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Search results for: GRÜNWALD-LETNIKOV DERIVATIVE
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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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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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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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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited...
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On Applications of Fractional Derivatives in Electromagnetic Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are analysed from the point of view of applications in the electromagnetic theory. The mathematical problems related to the FO generalization of Maxwell's equations are investigated. The most popular formulations of the fractional derivatives, i.e., Riemann-Liouville, Caputo, Grünwald-Letnikov and Marchaud definitions, are considered. Properties of these derivatives are...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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On Applications of Fractional Derivatives in Circuit Theory
PublicationIn this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling are formulated. Potential problems related to the generalization of transmission line equations with the use of FO derivatives are presented. It is demonstrated that some of formulations of the FO derivatives have limited...
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Crank–Nicolson FDTD Method in Media Described by Time-Fractional Constitutive Relations
PublicationIn this contribution, we present the Crank-Nicolson finite-difference time-domain (CN-FDTD) method, implemented for simulations of wave propagation in media described by time-fractional (TF) constitutive relations. That is, the considered constitutive relations involve fractional-order (FO) derivatives based on the Grünwald-Letnikov definition, allowing for description of hereditary properties and memory effects of media and processes....
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Comparative Study of Integer and Non-Integer Order Models of Synchronous Generator
PublicationThis article presents a comparison between integer and non-integer order modelling of a synchronous generator, in the frequency domain as well as in the time domain. The classical integer order model was compared to one containing half -order systems. The half-order systems are represented in a Park d-q axis equivalent circuit as impedances modelled by half-order transmittances. Using a direct method based on the approximation...
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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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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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Photoelectron spectroscopy of brominated derivative of pyrimidine: 2-bromopyrimidine
PublicationIn this study the brominated derivative of pyrimidine, 2-bromopyrimidine, was investigated by photoelectron spectroscopy. Outer valence photoelectron spectra recorded at 21.22, 45 and 100 eV photon energy for this compound are presented. The recorded spectra have a higher resolution than that previously reported in the literature. The bromine 3d and 3p edge photoelectron spectra have also been recorded in a photon impact experiment...
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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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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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Crystal Structures of d-Lyxono-1,4-lactone and Its O-Tosyl Derivative
Publicationγ- and δ-lactones were formed by bromine oxidation of commercially available D-lyxose, as confirmed by IR analysis. The former was isolated, and its structure was confirmed by NMR spectra and X-ray analysis. In this structure, the presence of both intermolecular and intramolecular hydrogen bonds was found. Intermolecular interactions in the crystal were illustrated using the Hirshfeld surfaces. Due to steric reasons, 3,5- O-isopropylidene-D-lyxono-1,4-lactone...
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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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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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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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Multiple Solutions to Third-Order Differential Equations with Derivative Dependence and Deviating Arguments
PublicationIn this paper, we give some new results for multiplicity of positive (nonnegative) solutions for third-order differential equations with derivative dependence, deviating arguments and Stieltjes integral boundary conditions. We discuss our problem with advanced argument α and arbitrary β ∈ C([0,1],[0,1]), see problem (2). It means that argument β can change the character on [0,1], so β can be delayed in some set J ⊂ [0,1] and advanced...
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Proportional-Derivative and Model-Based Controllers for Control of a Variable Mass Manipulator
PublicationIn the paper, numerical analysis of dynamics of a variable mass manipulator is presented. A revolute joints composed manipulator is considered. Payload of the gripper is considered as the only element characterized by unknown value of its mass (variable between subsequent operations). As in other cases of the revolute joints composed manipulators, its behaviour dependents significantly on the pose of the manipulator. When the manipulator...
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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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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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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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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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Metabolism of antitumour agent 1-nitroacridine derivative, C-1748 in pancreatic cancer cell lines
PublicationPancreatic cancer has the highest mortality rate of all major cancers because of limited treatment options. Surgical removal of the tumour is possible only in its early stage, nevertheless the asymptomatic development very often makes unable an accurate diagnose. In the case of metastatic pancreatic cancer only chemotherapy, mainly with gemcitabine, can be offered to patients. However, common resistance towards gemcitabine imposes...
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Antifungal action of the oxathiolone-fused chalcone derivative
PublicationAMG-148, pochodna chalkonu z pierścieniem oksatiolonowym, wykazuje aktywność przeciwgrzybową in vitro wobec szczepów grzybowych patogennych dla człowieka, z wartościami minimalnych stężeń hamujących wzrost mieszczących się w zakresie 1-16 mikrogramów na mililitr, natomiast w wyższych stężeniach związek ten działa grzybobójczo. Obecność głównych białek oporności wielolekowej, Cdr1p, Cgr2p lub Mdr1p nie wpływa znacząco na aktywność...
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Thermodynamic, Anticoagulant, and Antiproliferative Properties of Thrombin Binding Aptamer Containing Novel UNA Derivative
PublicationThrombin is a serine protease that plays a crucial role in hemostasis, fibrinolysis, cell proliferation, and migration. Thrombin binding aptamer (TBA) is able to inhibit the activity of thrombin molecule via binding to its exosite I. This 15-nt DNA oligonucleotide forms an intramolecular, antiparallel G-quadruplex structure with a chair-like conformation. In this paper, we report on our investigations on the influence of certain...
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Time fractional analysis of Casson fluid with application of novel hybrid fractional derivative operator
PublicationA new approach is used to investigate the analytical solutions of the mathematical fractional Casson fluid model that is described by the Constant Proportional Caputo fractional operator having non-local and singular kernel near an infinitely vertical plate. The phenomenon has been expressed in terms of partial differential equations, and the governing equations were then transformed in non-dimensional form. For the sake of generalized...
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Synthesis and application of oligomer with hydroxy groups based on peroxy derivative of ED-24 epoxy resin and POLYTHF-2000 oligoether
PublicationNew oligomer with peroxy, primary and secondary hydroxy groups has been synthesized on the basis of peroxy derivative of ED-24 epoxy resin (PO) and PolyTHF-2000 oligoether according to the developed procedure. The effect of the catalysts nature and amount, temperature and process time on the reaction rate has been studied. Benzyltriethylammonium chloride, potassium hydroxide,1,4-diazobicyclooctane and the mixture composed of benzyltriethylammonium...
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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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Investigation of an elutable N-propylphosphonic acid chitosan derivative composition with a chitosan matrix prepared from carbonic acid solution
PublicationPorous chitosan composites using CO2 dissolution procedure and including water soluble N-propylphosphonic chitosan derivative (p-CHI) were obtained and characterized. In contrast to the control material, composites containing modified chitosan distinguished by a rapid moisture absorption and good adhesion to the skin. The FTIR analysis confirmed the presence of propylphosphonic group in the structure of the polymer. The porosity...
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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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Proportional-Derivative and Model-based Controllers used for a Serial Type Manipulator in case of a Variable Mass Payload
PublicationIn the paper, numerical analysis of dynamics of a variable mass system is considered. Its reference example is a serial-like manipulator composed of revolute joints and rigid bodies. Payload of its gripper is considered as its variable mass element (mass and inertia irregularly between subsequent payloads). For the rest of the system, inertia parameters are considered as known (precisely identified during the assembling process)....
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On the derivative of the Legendre function of the first kind with respect to its degree
PublicationPokazano, że pochodna po indeksie funkcji Legendre'a pierwszego rodzaju, obliczona dla całkowitej wartości indeksu, może być wyrażona przez funkcje elementarne. Skonstruowano kilka jawnych reprezentacji tej pochodnej. Zaprezentowano przykłady zastosowań otrzymanych wzorów.
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Carboxy derivative of dioxydiphenylpropane diglycydyl ether monomethacrylate as an addtive for composites
PublicationThe modifier of composites was used in the presence of polyetylene polyamine. Physico-mechanical properties and chemical stability of coatings thus obtained were analyzed.
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Unexpected thioketene derivative formation during thioacyl dithiophosphate synthesis.
PublicationZbadano zakres i ograniczenia tioacylowania opartego na ditiofosforanach tioacylu. Ditiofosforany tioacylo otrzymano w wyniku reakcji ditiofosforanów acylu z kwasem ditiofosforowym. Obecność dwóch podstawników w pozycji alfa we fragmencie acylowym faworyzowała tworzenie pochodnych tioketenu tym samym obniżając wydajność oczekiwanych ditiofosforanów tioacylu.
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Synthesis and properties of carboxy derivative of Epidian 6 monomethacrylate (in English)
PublicationWe present the synthesis of an oligomer with carboxy and methacrylic groups based on Epidian 6. The effect of the catalyst nature and amount, solvent nature and process temperature on the rate of the reaction between Epidian6 monomethacrylate and adipic acid was examined at 313, 323 and 333 K in the presence of 4-dimethylaminopyridine, 1,4-diazobicyclo[2.2.2]octane, and benzyltriammonium chloride. The synthesized oligomer was characterized...
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Antitumor 1-nitroacridine derivative C-1748 induces significant apoptosis in pancreatic cancer cells.
PublicationPancreatic cancer is the fifth leading cause of cancer death and has the lowest survival rate of any solid cancer in the industrial countries. The poor prognosis of pancreatic cancer results from its tendency for late presentation, aggressive invasion, early metastasis, and resistance to chemotherapy. Gemcitabine still remains the best chemotherapeutic agent available for the treatment of advanced pancreatic cancer. However, gemcitabine...
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Addendum to ''On the derivative of the Legendre function of the first kind with respect to its degree''
PublicationPraca stanowi uzupełnienie wcześniejszej publikacji autora [J. Phys. A: Math. Gen. 39(2006) 15147-15172]. Przedstawiono w niej nowe wyrażenia dla pochodnej funkcji Legendre'a względem jej indeksu i zastosowano je do konstrukcji dwóch nowych reprezentacji funkcji Legendre'a drugiego rodzaju z całkowitym indeksem.
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Existence and uniqueness for neutral equations with delay dependant on a solution and its derivative
PublicationDla wykazania istnienia i jednoznaczności w pracy została zaprezentowana metoda porównawcza.
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Proportional-derivative and Model-based Controllers for Control of a Variable Mass Manipulator
PublicationW artykule prezentowano wyniki analiza numeryczna dynamiki manipulatora o zmiennej masie. W skład manipulatora wchodzą jedynie członu i przeguby obrotowe. Ładowność chwytaka jest traktowana jako jedyny element o zmiennej masie. Podobnie jak w przypadku innych manipulatorów wyposażonych w przeguby obrotowe, parametry jego dynamika zależą od aktualnego ustawienia. Gdy przemieszczenia obejmują większy zakres roboczy, w równaniach...
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Surface modification of PMMA polymer and its composites with PC61BM fullerene derivative using an atmospheric pressure microwave argon plasma sheet
PublicationThis paper presents the results of experimental investigations of the plasma surface modification of a poly(methyl methacrylate) (PMMA) polymer and PMMA composites with a [6,6]-phenyl-C61-butyric acid methyl ester fullerene derivative (PC61BM). An atmospheric pressure microwave (2.45 GHz) argon plasma sheet was used. The experimental parameters were: an argon (Ar) flow rate (up to 20 NL/min), microwave power (up to 530 W), number...
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Enantioselective sensing of (S)-Thalidomide in blood plasma with a chiral naphthalene diimide derivative
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Apoptosis of human leukemia cells induced by imidazoacridinone derivative C-1311 (Symadex)
PublicationPraca dotyczy różnej wrażliwości komórek białaczek ludzkich do ulegania apoptozie pod wpływem pochodnej imidazoakrydonu C-1311, co jest zgodne z aktywnością cytotoksyczną tego związku (EC90) wobec badanych komórek.
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Fractional Variable-Order Derivative and Difference Operators and Their Applications to Dynamical Systems Modelling
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Uniform expansion estimates in the quadratic map as a function of the parameter, using the “derivative” partition type
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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Uniform expansion estimates in the quadratic map as a function of the partition size, using the “derivative” partition type
Open Research DataThis dataset contains selected results of numerical computations described in the paper "Quantitative hyperbolicity estimates in one-dimensional dynamics" by S. Day, H. Kokubu, S. Luzzatto, K. Mischaikow, H. Oka, P. Pilarczyk, published in Nonlinearity, Vol. 21, No. 9 (2008), 1967-1987, doi: 10.1088/0951-7715/21/9/002.
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CYP3A4 overexpression enhances the cytotoxicity of the antitumor triazoloacridinone derivative C-1305 in CHO cells
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In vitro photodynamic activity of lipid vesicles with zinc phthalocyanine derivative against Enterococcus faecalis
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