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Search results for: WEAK SOLUTION
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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Publicationwe address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E ; (iii) we prove that the set of placements for which the strain...
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Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity
PublicationIn this paper we consider existence and uniqueness of the three-dimensional static boundary-value problems in the framework of so-called gradient-incomplete strain-gradient elasticity. We call the strain-gradient elasticity model gradient-incomplete such model where the considered strain energy density depends on displacements and only on some specific partial derivatives of displacements of first- and second-order. Such models...
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Regularity of weak solutions for aclass of elliptic PDEs in Orlicz-Sobolev spaces
PublicationWe consider the elliptic partial differential equation in the divergence form $$-\div(\nabla G(\nabla u(x))) t + F_u (x, u(x)) = 0,$$ where $G$ is a convex, anisotropic function satisfying certain growth and ellipticity conditions We prove that weak solutions in $W^{1,G}$ are in fact of class $W^{2,2}_{loc}\cap W^{1,\infty}_{loc}$.
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On existence and uniqueness of weak solutions for linear pantographic beam lattices models
PublicationIn this paper, we discuss well-posedness of the boundary-value problems arising in some “gradientincomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class ofmetamaterials whosemicrostructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-incomplete” strain-gradient elasticity for a model in which the considered strain energy...
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On weak solutions of boundary value problems within the surface elasticity of Nth order
PublicationA study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining...
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On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains
PublicationWe provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of...
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On Solvability of Boundary Value Problems for Elastic Micropolar Shells with Rigid Inclusions
PublicationIn the framework of the linear theory of micropolar shells, existence and uniqueness theorems for weak solutions of boundary value problems describing small deformations of elastic micropolar shells connected to a system of absolutely rigid bodies are proved. The definition of a weak solution is based on the principle of virial movements. A feature of this problem is non-standard boundary conditions at the interface between the...
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On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions
PublicationThe problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated...
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NEW CONCEPT OF HYBRID PROPULSION WITH HYDROSTATIC GEAR FOR INLAND WATER TRANSPORT
PublicationThe article presents the development of author’s concept of a diesel/hydraulic propulsion system for inland watercraft. Due to specific nature of vessel navigation on rivers, classical propulsion systems with shaft lines can be effectively replaced by systems with hydraulic power transmission. A solution is also presented of a hybrid design with extra electric port having the form of a pumping system driven from a battery of accumulators....
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Photophysics of Soret-Excited Tin(IV) Porphyrins in Solution
PublicationThe photophysics of low-chlorin tin(IV) tetraphenylporphyrin dihydroxide, a core building block for axially substituted supramolecular tin porphyrin constructs, has been studied in a variety of hydrogen-bonding, nonpolar, and aprotic polar solvents using steady-state, nanosecond, and femtosecond time-resolved emission, and femtosecond time-resolved absorption methods. In hydrogen-bonding solvents the metalloporphyrin exists as...
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Homoclinics for singular strong force Lagrangian systems in R^N
PublicationWe will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove...
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On well-posedness of the first boundary-value problem within linear isotropic Toupin–Mindlin strain gradient elasticity and constraints for elastic moduli
PublicationWithin the linear Toupin–Mindlin strain gradient elasticity we discuss the well-posedness of the first boundary-value problem, that is, a boundary-value problem with Dirichlet-type boundary conditions on the whole boundary. For an isotropic material we formulate the necessary and sufficient conditions which guarantee existence and uniqueness of a weak solution. These conditions include strong ellipticity written in terms of higher-order...
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Bearing capacity of the working platform with kinematic method
PublicationBearing capacity of the working platform for heavy tracks was analysed using Distinct Layout Optimization (DLO) method. The platform layer constructed from cohesionless soils is resting on weak cohesive subgrade. Different thickness of the platform, its effective angle of internal friction and undrained shear strength of the soft soil were taken into consideration. Kinematic method permits different failure mechanisms to be analyzed....
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Quasilinear elliptic problem in anisotropic Orlicz–Sobolev space on unbounded domain
PublicationWe study a quasilinear elliptic problem $-\text{div} (\nabla \Phi(\nabla u))+V(x)N'(u)=f(u)$ with anisotropic convex function $\Phi$ on the whole $\R^n$. To prove existence of a nontrivial weak solution we use the mountain pass theorem for a functional defined on anisotropic Orlicz-Sobolev space $\WLPhispace(\R^n)$. As the domain is unbounded we need to use Lions type lemma formulated for Young functions. Our assumptions broaden...
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Calculations of notch stress factor of a thin-walled spreader bracket fillet weld with the use of a local stress approach
PublicationPresence of geometric notches in welded joints causes concentration of strains and stresses, therefore reducing fatigue strength of such joints. This article presents an analysis of stress concentrations in a fillet weld of a spreader mounting bracket on a small sailing yacht. The aim of this article is to direct the attention of designers, manufacturers and regulatory bodies to issues of fatigue cracks that form in brackets fastening...
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Harmonic Vibrations of Nanosized Magnetoelectric Bodies with Coupled Surface and Interphase Effects: Mathematical Models and Finite Element Approaches
PublicationThe harmonic problems for piezomagnetoelectric nanosized bodies with taking into account the coupled damping and surface effects are considered on the base of the generalized Gurtin-Murdoch model. In the development of previous investigations, the coupled mechanical, electric and magnetic surface effects with surface inertial terms are introduced into the model. For a homogeneous model, the composite material is considered as homogeneous...
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Study of the Resistance to Influence of Aggressive Liquids on Concrete with Lightweight Aggregate
PublicationThe corrosion of the structure of concrete caused by the aggressive external environment is one of the main problems that can reduce the durability of buildings. The paper analyzes the influence of the type of component on selected properties of lightweight concrete (LWC) exposed to aggressive liquids. When lightweight concrete containing porous aggregates is used, the influence of an aggressive environment may be of particular...
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Interactions in aqueous solutions of K-peptide and DMSO – spectroscopic and calorimetric studies
PublicationIntroduction K-peptide (GILQINSRW) – short 9 amino acid fragment of the hen egg white lysozyme has the ability to form amyloid structures. Dimethyl sulfoxide (DMSO) is an osmolyte which can alter this ability. Our goal was to get an insight into the mechanism of Kpeptide-DMSO interactions in aqueous solutions. Such a knowledge can be helpful to understand processes leading to various neurodegenerative diseases. Methods ATR-FTIR...
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Experimental Study of the Resistance to Influence of Aggressive Liquids on Lightweight Concrete
PublicationIn light of the scientific research, the corrosion of concrete structures is one of the main problems that may reduce their durability due to the negative impact of the natural environment. The paper analyzes the influence of the type of component on the selected properties of lightweight concrete subjected to the influence of aggressive liquids. Four concrete mixes were prepared with a granular aggregate made of foamed glass (GEGA)...
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Reactive imines: Addition of 2-aminopyrimidine to the imine bond and isolation of the aminal from the equilibrium mixture aminal/imine
PublicationThe reaction between o-vanillin and 2-aminopyrimidine leads to the formation of a single crystalline product: aminal, 1, which results from the reaction of the initially formed imine with 2-aminopyrimidine. The reaction was followed by the NMR spectroscopy. VT NMR studies prove that in solution two major species are observed: aminal and imine and their ratio depends on the time or/and temperature with the imine content increasing...
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Medium-sized cyclic bis(anisylphosphonothioyl)- disulfanes and their corresponding cyclic sulfane-structures and most characteristic reactions
PublicationCyclic 8-, 9-, 10-, and 12-membered bis(anisylphosphonothioyl)disulfanes were synthesized. Next, structurally related 7 to 9-membered cis and trans sulfanes were isolated as a result of sulfur atom extrusion from the parent cyclic disulfanes. The results of the desulfurization of the disulfanes were compared to the results obtained for desulfurization of the respective bis(anisylphosphodithioates). Cyclic disulfanes predominantly...
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The effect of shear deformations' rotary inertia on the vibrating response of multi-physic composite beam-like actuators
PublicationIn consecutive studies on flexomagneticity (FM), this work investigates the flexomagnetic reaction of a vibrating squared multi-physic beam in finite dimensions. It is assumed that the bending and shear deformations cause rotary inertia. In the standard type of the Timoshenko beam the rotary inertia originated from shear deformations has been typically omitted. It means the rotary inertia resulting from shear deformation is a new...
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Organic solvents aggregating and shaping structural folding of protein, a case study of the protease enzyme
PublicationLow solubility of reactants or products in aqueous solutions can result in the enzymatic catalytic reactions that can occur in non-aqueous solutions. In current study we investigated aqueous solutions containing different organic solvents / deep eutectic solvents (DESs) that can influence the protease enzyme's activity, structural, and thermal stabilities. Retroviral aspartic protease enzyme is responsible for the cleavage of the...
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Cu( II ) ions removal from wastewater using starch nanoparticles ( SNPs ): An Eco‐sustainable approach
PublicationThe complex structured starch particles were reduced to the nanoscale size range through hydrolysis utilizing low concentration acid assisted with ultrasound irradiation. The synthesized starch nanoparticles (SNPs) were characterized by TEM, FTIR, and XRD techniques. The synthesized SNPs possessed surface activated entities, as many cationic functional groups were confirmed through the FTIR spectrum. Also, these SNPs were effectively...
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Effect of asymmetric fluid flow distribution on flow boiling in a microchannel heat sink – An experimental investigation
PublicationFlow boiling in microchannels is emerging as an exclusive cooling solution for miniaturized high-power electronic devices alongside having other high heat flux applications. Size miniaturization at microscale strangely increases heat transfer performance as well as flow boiling instabilities. Many flow boiling instabilities are interrelated and result from imperfect hydrodynamic conditions. One of such problems is flow maldistribution among...
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Robust amplification of Santha-Vazirani sources with three devices
PublicationWe demonstrate that amplification of arbitrarily weak randomness is possible using quantum resources. We present a randomness amplification protocol that involves Bell experiments. We find a Bell inequality which can amplify arbitrarily weak randomness and give a detailed analysis of the protocol involving it. Our analysis includes finding a sufficient violation of Bell inequality as a function of the initial quality of randomness....
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Feature Reduction Using Similarity Measure in Object Detector Learning with Haar-like Features
PublicationThis paper presents two methods of training complexity reduction by additional selection of features to check in object detector training task by AdaBoost training algorithm. In the first method, the features with weak performance at first weak classifier building process are reduced based on a list of features sorted by minimum weighted error. In the second method the feature similarity measures are used to throw away that features...
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The XRD diffraction patterns of Ce0.8La0.2O2/Ni prepared using soft template method and impregnation
Open Research DataThe dataset includes XRD patterns of Ce0.8La0.2O2-s nanopowders (nanoparticles,nanocatalyst) prepared using soft template method and further impregnated with 10wt.%Ni using aqueous nitrate solution.
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Mineral and Organic Matter Constituents in Weak Interfaces in Shales
PublicationThis paper identifies formation interfaces that would appear to be "weak interfaces", in the Jurassic, Early- Cretaceous Vaca Muerta formation, in the Neuquén Basin, Argentina. Significant distribution of the weak interfaces was observed including contacts between volcanic ash layers of varying thicknesses, calcite-filled veins, and contacts between lithology changes, such as between argillaceous mudstone and mottled carbonates....
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Study on some of the strength properties of soft clay stabilized with plastic waste strips
PublicationIt is well known that if plastic wastes are not well managed, it has a negative impact on the environment as well as on human health. In this study, recycling plastic waste in form of strips for stabilizing weak subgrade soil is proposed. For this purpose, a weak clay soil sample was mixed with 0.2%, 0.3%, and 0.4% of plastic strips by weight of soil, and the experimental results were compared to the control soil sample with 0%...
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Properties and Formation of Mineralized Veins in an Organic-Rich Shale Formation
PublicationAn earlier paper defined mineral and organic matter constituents in weak interfaces in shale formations (Ptaszynska, et. al., 2016). The formation studied in the earlier work and here is the Jurassic, early-Cretaceous Vaca Muerta formation in the Neuquen basin in Argentina. In this earlier work, mineralized "veins" were noted to be prevalent and complicated, sometimes being shear weak interfaces while in other cases they were not....
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The SEM images of Ce0.8La0.2O2 nanocatalyst infiltrated with 10wt.% Ni prepared using soft template method
Open Research DataThe dataset includes SEM images of Ce0.8La0.2O2-s nanopowder (nanoparticles) prepared using soft template method and infiltrated to 10wt.% Ni in the catalyst. CTAB was used as a micelle-based templating agent. The powder was precipitated from aqueous nitrate solution using NaOH solution and 250xCMC (critcal micelle concentration) of CTAB. Precipitate...
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The XRD pattern of CeO2/10wt.%Cu prepared without BCD
Open Research DataThe dataset includes the XRD pattern of CeO2/10wt.%Cu. The samples of nanoCeO2 were impregnated without BCD-assisted precursor solution (betacyclodextrin) - pure nitarte solution 1M. The dataset includes the 5-90 2theta degree measurement. Nonreduced. Sintered at 400oC for 4 h in air.
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The XRD pattern of CeO2/10wt.%Fe prepared without BCD
Open Research DataThe dataset includes the XRD pattern of CeO2/10wt.%Fe. The samples of nanoCeO2 were impregnated without BCD-assisted precursor solution (betacyclodextrin) - pure nitarte solution 1M. The dataset includes the 5-90 2theta degree measurement. Nonreduced. Sintered at 400oC for 4 h in air.
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The XRD pattern of CeO2/10wt.%Mn prepared without BCD
Open Research DataThe dataset includes the XRD pattern of CeO2/10wt.%Mn. The samples of nanoCeO2 were impregnated without BCD-assisted precursor solution (betacyclodextrin) - pure nitarte solution 1M. The dataset includes the 5-90 2theta degree measurement. Nonreduced. Sintered at 400oC for 4 h in air.
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The XRD pattern of CeO2/10wt.%Co prepared without BCD
Open Research DataThe dataset includes the XRD pattern of CeO2/10wt.%Co. The samples of nanoCeO2 were impregnated without BCD-assisted precursor solution (betacyclodextrin) - pure nitarte solution 1M. The dataset includes the 5-90 2theta degree measurement. Nonreduced. Sintered at 400oC for 4 h in air.
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The XRD pattern of CeO2/10wt.%Ni prepared without BCD
Open Research DataThe dataset includes the XRD pattern of CeO2/10wt.%Ni. The samples of nanoCeO2 were impregnated without BCD-assisted precursor solution (betacyclodextrin) - pure nitarte solution 1M. The dataset includes the 5-90 2theta degree measurement. Nonreduced. Sintered at 400oC for 4 h in air.
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Antagonist adhesion effects due to variable substrate surface
PublicationThe effects of variability of intrinsic adhesion within a joint have been studied using a single cantilever beam (SCB) test. Fracture energy was found not to be a simple function of relative areas of 2 surface pre-treatments: a 'weak' zone decreased strength more than expected from simple, additive considerations. By severing the adhesive along the strong-weak transition, fracture energy increased.The prior antagonist effect appears...
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Weak Stability of Centred Quadratic Stochastic Operators
PublicationWe consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is shown that for the existence of a weak limit, it...
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The SEM images of Ce0.8La0.2O2 nanopowder prepared using soft template method
Open Research DataThe dataset includes SEM images of Ce0.8La0.2O2-s nanopowder (nanoparticles) prepared using soft template method. CTAB was used as a micelle-based templating agent. The powder was precipitated from aqueous nitrate solution using NaOH solution and 250xCMC (critcal micelle concentration) of CTAB. Precipitate was heated up to 90oC, centrifuged and washed...
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The SEM images of CeO2 nanopowder prepared using soft template method
Open Research DataThe dataset includes SEM images of CeO2-s nanopowder (nanoparticles) prepared using soft template method. CTAB was used as a micelle-based templating agent. The powder was precipitated from aqueous nitrate solution using NaOH solution and 250xCMC (critcal micelle concentration) of CTAB. Precipitate was heated up to 90oC, centrifuged and washed several...
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Luminescence properties of TeOx gels
Open Research DataThe DataSet contains the emission and excitation spectra of TeOx gels. The material was obtained by the sol-gel method. The starting solution was prepared by mixing telluric acid (precursor) with thetraetylene glycol, water, and ethanol. The sol was obtained by vigorously stirring precursor solution at 50°C for 2h, then the temperature was raised...
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The XRD diffraction patterns of Ce0.8La0.2O2 and CeO2 prepared using soft template method
Open Research DataThe dataset includes XRD patterns of Ce0.8La0.2O2-s and CeO2-s nanopowders (nanoparticles) prepared using soft template method. CTAB was used as a micelle-based templating agent. The powders were precipitated from aqueous nitrate solution using NaOH solution and 250xCMC (critcal micelle concentration) of CTAB. Precipitates were heated up to 90oC, centrifuged...
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The XRD diffraction patterns of Ce0.9Gd0.1O2 prepared using soft template precipitation method
Open Research DataThe dataset includes XRD patterns of Ce0.9Gd0.1O2-s nanopowder (nanoparticles) prepared using soft template precipitation method. CTAB was used as a micelle-based templating agent. The powders were precipitated from aqueous nitrate solution using NaOH solution and 25xCMC (critcal micelle concentration) of CTAB. Precipitates were heated up to 90oC,...
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The XRD diffraction patterns of Ce0.9Gd0.1O2 prepared using soft template precipitation method - 50xCMC
Open Research DataThe dataset includes XRD patterns of Ce0.9Gd0.1O2-s nanopowder (nanoparticles) prepared using soft template precipitation method. CTAB was used as a micelle-based templating agent. The powders were precipitated from aqueous nitrate solution using NaOH solution and 50xCMC (critcal micelle concentration) of CTAB. Precipitates were heated up to 90oC,...
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Can augmented democracy fulfil the ideal of deliberative democracy?
PublicationNew technologies can broaden the scope of human limits. We can fly to the moon thanks to rocket science, we can communicate with each other by mobile phones and WiFi and we can exceed human life with medical equipment like pacemakers. But there are aspects of our life that still are very distrustful of implementing new technology into functioning. An example of such a field of our everyday life is...
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Acid site concentrations of the MXenes samples
Open Research DataData contains the pH of 0.01M NaOH solution, before and after mixing with the MXenes samples.
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Structured populations with diffusion and Feller conditions
PublicationWe prove a weak maximum principle for structured population models with dynamic boundary conditions. We establish existence and positivity of solutions of these models and investigate the asymptotic behaviour of solutions. In particular, we analyse so called size profile.
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Relativistic two-dimensional hydrogen-like atom in a weak magnetic field
PublicationA two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections to energy levels are calculated analytically, within the framework of the Rayleigh–Schrödinger perturbation theory, for an arbitrary electronic bound state. The second-order calculations are...
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Nitrate and nitrite silver complexes with weakly coordinating nitriles
PublicationSimple system of weak nitrile ligands and silver nitrite/nitrate allowed the formation and isolation of coordination compounds of diverse nuclearity and dimensionality. The extension of the network does not enhance the luminescent properties of the ligands however it gives rise to the new MLCT bands in the visible region.