundum derivative compounds, Fe3−xInSnxO6 (x = 0. 0.25, or 0.5), were synthesized at high pressure and temperature (6 GPa and 1400− 1450 °C). All of the compounds order antiferromagnetically well above room temperature (TN = 608, 532, and 432 K for x = 0, 0.25, and 0.5, respectively). The x = 0 phase crystallizes as centrosymmetric R3̅c, but the inclusion of closed-shell d10 Sn4+ induces x = 0.25 and 0.5 to crystallize...
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Cross-talk Between the Heart and Arteries in Older 65+ Adults
PublicationRegulatory synchronization between the heart and the arterial walls is essential for optimal blood delivery to tissues. We investigated functional coherence between heart rhythm and aortic wall compliance in 30 volunteers aged 65 – 74. ECG and carotid and iliac pulse-wave were recorded and digitized at 2 kHz. Carotid-femoral pulse-wave transit time (cfTT) which reflex aortic compliance was assessed using the intersecting tangent...
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Thermogravimetric analysis (TGA ) and derivative thermogravimetry (DTG) results for potassium citrate
Open Research DataThese data contains thermogravimetric analysis (TGA ) and derivative thermogravimetry (DTG) results for thermal decomposition of potassium citrate.
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Copper(I) iodide ribbons coordinated with thiourea derivatives
PublicationTwo products of the reactions of CuI with 1-benzoyl-3-(4-bromophenyl)thiourea and with 1-benzoyl-3-(2-iodophenyl)thiourea have been obtained and characterized, namely poly[[[1-benzoyl-3-(4-bromophenyl)thiourea-κS]-µ3-iodidocopper(I)] acetone hemisolvate], {[CuI(C₁₄H₁₁BrN₂OS)]‧0.5C₃H₆O}ₙ, and poly-[µ₄-iodido-µ₃-iodido-[N-(benzo[d]thiazol-2-yl)benzamide-κN]dicopper(I)], [Cu₂I₂(C₁₄H₁₀N₂OS)]ₙ. Their structures, determined by single-crystal...
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Signal Propagation in Electromagnetic Media Modelled by the Two-Sided Fractional Derivative
PublicationIn this paper, wave propagation is considered in a medium described by a fractional-order model, which is formulated with the use of the two-sided fractional derivative of Ortigueira and Machado. Although the relation of the derivative to causality is clearly specified in its definition, there is no obvious relation between causality of the derivative and causality of the transfer function induced by this derivative. Hence, causality...
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Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
PublicationStarting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
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Analysis of latency between quotations and capital flow in capital markets.
PublicationThe aim of this paper is to prove that the derivative of the log of capital flow understood as price times volume advances the derivative of log of the price. A certain concept of signal processing using linear filtering has been proposed to conduct the research.
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Fully scalable one-pot method for the production of phosphonic graphene derivatives
PublicationGraphene oxide was functionalized with simultaneous reduction to produce phosphonated reduced graphene oxide in a novel, fully scalable, one-pot method. The phosphonic derivative of graphene was obtained through the reaction of graphene oxide with phosphorus trichloride in water. The newly synthesized reduced graphene oxide derivative was fully characterized by using spectroscopic methods along with thermal analysis. The morphology...
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Oxolane Ammonium Salts (Muscarine-Like)—Synthesis and Microbiological Activity
PublicationCommercially available 2-deoxy-D-ribose was used to synthesize the appropriate oxolane derivative—(2R,3S)-2-(hydroxymethyl)oxolan-3-ol—by reduction and dehydration/cyclization in an acidic aqueous solution. Its monotosyl derivative, as a result of the quaternization reaction, allowed us to obtain eight new muscarine-type derivatives containing a quaternary nitrogen atom and a hydroxyl group linked to the oxolane ring. Their structure...
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Propeller-Like Chirality of Methyl-Tris (2,6-diisopropylphenoxy)Silylsulfide
PublicationTwo new methylsilylsulfides are synthesized. Propeller-like chirality is described for triaryloxysilanethiol and its methyl derivative. S-methylation of the silanethiol lowers the overall symmetry of the unit cell.
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Numerical and quantitative analysis of HIV/AIDS model with modified Atangana-Baleanu in Caputo sense derivative
PublicationFractional calculus plays an important role in the development of control strategies, the study of the dynamical transmission of diseases, and some other real-life problems nowadays. The time-fractional HIV/AIDS model is examined using a novel method in this paper. Based on the Atangana-concept Baleanu’s of a derivative in the Caputo sense, the current modified fractional derivative operator uses singular and non-local kernels....
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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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Sensitive Demonstration of the Twin-Core Couplers including Kerr Law Non-Linearity via Beta Derivative Evolution
PublicationTo obtain new solitary wave solutions for non-linear directional couplers using optical meta-materials, a new extended direct algebraic technique (EDAT) is used. This model investigates solitary wave propagation inside a fiber. As a result, twin couplers are the subject of this study. Kerr law is the sort of non-linearity addressed there. Because it offers solutions to problems with large tails or infinite fluctuations, the resulting...
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Killing kinetics analysis of C-1311 derivative with octaarginine (Compound 1-R8) against Candida albicans
Open Research DataThe datasets contain the results of killing kinetics analysis of imidazoacridinone derivative and fluconazole against C. albicans ATCC 10231. The suspensions of Candida albicans ATCC 10231 cells (500 µL) in RPMI 1640 at cell density of 104 cells /mL were added to 500 µL of RPMI 1640 medium with various concentrations of the compounds, corresponding...
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Polyurethane Nanocomposites Containing Reduced Graphene Oxide, FTIR, Raman, and XRD Studies
PublicationRecently, graphene and other graphene-based materials have become an essential part of composite science and technology. Their unique properties are not only restricted to graphene but also shared with derivative compounds like graphene oxide, reduced graphene oxide, functionalized graphene, and so forth. One of the most structurally important materials, graphene oxide (GO), is prepared by the oxidation of graphite. Though removal...
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On the dervative of the Legendre function of the first kind with respect to its degree [Corrigendum]
PublicationSkorygowano błąd matematyczny w pracy: R. Szmytkowski, On the derivative of the Legendre function of the first kind with respect to its degree, J. Phys. A: Math. Gen. Vol. 39(2006) s. 15147-15172 [744014]
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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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A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
PublicationThe aim of this paper is to study the dynamics of Dengue disease model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative are examined for the aforementioned problem. The suggested...
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Studies on Aminoanthraquinone-Modified Glassy Carbon Electrode: Synthesis and Electrochemical Performance toward Oxygen Reduction
PublicationIn this paper, 9,10-anthraquinone (AQ) derivative-modified glassy carbon (GC) electrodes were studied towards the electrochemical reduction of oxygen in aqueous and non-aqueous solutions. The reaction of 1-chloro-9,10-anthraquinone with aliphatic diamines was applied for the synthesis of amino-9,10-anthraquinone derivatives. The obtained AQ derivatives were grafted onto the surface of glassy carbon electrodes by electropolymerisation...
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublicationIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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Studies on Aminoanthraquinone-Modified Glassy Carbon Electrode: Synthesis and Electrochemical Performance toward Oxygen Reduction
PublicationIn this paper, 9,10-anthraquinone (AQ) derivative-modified glassy carbon (GC) electrodes werestudied towards the electrochemical reduction of oxygen in aqueous and non-aqueous solutions. The reaction of 1-chloro-9,10-anthraquinone with aliphatic diamines was applied for the synthesis of amino-9,10-anthraquinone derivatives. The obtained AQ derivatives were grafted onto the surface of glassy carbon electrodes by electropolymerisation...
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The BDD electrodes wettability modification by anodic polarization treatment
Open Research DataThe dataset contains the raw images, photographs obtained for the contact angle measurement at the surface of the boron-doped diamond (BDD) electrode. The measurements were carried out on after potentiodynamic polarization procedure, at various anodic polarization scan range (no polarization - HTBDD; 1.0 V; 1.4 V; 1.9 V; 2.5 V vs Ag|AgCl, scan rate...
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TMSCL as a rate accelerating additive in acylations of amines with 5-(α- amino-α'-hydroxy)methylene meldrum's acids
PublicationAspects are presented of the acylation of amines, alcohols and thiols with 5-(α-amino- α'-hydroxy)methylene Meldrum's acids. We placed special emphasis on the acylation reaction of secondary amines with 5-(α-amino- α'-hydroxy)methylene Meldrum's acids, which, due to their basicity, caused problems concerning salt formation with a Meldrum acid derivative. We found that secondary amines, which react at the slowest rate and with a...
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Tmscl as a rate accelerating additive in acylations of amines with 5-(α-amino- α'-hydroxy)methylene meldrum's acids
PublicationAspects are presented of the acylation of amines, alcohols and thiols with 5-(α-amino- α'-hydroxy)methylene Meldrum's acids. We placed special emphasis on the acylation reaction of secondary amines with 5-(α-amino- α'-hydroxy)methylene Meldrum's acids, which, due to their basicity, caused problems concerning salt formation with a Meldrum acid derivative. We found that secondary amines, which react at the slowest rate and with a...
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The crystal structure of (1RS,4RS,5RS,6SR)-5-cyano-5-nitro-6-phenyl-bicyclo[2.2.1]hept-2-ene
PublicationStructure of nitronorbornene derivative C14H12N2O2 synthesized in the reaction of cyclopentadiene with E-2-phenyl-1-cyano-1-nitroethene was determined by single crystal X-ray diffraction analysis. It was found that in analyzed molecule the nitro group is in endo-position whereas phenyl group have exo-ori-entation.
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FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
PublicationIn this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced....
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First Copper(I) and Silver(I) Complexes Containing Phosphanylphosphido Ligands
PublicationThree new complexes with phosphanylphosphido ligands, [Cu4{μ2-P(SiMe3)-PtBu}4](1), [Ag4{μ2-P(SiMe3)-PtBu2}4](2) and [Cu{η1-P(SiMe3)-PiPr2}2]–[Li(Diglyme)2] (3) were synthesized and structurally characterized by X-ray diffraction, NMR spectroscopy, and elemental analysis. Complexes 1 and 2 were obtained in the reactionsof lithium derivative of diphosphane tBu2P-P(SiMe3)Li·2.7THF withCuCl and [iBu3PAgCl]4, respectively....
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Analysis of Crash Computation on a Basis of the Pronciple of Linear Momentum and Kinetic Energy
PublicationThe article shows the calculation of a vehicle crash with a fixed pile, modelled by the finite element method. There were compared during the crash simulations changes in kinetic energy, as well as – changes in linear momentum and its derivative, with respect to time. Calculations were made in the HyperWorks CAE software environment. The obtained results show influence of various body parts and devices of the deceleration on...
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The synthesis and structure of a potential immunosuppressant: N-mycophenoyl malonic acid dimethyl ester
PublicationThe synthesis of a potential immunosuppressant, i.e. dimethyl ester of N-mycophenoyl malonic acid was optimized in the reaction of mycophenolic acid (MPA) with amino malonic dimethyl ester in the presence of propanephosphonic anhydride (T3P) as a coupling reagent. The structural properties of the obtained MPA derivative were investigated by NMR, MS and single crystal X-ray diffraction methods. Theoretical considerations of conformational...
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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublicationIn this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...
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Photoresponsive, amide-based derivative of embonic acid for anion recognition
PublicationThe synthesis and ion-binding properties of amide-based derivative of embonic acid andp-aminoazobenzenewere described. The new compound was characterized by X-ray structural analysis and spectroscopic methods.Ligand interacts in acetonitrile with Y-shaped anions (benzoates and acetates) and dihydrogen phosphatesforming complexes of 1:1 stoichiometry. In more polar DMSO the complexes stoichiometry changes to 2:1(L:anion). Light-inducedtranstocisisomerization...
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Pre-treatment of bio fraction waste prior to fermentation processes
PublicationCurrent efforts are taken to increase resource efficiency, close material loops, and improve sustainable waste and by-products management. Thus, networking agro-food by-products and converting them into valuable products completely exhausting the potential of the raw material becomes significant. Model lignocellulosic and starch based biomass were subjected to pre-treatment with the application of acidic compounds, i.e. sulphuric...
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Photosensitive and pH-dependent activity of pyrazine-functionalized carbazole derivative as promising antifungal and imaging agent
PublicationCarbazole skeleton plays a significant role as a structural scaffold of many pharmacologically active compounds. Pyrazine-functionalized carbazole derivative was constructed by coupling 2-amino-5-bromo-3-methylaminepyrazine (ABMAP) into 3 and 6 positions of the carbazole ring. Multi-experimental methods were used, e.g., potentiometric, spectroscopic (ATR, UV, XRD powder,1H and13C NMR), electrochemical (cyclic voltammetry), and...
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Epoxy Composites Filled with Natural Calcium Carbonate. 1. Epoxy Composites Obtained in the Presence of Monoperoxy Derivative of Epidian-6 Epoxy Resin
PublicationPhysico-mechanical properties of the products based on filled epoxy-oligomeric mixtures composed of Epidian-5 epoxy resin, oligoesteracrylate TGM-3 and monoperoxide derivative of Epidian-6 epoxy resin (PO) have been investigated. CaCO3 was used as a filler and polyethylene polyamine was a curing agent. The effect of PO and CaCO3 on the gel-fraction content and physico-mechanical properties was examined. Using a scanning electron...
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Reduction of Derivative pipeline effort in water turbine
PublicationThe paper presents an approach to evaluate and reduce the effort of the derivative pipeline in a water turbine of a hydrostatic power station in its vulnerable spots. Potential places of the biggest effort of the structure, as well as the coefficient of displacement and safety factor related to them were identified using FEM numerical method. Pipeline reinforcement was designed and made based on FEM analysis. Original technology...
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The Effect of Conjugation with Octaarginine, a Cell-Penetrating Peptide on Antifungal Activity of Imidazoacridinone Derivative
PublicationAcridine cell-penetrating peptide conjugates are an extremely important family of compounds in antitumor chemotherapy. These conjugates are not so widely analysed in antimicrobial therapy, although bioactive peptides could be used as nanocarriers to smuggle antimicrobial compounds. An octaarginine conjugate of an imidazoacridinone derivative (Compound 1-R8) synthetized by us exhibited high antifungal activity against reference...
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Does the chemical modification of Nystatin A1 affect the drug's ability to overcome the multidrug resistance of fungi?
PublicationAlthough the contemporary medicine keeps moving forward, disseminated infections caused by fungal pathogens are an emerging challenge. The dramatic rise of fungal diseases, especially the most life-threatening systemic mycoses is associated with a permanently growing number of immunodeficient patients. Undoubted difficulties in the treatment of fungal infections are caused by lack of highly effective and selective antifungal drugs,...