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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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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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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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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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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.
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Multi-instrument analysis of L-band amplitude scintillation observed over the Eastern Arabian Peninsula
PublicationThe study of scintillation-causing ionospheric irregularities is important to mitigate their effects on satellite communications. It is also important due to the spatial and temporal variability of these irregularities, given that their characteristics differ from one region to another. This study investigates the spatial and temporal characteristics of L1 amplitude scintillation-causing ionospheric irregularities over the Eastern...
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Realistic noise-tolerant randomness amplification using finite number of devices
PublicationRandomness is a fundamental concept, with implications from security of modern data systems, to fundamental laws of nature and even the philosophy of science. Randomness is called certified if it describes events that cannot be pre-determined by an external adversary. It is known that weak certified randomness can be amplified to nearly ideal randomness using quantum-mechanical systems. However, so far, it was unclear whether randomness amplification...
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Shub’s conjecture for smooth longitudinal maps of S^m
PublicationLet f be a smooth map of the m-dimensional sphere Sm to itself, preserving the longitudinal foliation. We estimate from below the number of fixed points of the iterates of f , reduce Shub’s conjecture for longitudinal maps to a lower dimensional classical version, and prove the conjecture in case m = 2 and in a weak form for m = 3.
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<i>N,N</i>'-diphenylthiourea acetone monosolvate
PublicationIn the title compound, C13H12N2S·C3H6O, the phenyl rings of the thiourea molecule are in syn and anti positions in relation to the C=S bond. Two molecules are connected by N-HS=C hydrogen bonds into a centrosymmetric dimer. An additional N-HO=C hydrogen bond to the acetone solvent molecule and some weak C-H interactions reinforce the crystal structure.
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Cryptocurrencies as a Speculative Asset: How Much Uncertainty is Included in Cryptocurrency Price?
PublicationThe aim of this paper is to examine the relationship between uncertainty indices (Geopolitical Uncertainty Index and Global Economic Policy Uncertainty Index) and cryptocurrencies. This study evaluated the behavior of cryptocurrencies with the evolution of uncertainties (GPU, EPU) on returns and volatility in terms of safe heaven as in traditional specualtive assets it increases their volaitility and reduces risk. For this purpose,...
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Extending the Frequency Limit of Microstrip-Coupled CSRR Using Asymmetry
PublicationAbstract— This article explains the frequency limitation in designing microstrip circuits based on a complementary split-ring resonator (CSRR) and reports a novel technique for increasing its operating frequency, which makes the CSRR suitable for high-frequency applications. This study helps in synthesizing the dimensions of symmetric CSRR (SCSRR) and asymmetric CSRR (ACSRR) circuits, which shows the applicability of the proposed...
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On thermal stability of topological qubit in Kitaev's 4D model
PublicationWe analyse stability of the four-dimensional Kitaev model-a candidate for scalable quantum memory - in finite temperature within the weak coupling Markovian limit. It is shown that, below a critical temperature, certain topological qubit observables X and Z possess relaxation times exponentially long in the size of the system. Their construction involves polynomial in system size algorithm which uses as an input the results of...
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4-[(tert-Butyldimethylsilyl)oxy]-6-methoxy-7-methyl-5-(oxiran-2-ylmethyl)-2-benzofuran-3(1H)-one
PublicationThe title compound, C19H28O5Si, was obtained in the reaction of 1,3-dihydro-4-[(tert-butyldimethylsilyl)oxy]-6-methoxy-7-methyl-3-oxo-5-(prop-2-enyl)isobenzofuran with meta-chloroperbenzoic acid. This reaction is one of the stages of the total synthesis of mycophenolic acid, which we attempted to modify. The title compound forms crystals with only weak intermolecular interactions. The strongest stacking interaction is found between...
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Acceleration waves in the nonlinear micromorphic continuum
PublicationWithin the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortion tensor may undergo jump discontinuities. Here we obtain the acoustic tensor for...
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Noise in biological Raman spectroscopy
PublicationRaman spectroscopy is a widely used method to investigate chemical molecules by analyzing their vibrational transitions. It utilizes inelastic scattering of the laser light irradiating the investigated object. The scattered light requires appropriate filtering to reduce dominant laser light and expose much weaker components having shifted wavelengths of a characteristic spectral pattern. These components are measured by dispersing...
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Syntheses, spectroscopic and structural properties of phenoxysilyl compounds: X-ray structures, FT-IR and DFT calculations
PublicationThe reaction of silicon disulfide with alkylphenols leads to tetraphenoxysilane, cyclodisilthiane and silanethiol. The products of the reaction of silicon disulfide with phenols are characterized by FT-IR, NMR, X-ray diffraction and DFT calculations. The intramolecular interactions in the compounds are mainly XH---π (X = C, S) whereas the intermolecular interactions are either very weak CH---π/CH---O contacts found in aryloxysilane...
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Analysis of radiometric signal in sedimentating suspension flow in open channel
PublicationThe article discusses issues related to the estimation of the sedimentating solid particles average flow velocity in an open channel using radiometric methods. Due to the composition of the compound, which formed water and diatomite, received data have a very weak signal to noise ratio. In the process analysis the known determining of the solid phase transportation time delay the classical cross-correlation function is the most...
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The (over)touristification of European historic cities: a relation between urban heritage and short-term rental market demand
PublicationIn this chapter, I wish to highlight the critical relationship between heritage management issues and building environment transformation. I argue that such a relationship is directly expressed through the tourism phenomenon, and it should be measured through the economic dimension of the short-term rental market, which introduces this rule of thumb: if there is a lack of demand, the brand of the city is weak; if there is too much...
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Two-dimensional hydrogen-like atom in a weak magnetic field
PublicationWe consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr¨odinger perturbation theory, using the Sturmian expansion of the generalized radial Coulomb Green function, we derive explicit analytical expressions for corrections to an arbitrary planar hydrogenic bound-state energy level, up to the fourth...