Linear Coordination Research Articles

INTONATION ANALYSIS OF THE PIANO TEXTURE AS A MEANS OF DEVELOPING THE PIANIST’S PERFORMANCE THINKING: THE CONTENT, HEARING STRATEGIES, AND THE METHODS

Intonation analysis of the piano texture as a means of developing the pianist’s performance thinking: the content, hearing strategies, and the methods The aim of this research is to substantiate the content of the piano texture intonation analysis, a means of developing the pianist’s performance thinking, with defining the auditory strategies, techniques, and relevant intonation-analytical skills that form the basis for piano intonation skills. The research methodology is based on the phenomenological approach. The author, by reducing, applying phenomenological analysis, and describing the content of the intonation performance thinking in the “phonic space” of piano texture, has sought to explore the intramusical nature of its essential components, which can be analyzed theoretically. The scientific novelty is in transferring the content basis of the intonation thinking to the plane of rationality by appealing to the intramusical factors of the intonation processes in the musical piece’s performance texture. Thus, it allowed us to single out the auditory strategies, the methods of the intonation analysis, which are methodologically important for the formation of the pianist’s performance skills, and to determine the system of the intonation-analytical skills, that provide access to the artistic level of performance. Conclusions. Being a modality of developing the pianist’s performance thinking, the intonation analysis is aimed at understanding the sources of dynamic integrity of the performance form at different levels of its organization, namely phonic (overtone micro-intonation), morphological (microstructural motive intonation and/or articulation), syntactic (organic, expressive semantic accentuation phrasing), compositional (intonation dramaturgy of the musical piece as an artistic whole). The object of the intonation analysis is the phonic environment of the musical piece performing texture, while its subject is the internal meaning-creating logic of the tonal connections in the projection of the melodic harmony and spatial timbre dynamics, a linear and deep coordinate of the intonation texture of the sound image. There are semantic guidelines for the analysis of the performance texture that are essential for the piano intonation, such as semantically significant melodic and harmonic tonal connections; features of the “declamatory” articulation of the motives in the projection of the integral texture; the syntactic structure of the melody and its corresponding voices and/or texture fragments; the intramusical logic of dynamic phrasing. The shift of the content orientation of the intonation analysis, proposed in the article, to the corresponding intonation-analytical skills, which form the basis for performing intonation mastery, demonstrates the direct connection between the appealing to the intramusical parameters of music in the intonation texture study and the formation of important thinking qualities. That is, the ability to hear the most subtle, high-pitched, timbre-dynamic changes within each tone embedded in the melodic line; the natural (corresponding to the internal musical logic) declamatory articulation of the text’s semantic structures; the expressive (in the sense of expressed) phrasing; the shift of the textual vision of the texture into intonationally flexible sound images; the coverage of the textural vertical in the dynamics of the figure-background relations of its elements; tracking of the forming intonation lines in the depth of textural fabric (harmonious voice leading).

MODELLING OF VARIABLE BAND-GAP SUPERLATTICES WITH USING A GENETIC ALGORITHM

The numerical calculation of the coordinate distributions of the electrostatic potential in an asymmetric variable-band superlattice with piecewise linear coordinate profiles of the gap width and electron affinity was performed using a genetic algorithm. A mathematical model is formulated, represented by two nonlinear Poisson equations and four boundary conditions, which reflect the continuity of the electrostatic potential and electric field strength at the boundaries of the variable band-gap superlattice, as well as the spatial periodicity of its physical quantities. The solution of the three-point boundary value problem for the electrostatic potential is reduced to the solution in an iterative cycle of two Cauchy problems with initial conditions determined using a genetic algorithm. The search space was chosen in the form of a rectangular region centered at a point that corresponded to the values of the electrostatic potential and electric field strength on one of the boundaries of the superlattice. These values were obtained by analytically solving the corresponding Poisson equations. An initial population of 50-100 trial solutions (chromosomes) was created by selection with equal probability in the search area. The coding of chromosomes and their modification under the action of crossover and mutation operations were used. The genetic algorithm was implemented in the Matlab environment using the Genetic Algorithm package. Numerical experiments showed that the initial population of trial solutions no later than after 20 -30 generations approaches to the desired initial values for the Cauchy problems. The latter were solved by the Runge-Kutta method of the 4th order. The obtained dependences of the electrostatic potential show that its maximum value, which corresponds to the zero intensity of the internal electric field, in contrast to symmetric variable band-gap superlattices, is observed not at the interface of layers, but in a layer of greater thickness. The results of the calculations indicate a substantial quantitative difference in the values of the electrostatic potential for the nonlinear and linearized models. Key words: variable band-gap semiconductors, superlattices, modelling, genetic algorithms.

RESEARCH OF THE WORK OF A MULTI-COORDINATE VIBROSTAND

The article discusses a multi-axis electromagnetic vibration stand (EMVS), in which oscillations of the platform are excited, connected in a certain way with three armatures, and an alternating magnetic field acts on the armatures. For rational design and subsequent analysis of the properties of EMVS on the basis of the apparatus of analytical mechanics, a correct mathematical model has been developed, which contains the differential equations of mechanical motion, as well as the equations of electromagnetic processes. Electromagnetic and mechanical quantities that characterize the movement of systems appear as formally equal. The mathematical model includes a system of nine differential equations with the same number of unknowns. Considering the complexity of the resulting system, its further research was carried out using computer technology. As a result, the dependences of the linear and angular coordinates and velocities, as well as the current strength in time, were obtained. The corresponding graphs have been built. Also built phase portraits for linear and angular parameters. The resulting mathematical model takes into account the features of the nonlinearity of the system. Under certain conditions, chaotic behavior of the system is possible. The calculation formulas obtained in the process of mathematical modeling and presented in this article, as well as the program created and implemented on a computer, make it possible to analyze the influence of all EMVS parameters both separately and in their relationship on the characteristics of the system. In addition, the obtained formulas provide the possibility of designing EMVS with the most rational characteristics and the optimal ratio of design parameters. The obtained mathematical model of EMVS is the basis for mathematical modeling when testing vibration stands, as well as for the analysis and synthesis of control systems with feedback on acceleration, force, product of force and acceleration.

Synthesis and structural characterization of new gold(I) complexes as bioactive and antitumor agents

New mononuclear gold(I) complexes based on 1-thiocarbamoyl-3,5-diaryl-pyrazoline ligands were synthesized and structurally characterized using X-ray crystallography, 13C and 1H NMR studies, and elemental analysis combined with FT-IR and UV-Vis spectroscopy. Complexes 1–3 were prepared in good yields and characterized by X-ray diffraction as neutral mononuclear complexes of the [Au(L)Cl] type with linear coordination geometry around AuI atoms. The UV-Vis absorption profiles of the compounds prepared exhibited two strong absorption bands between 225 and 400 nm, attributed to HOMO → LUMO electronic transitions of the (M + X)LCT type (charge transfer excitations arising from metal plus halogen to ligand) and mixed XLCT + IL type (charge transfer excitations arising from halogen to ligand plus intraligand), based on DFT studies. Assayed for antitumor activity against B16-F10 murine melanoma cells, 4 T1 murine mammary carcinoma cells, and a normal BHK-21 baby hamster kidney cells line, complexes 1–3 exhibited higher bioactivity and selectivity than their respective free ligands. The preliminary results showed these complexes to be good candidates for the development of new metallodrugs based on gold(I) compounds.

Investigation of the influence of mechanochemical effects on the structure and properties of vermiculite sorbents

The work investigates the effect of mechanochemical activation (MCA) on the structure and properties of vermiculite. The process of activation is controlled by X–ray diffraction (XRD), IR–spectroscopy, and scanning electron microscopy. The thermal stability of the vermiculite was studied by the differential thermal analysis. It was found that an increase in the degree of MCA of vermiculite makes it possible to change the vermiculite hydration states and its mica package passed into a zero hydration state, one– or two–layer state. In the study of the samples sorption capacity as related to oil products, it was shown that adsorption proceeded according to a competitive mechanism. The linearization of experimental data on the adsorption of oil products was achieved in linear coordinates of the Freundlich isotherm, that confirmed adsorption in the volume of energetically inhomogeneous porous adsorbent. A positive effect of MCA on the sorption capacity of the samples was noted.

Aggregation-Enhanced Room-Temperature Phosphorescence from Au(I) Complexes Bearing Mesogenic Biphenylethynyl Ligands.

Gold(I) complexes, enabling to form linear coordination geometry, are promising materials for manifesting both aggregation-induced emission (AIE) behavior due to strong intermolecular Au–Au (aurophilic) interactions and liquid crystalline (LC) nature depending on molecular geometry. In this study, we synthesized several gold(I) complexes with rod-like molecular skeletons where we employed a mesogenic biphenylethynyl ligand and an isocyanide ligand with flexible alkoxyl or alkyl chains. The AIE behavior and LC nature were investigated experimentally and computationally. All synthesized gold(I) complexes exhibited AIE properties and, in crystal, room-temperature phosphorescence (RTP) with a relatively high quantum yields of greater than 23% even in air. We have demonstrated that such strong RTP are drastically changed depending on the crystal-size and/or crystal growth process that changes quality of crystals as well as the aggregate structure, of e.g., Au–Au distance. Moreover, the complex with longer flexible chains showed LC nature where RTP can be observed. We expect these rod-like gold(I) complexes to have great potential in AIE-active LC phosphorescent applications such as linearly/circularly polarizing phosphorescence materials.

Synthesis and coordination to the coinage metals of a trimethylpyrazolyl substituted 3-arylacetylacetone

AbstractThe ligand 3-(4-(1,3,5-trimethyl-1H-pyrazol-4-yl)phenyl)acetylacetone (1) combines a Pearson hard O,O′ chelating acetylacetone donor with a softer pyrazole N donor bridged by a phenylene spacer. Deprotonation and coordination to CuIIleads to a square planar bis-acetylacetonato complex; interpreting the close proximity of an adjacent complex’s pyrazole moiety as anη2${{\eta}}^{2}$coordination to the axial CuIIposition leads to a two dimensional extended structure. The N donor capabilities are proven by coordination to AgPF6and AuCl; for AgIa cationic linear bis-pyrazole complex as a toluene solvate is obtained with toluene-pyrazole π-interactions and an essentially uncoordinatedPF6-${{\mathrm{PF}}_{6}}^{-}$anion. In the case of AuCl a neutral linear coordination compound with one chlorido and one pyrazole ligand1is obtained. Comparing the dihedral angles with a closely related but shorter ligand reveals a larger rotational degree of freedom in1, allowing for richer architectures in emerging coordination polymers.

Smolyak representations with absorbing boundary conditions for reaction path Hamiltonian model of reactive scattering

In this work, we present the efficient combination of Smolyak representations with time independent quantum mechanical approach using absorbing boundary conditions for the cumulative reaction probability calculations of a multidimensional reactive scattering problem. Our approach uses both kinds of Smolyak representations (finite basis and grid) which drastically reduces the size of the basis representation for the cumulative reaction operator. The cumulative reaction probability is thus obtained by solving the eigenvalue problem within the context of reaction path Hamiltonian using the compact Smolyak basis combined with an iterative Lanczos algorithm. Benchmark calculations are presented for reactive scattering models with a linear reaction coordinate and applied to a 25D model highlighting the efficiency of the present approach for multidimensional reactive processes.

Electronic structure and chemical bonding in smart anti-corrosion coatings

Nitrilotris-(Methylenephosphonato)-Three-aqua-Iron(II) (FeNTP) is a linear organic-inorganic coordination polymer forming an anti-corrosion coating on the steel surface in aqueous medium with NTP-based corrosion inhibitors. The Cd-containing NTP-based inhibitor has higher protective properties than the inhibitor without cadmium. At the same time, the Fe–O bonds are more covalent, and the data from X-ray photoelectron and Mössbauer spectroscopy allow one to suppose that the Fe atoms within the polymer with Cd are in a different magnetic state. However, the causes of these phenomena and their relationship were not studied before. Here, for the first time, the electronic structure of FeNTP is calculated using density functional theory. A stable solution with a large magnetic moment at Fe atoms (4 μB) is found for FeNTP. The calculated properties correspond to the experimental ones obtained earlier: the Fe magnetic moment (estimated by XPS), the quadrupole splitting (Mössbauer spectroscopy), and the character of the chemical bond between Fe and O atoms (X-ray diffraction). Also, a second, nonmagnetic, solution is found, the calculated properties of which are identical to those of the Cd-containing FeNTP. The difference in electronic structure between these two states manifests itself in different Fe 3d occupancy, angular electron density distribution around the Fe atoms, and magnetic state. The interrelation between the magnetic state of the Fe atoms and their chemical bonds is described. This made it possible to reveal the mechanism for the effect of Cd doping of the protective layers on their anti-corrosive properties. Thus, an approach to developing the more effective and efficient corrosion inhibitors in the neutral aqueous media is proposed.

Экспериментальные исследования колебаний груза при перемещении грузоподъёмного крана ДЭК-251

Measurement of the parameters of vibrations of the load moved by a self-propelled crane with a flexible rope suspension when the crane moves along an unprepared construction site with irregularities is an urgent task, since it will allow using the obtained numerical values of the vibration parameters to improve the accuracy of the crane’s operation in terms of moving loads. Based on the solution of this problem, it is possible to create systems for automatic damping of cargo vibrations. This will reduce the time spent on performing a work step when moving a load. This also solves the problem of reducing the dynamic loads on the elements of the crane. The article discusses one of the methods for determining the angles of deviations of the point of the load and the point of suspension of the load on the boom when moving the DEK-251 mobile crane along the unevenness of the construction site using the projection-polynomial mathematical model of the optoelectronic system. As an example, the article presents a number of graphs of time dependences of changes in the values of the angles of deviations of the load and the point of suspension of the load when moving over the unevenness of the site of a crane with a boom length of 22 meters and an angle of inclination of the boom of 48 degrees. The cargo was at a height of 4.8 meters, the weight of the cargo was 200 kilograms. The graphical time dependences of the load fluctuations and the load suspension point in the longitudinal plane are given in the form of angles of deviations from the lens center, taking into account the microrelief. The data allows you to calculate the linear coordinates of objects in space. Moreover, the results were obtained taking into account the camera errors.

A trigonal coordination of Au(I) phosphane complexes stabilized by O\u2013H\u22efX (X\u2009=\u2009Cl\u2013, Br\u2013, I\u2013) interactions

In this work, we show that intramolecular hydrogen bonding can be used to stabilize tri-coordinated phosphane-gold(I) complexes. Two molecular structures of 2-(diphenylphosphino)benzoic acid (L) coordinated to a gold(I) atom were determined by single-crystal X-ray diffraction. The linear L–Au–Br shows a standard linear coordination and dimerizes via hydrogen bonds of the carboxylic acid. Upon addition of two additional phosphane ligands the complex [L3Au]X is formed which is stabilized by three intramolecular –C(O)O–H…X hydrogen bonds as proven by the X-ray structure of the respective chlorido-complex. X-ray powder diffractograms suggest the same structure also for X– = Br– and I–.Graphic abstract

New-Generation Ligand Design for the Gold-Catalyzed Asymmetric Activation of Alkynes.

Gold(I) catalysts are ideal for the activation of alkynes under very mild conditions. However, unlike allenes or alkenes, the triple bond of alkynes cannot be prochiral. In addition, the linear coordination displayed by gold(I) complexes places the chiral ligand far away from the substrate resulting in an inefficient transfer of chiral information. This poses a significant challenge for the achievement of high enantiocontrol in gold(I)‐catalyzed reactions of alkynes. Although considerable progress on enantioselective gold(I)‐catalyzed transformations has recently been achieved, the asymmetric activation of non‐prochiral alkyne‐containing small molecules still represents a great challenge. Herein we summarize recent advances in intra‐ and intermolecular enantioselective gold(I)‐catalyzed reactions involving alkynes, discussing new chiral ligand designs that lie at the basis of these developments. We also focus on the mode of action of these catalysts, their possible limitations towards a next‐generation of more efficient ligand designs. Finally, square planar chiral gold(III) complexes, which offer an alternative to chiral gold(I) complexes, are also discussed.

Active sites and effects of co-adsorbed H2O on isolated methanol dehydrogenation over Pt/γ-Al2O3

Dehydrogenation is the first reaction of the aqueous phase reforming (APR) mechanism of polyols, and its rate is likely affected by the environment at the active site. This study focuses on reactions of methanol on benchmark Pt/γ-Al2O3 catalysts probed by infrared spectroscopy under high vacuum. CO in linear and bridging coordination are the dominant surface species on metal sites. Pt particle sizes and reaction temperatures are varied to identify the kinetically preferred active site for methanol dehydrogenation as either lowly coordinated (edges, corners, interface) or highly coordinated (terraces) metal atoms. Interpretation of temperature-dependent IR spectra up to 450 °C show that larger Pt particles produce more CO at lower temperatures from complete methanol dehydrogenation. Similarly, time-resolved isothermal experiments at 150 °C showed equilibrium conversion occurred much faster on larger Pt particles than smaller ones. Features of evolving ν(C≡O) bands (shape, vibrational frequencies, integrals) suggest that, even on small Pt particles, CO first forms on the scarcely available terraces, or possibly in the form of islands. We have thus experimentally identified highly coordinated Pt metal as the more active site in overall methanol dehydrogenation. The electronic and chemical effects of co-adsorbed water and hydrogen on dehydrogenation activity and the CO spectra are discussed. The co-adsorption of water, an abundant APR component needed for the water-gas shift reaction, does not appear to affect methanol dehydrogenation on large Pt particles but hinders the reaction on small Pt particles as evident by limited growth in the respective ν(C≡O) bands.

Approaches to Numerical Solution of Optimal Control Problem Using Evolutionary Computations

Two approaches to the numerical solution of the optimal control problem are studied. The direct approach is based on the reduction of the optimal control problem to a nonlinear programming problem. Another approach is so-called synthesized optimal control, and it includes the solution of the control synthesis problem and stabilization at some point in the state space, followed by the search of stabilization points and movement of the control object along these points. The comparison of these two approaches was carried out as the solution of the optimal control problem as a time function cannot be directly used in the control system, although the obtained discretized control can be embedded. The control object was a group of interacting mobile robots. Dynamic and static constraints were included in the quality criterion. Implemented methods were evolutionary algorithms and a random parameter search of piecewise linear approximation and coordinates of stabilization points, along with a multilayer network operator for control synthesis.

Equation-of-Motion Coupled-Cluster Protocol for Calculating Magnetic Properties: Theory and Applications to Single-Molecule Magnets.

We present a new computational protocol for computing macroscopic magnetic properties of transition-metal complexes using the equation-of-motion coupled-cluster (EOM-CC) framework. The approach follows a two-step state-interaction scheme: we first compute zero-order states using nonrelativistic EOM-CC and then use these states to evaluate matrix elements of the spin-orbit and Zeeman operators. Diagonalization of the resulting Hamiltonian yields spin-orbit- and field-perturbed eigenstates. Temperature- and field-dependent magnetization and susceptibility are computed by numerical differentiation of the partition function. To compare with powder-sample experiments, these quantities are numerically averaged over field orientations. We applied this protocol to several single-molecule magnets (SMMs) with Fe(II) and Fe(III) in trigonal pyramidal, linear, and trigonal bipyramidal coordination environments. We described the underlying electronic structure by the electron-attachment (EOM-EA) and spin-flip (EOM-SF) variants of EOM-CC. The computed energy barriers for spin inversion, and macroscopic magnetization and susceptibility agree well with experimental data. Trends in magnetic anisotropy and spin-reversal energy barriers are explained in terms of a molecular orbital picture rigorously distilled from spinless transition density matrices between many-body states. The results illustrate excellent performances of EOM-CC in describing magnetic behavior of mononuclear transition-metal SMMs.

Structural and Thermal Investigations of Co(II) and Ni(II) Coordination Polymers Based on biphenyl-4,4'-dioxydiacetate Linker.

Two coordination polymers, [Co(µ4-L)(H2O)2]n (1) and [Ni(µ-L)(H2O)4]n (2), were solvothermally assembled from the corresponding metal(II) chlorides and biphenyl-4,4-dioxydiacetic acid (H2L) as a flexible dicarboxylate linker. The cobalt(II) compound 1 featured a layer-pillared 3D metal-organic network with a cds topology, while the nickel(II) derivative 2 represented a linear chain 1D coordination polymer with a 2C1 topology. The µ4− and µ-L2− linkers exhibited different denticity and coordination modes in the synthesized compounds, thus contributing to their structural diversity. The dimensionality of 1 and 2 had an influence on their thermal stability and decomposition processes, which were investigated in detail by TG-DSC and TG-FTIR methods. Thermal decomposition products of coordination polymers were also analyzed by PXRD, confirming the formation of Co3O4/CoO and NiO as final materials. The obtained compounds broaden a family of coordination polymers assembled from flexible dicarboxylate linkers.

The Quest for Optimal 3 d Orbital Splitting in Tetrahedral Cobalt Single‐Molecule Magnets Featuring Colossal Anisotropy and Hysteresis

AbstractOnly a few four‐coordinated Co2+‐complexes show single‐molecule magnet (SMM) properties without an applied dc field. Common for those is a large magnetic anisotropy generated by the close proximity of the and orbitals. This type of magnetic anisotropy is strongly correlated with the extent of structural distortion from ideal tetrahedral towards linear coordination. Quantification of the governing magneto‐structural correlations is hence crucial for the development of better SMMs. For this purpose, we synthesized and analyzed four significantly distorted tetrahedral cobalt complexes that exhibit extremely large magnetic anisotropies and slow relaxation of magnetization in zero field. The N−Co−N bite angles vary from 70.8 to 72.7°, and magnetic measurements show strong anisotropy with D‐values in the range from 75 to 114 cm−1. Ab initio calculations supported the experimental results and highlighted a significant increase of D up to 141 cm−1, correlated with the reduction of the energy difference between the and orbitals. Based on these magneto‐structural correlations and in contrast to the current assumption that the smaller bite angle is the better, we predict that with an ideal bite angle in the range from 76–78° in distorted Co(N2R)2 complexes, the energy difference between the two important d‐orbitals is at a minimum and hence the magnetic anisotropy is maximized.

Evolution from discrete mononuclear complexes to trinuclear linear cluster and 2D coordination polymers of Mn(II) with dihydrazone Schiff bases: Preparation, structure and thermal behavior

Four Mn(II) coordination compounds based on the 2,6-diacetylpyridine bis(isonicotinoylhydrazone) (H2L1) and 2,6-diacetylpyridine bis(nicotinoylhydrazone) (H2L2), were prepared using different synthetic conditions and starting manganese salts: discrete mononuclear [Mn(H2L1)2(H2O)2](NO3)2 (1) and trinuclear [Mn3(H2L1)2(NCS)2Cl4(H2O)2] (2) complexes and two 2D coordination polymers {[Mn3(L1)3(H2O)2]·1.5C2H5OH}n (3) and {[MnL2]·dmf}n (4), where dmf = N,N-dimethylformamide. Single-crystal X-ray diffraction study shows that H2L1 and H2L2, which differ only by para- or meta- position of radicals with respect to the nitrogen atoms in the terminal pyridyl fragments, demonstrate chelate or chelate-bridging coordination mode with N3O2, or N4O2 and N5O2 donor atoms, respectively. The planar-chelate coordination of these ligands provides the pentagonal-bipyramidal surrounding of Mn(II) and the terminal pyridyl moieties promote bridging function and structure expansion in 2–4 as well as octahedral Cl2N4 coordination geometry for one of Mn(II) atoms in the trinuclear complex 2. All compounds have been investigated in the solid state by IR spectroscopy and thermal analysis in order to understand the influence of the inorganic anion presence/absence on the stability of synthesized compounds.

HIGHLY EFFICIENT REMOVAL OF COPPER(II) IONS FROM AQUEOUS SOLUTION BY NICKEL 2-ETHYLIMIDAZOLATE

Nickel 2-ethylimidazolate was obtained and characterized, which is used in this work as a sorbent for the removal of copper (II) ions. The sample characterization was carried out by scanning electron microscopy, low-temperature nitrogen adsorption. It was found that the obtained sorbent is a microheterogeneous material with the size of individual particles in the range of 0.4-0.7 μm. Nitrogen adsorption isotherms in the pores of nickel 2-ethylimidazolate were obtained. It was found that when processing the experimental data in linear coordinates of TVFM, linearization is reached in coordinates lnV-lnPs/P, which indicates the predominance of mesopores in the structure of nickel 2-ethylimidazolate. The total pore volume was determined from the TVFM linear coordinates. It was 0.21 cm3/g. According to obtained differential pore size distribution, the most probable average pore radius corresponds to 7.5 nm. One of the main characteristics of nickel 2-ethylimidazolate as a sorbent, the surface area was determined by the A.V. Kiselev method and amounted to 703.56 m2/g. The efficiency verification of using nickel 2-ethylimidazolate in the heavy metal ions sorption processes was carried out by removal of copper(II) ions from aqueous solutions by the limited solution volume method at different contact times. The copper(II) sorption kinetics in the presence of nickel 2-ethylimidazolate was studied by processing experimental data in the first and second orders linear coordinates. It was found that the adsorption kinetics of copper(II) ions is described by a second order model, which indicated ion-exchange adsorption. Equilibrium adsorption capacity in the sorbent-solution system is reached at a contact time of 90-120 min.

Coordinate structure of feature geometrical location specifications

The paper proposes a systemic transition from the location and orientation of tolerance product features to linear and angular coordinates in the coordinate system of the product electronic model. The coordinate system is formed by designing datums set with a total informativeness content of six constrains on the object degrees of freedom, three of them being linear and three of them being angular constrains. The main design datums determine the object position in the product and form a generalized coordinate system. Auxiliary design datums determine the position of the attached object on the considered object and form an auxiliary coordinate system. Each element of the product has a certain informativeness content to limit the degrees of freedom, both linear and angular. When forming a Cartesian coordinate system, the datum element transfers piece or all of its informativeness content to it. As a result, the coordinate planes acquire different informativeness of three, two and one, and the coordinate axes acquire that of four, two and zero. The coordinate axes and planes informativeness content determines the number of linear and angular coordinates that can be set relative to them. Similarly, the feature datums informativeness means the number of linear and angular coordinates that must be specified in the coordinate system for its single-task location and orientation. The transition to a coordinate system for standardizing location and orientation deviations demonstrates compliance with a systematic approach that improves the quality of products in terms of the geometric specifications accuracy.