Riemann Sphere Research Articles

Spectral-luminescent characteristics of coordination compounds and metal polymers of Yb(III)

New mono- and heteroligand (with phenanthroline or dipyridyl) metal complexes of ytterbium (III) with 2-methyl-5-biphenylpentene-1-3,5-dione were synthesized in this work. Homo- and copolymers of ytterbium complex with methyl methacrylate or styrene were obtained by the method of radical polymerization. Coordination compounds were investigated by IR spectroscopy, diffuse reflectance spectroscopy, thermal and luminescence analyses. It was determined that the -diketone molecules are bidentate-cyclically coordinated to the central atom, and the coordination sphere of the monoligand complex is supplemented by two water molecules, which in the case of heteroligand complexes (HLC) are replaced by phenanthroline or dipyridyl molecules. An increase in thermal stability of heteroligand complexes and metallopolymers was observed compared to the metallocomplex. The spectral properties of the synthesized compounds were studied and it was established that the structure of the coordination node of the elementary link of polymer macromolecules does not change during the polymerization process. It was shown that all the studied samples exhibited 4f-luminescence in the near-infrared region of the spectrum, while the lowest relative luminescence intensity was characteristic of ytterbium (III) homopolymer and copolymers, and the highest values were shown by heteroligand complexes with phenanthroline, which allows us to propose them as precursors of luminescent materials.

Loxodromes in open multisection lasers

We introduce a formalism to efficiently calculate lasing modes and optical power flow in multisection lasers with open boundaries. The formalism is underpinned by a projection of the complex-valued electric field and its spatial derivative onto a suitably extended complex $\mathcal{Z}$ plane to reduce the order of the problem and simplify analysis. In a single-section laser, we show that a laser mode is a loxodrome on the extended complex $\mathcal{Z}$ plane. In a multisection laser, we obtain loxodromes for individual sections of the laser. Then, a multisection mode is constructed by continuously concatenating individual loxodromes from each section using the open boundary conditions. A natural visualization of this construction is given by stereographic projection of the extended complex $\mathcal{Z}$ plane onto the Riemann sphere. Our formalism simplifies the analysis of lasing modes in open multisection lasers and provides insight into the mode geometry and degeneracy.

The Multi-Valued Quasimöbius Mappings on the Riemann Sphere

The Multi-Valued Quasimöbius Mappings on the Riemann Sphere

Recent Advances in Bioconjugated Transition Metal Complexes for Cancer Therapy

The introduction of biologically relevant organic moieties in the coordination sphere of transition metal complexes has recently become a well-established strategy to increase the selectivity and biocompatibility of metallodrugs. In this review, the major advances achieved in this area of research in the last three years are described in detail. Particular attention is given to the metal complexes bearing the main biomolecules of life: carbohydrates, lipids, nucleotides, proteins and vitamins. Each paragraph summarizes the synthetic strategy employed to obtain the complexes of interest as well as the most interesting biological results obtained with these potential metallodrugs. Moreover, the structure–activity relationships observed by the different research groups are described and discussed, with the goal of suggesting to the reader the ligand/metal centre combinations that provide the most promising results in the fight against cancer. Some of the compounds examined in this review as well as other bioconjugated metal complexes published in recent decades exhibit interesting selectivity towards cancer cells over normal ones and a specific mode of action. These latter aspects are the basis of what is commonly known as anticancer target therapy.

Perverse schobers and Orlov equivalences

A perverse schober is a categorification of a perverse sheaf proposed by Kapranov–Schechtman. In this paper, we construct examples of perverse schobers on the Riemann sphere, which categorify the intersection complexes of natural local systems arising from the mirror symmetry for Calabi–Yau hypersurfaces. The Orlov equivalence plays a key role for the construction.

Explanation before Adoption: Supporting Informed Consent for Complex Machine Learning and IoT Health Platforms

Explaining health technology platforms to non-technical members of the public is an important part of the process of informed consent. Complex technology platforms that deal with safety-critical areas are particularly challenging, often operating within private domains (e.g. health services within the home) and used by individuals with various understandings of hardware, software, and algorithmic design. Through two studies, the first an interview and the second an observational study, we questioned how experts (e.g. those who designed, built, and installed a technology platform) supported provision of informed consent by participants. We identify a wide range of tools, techniques, and adaptations used by experts to explain the complex SPHERE sensor-based home health platform, provide implications for the design of tools to aid explanations, suggest opportunities for interactive explanations, present the range of information needed, and indicate future research possibilities in communicating technology platforms.

Graviton scattering in self-dual radiative space-times

The construction of amplitudes on curved space-times is a major challenge, particularly when the background has non-constant curvature. We give formulae for all tree-level graviton scattering amplitudes in curved self-dual (SD) radiative space-times; these are chiral, source-free, asymptotically flat spaces determined by free characteristic data at null infinity. Such space-times admit an elegant description in terms of twistor theory, which provides the powerful tools required to exploit their underlying integrability. The tree-level S-matrix is written in terms of an integral over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map corresponding to the helicity configuration of the external gravitons. For the MHV sector, we derive the amplitude directly from the Einstein–Hilbert action of general relativity, while other helicity configurations arise from a natural family of generating functionals and pass several consistency checks. The amplitudes in SD radiative space-times exhibit many novel features that are absent in Minkowski space, including tail effects. There remain residual integrals due to the functional degrees of freedom in the background space-time, but our formulae have many fewer such integrals than would be expected from space-time perturbation theory. In highly symmetric special cases, such as SD plane waves, the number of residual integrals can be further reduced, resulting in much simpler expressions for the scattering amplitudes.

Dimensional estimates for measures on quaternionic spheres

In this article we provide lower bounds for the lower Hausdorff dimension of finite measures assuming certain restrictions on their quaternionic spherical harmonics expansions. This estimate is an analog of a result previously obtained by the authors for the complex spheres.

Structure and thermodynamic properties of adducts based on cucurbit[6]uril and Fe(III)/Fe(II) aqua complexes: A DFT examination

AbstractThis study carried out a detailed step‐by‐step PBE/TZVP level analysis of the inclusion of Fe(III)/Fe(II) aqua complexes into the cavity of cucurbit[6]urils (CB[6]). The structural characteristics of all intermediate stable structures formed during the inclusion process from the bulk of aqueous solution to the inclusion compound were obtained. To account for solvation effects, a molecular‐continuum model was used in which six water molecules of the first coordination sphere of aqua complexes and 12 water molecules of the second coordination sphere were taken into account, while the interaction of such a supermolecule with a dielectric medium was accounted within the continuum model (PCM) [Correction added on 9 June 2023, after first online publication. The word molecular continual has been changed to molecular‐continuum in the sentence.]. The process of incorporation of the aqua complex into the cavity was found to be accompanied by a partial desolvation of the second coordination sphere of the aqua complex and a change in the structure of the first coordination sphere. Additionally, the standard electrode potential of the half‐reaction Fe3+(aq) + e = Fe2+(aq) was estimated for all adducts formed in the reaction.

THEOLOGY AND PHILOSOPHY IN THEIR RELATION TO LOGIC

This article analyzes the relationship of philosophy and theology to the phenomenon of thinking–logic culture. Religions, as you know, can be divided on different grounds. Religion is, of course, not only a form of social consciousness, as, for example, he taught the official world communication. Religion is a rather complex sphere of culture. The article is based on some of the paradigms of religions: firstly, it is the recognition or non-recognition of the existence of God (gods). In this case, religions are divided into non-theistic (recognizing the existence of God or gods) and non-theistic (denying the existence of God or gods. The second type includes, for example, Buddhism. The second basis for distinguishing religions is the number of postulated and revered gods. As a rule, either many gods are postulated (this is polytheism) or one god (this is monotheism). Finally, the third foundation is the status of religion in humanity, the degree of its prevalence, and the number of its adherents. In particular, philosophy is, as is well known, a critical reflection on ideological and world-related problems. The authors argue that the formation of logic in the period of the medieval Muslim East is due to the complex process of the formation of philosophy, humanities, and medieval science in general, in the process of a complex dispute with theology.

Isomonodromic Deformations: Confluence, Reduction and Quantisation

In this paper we study the isomonodromic deformations of systems of differential equations with poles of any order on the Riemann sphere as Hamiltonian flows on the product of co-adjoint orbits of the truncated current algebra, also called generalised Takiff algebra. Our motivation is to produce confluent versions of the celebrated Knizhnik–Zamolodchikov equations and explain how their quasiclassical solution can be expressed via the isomonodromic tau -function. In order to achieve this, we study the confluence cascade of r+ 1 simple poles to give rise to a singularity of arbitrary Poincaré rank r as a Poisson morphism and explicitly compute the isomonodromic Hamiltonians. In loving memory of Igor KricheverA great man and outstanding mathematician

Stability Analysis of Simple Root Seeker for Nonlinear Equation

In this paper, the stability of a class of Liu–Wang’s optimal eighth-order single-parameter iterative methods for solving simple roots of nonlinear equations was studied by applying them to arbitrary quadratic polynomials. Under the Riemann sphere and scaling theorem, the complex dynamic behavior of the iterative method was analyzed by fractals. We discuss the stability of all fixed points and the parameter spaces starting from the critical points with the Mathematica software. The dynamical planes of the elements with good and bad dynamical behavior are given, and the optimal parameter element with stable behavior was obtained. Finally, a numerical experiment and practical application were carried out to prove the conclusion.

Digital Technologies in the Agro-Industrial Complex on the Example of the Electronic Platform of Rosselkhozbank svoe-rodnoe.ru

The subject of the study is digital technologies in the sphere of agro-industrial complex on the example of Ecosystem “Svoe” of JSC Rosselkhozbank. The purporse of the work are: analytical assessment of the essence and function of digital technologies in the Russian agricultural industry using economic and statistical methods; identification of the problems that are an obstacle to the introduction of modern technologies; and providing practical recommendations on informing more agro-industrial companies about the resources of the “Svoe’’ ecosystem for their use in their current activities. In recent years, the digitalization processes in the industry have intensified, but not yet reached the required level for more efficient business. In addition, for the most part only large enterprises and agricultural holdings can afford the introduction of innovative products. Big business is ensuring the continuous growth of economic indicators in the industry. Small enterprises digitalization processes due to a lack of financial and human resources are slow. To assist small and medium-sized businesses, the ecosystem “Svoe” of Rosselkhozbank was launched in 2020, which is a high-quality example of the introduction of digitalization in agro-industrial complex. Finally, the conclusions are drawn in relation to the need of state support for digitalization pro­cesses in the agro-industrial sector, both through financial investments in the activities of enterprises and through reforming the educational sphere connected with training, education and retraining of industry representatives using the achievements of scientific and technological progress; participation of the state in the formation of the countryside as an attractive place to live. Some conclusions about the uneven nature of the implementation of digitalization processes at the enterprises of the industry, the need to reform the education system using innovative developments in the training of specialists for agribusiness enterprises, and the inevitability of improving rural areas to attract additional human resources to the industry are drawn. Despite the existence of the “Svoe” ecosystem of Rosselkhozbank for a short time, it is worth noting the huge benefit of the platform in solving many problems of its users.

On dynamical gaskets generated by rational maps, Kleinian groups, and Schwarz reflections

According to the Circle Packing Theorem, any triangulation of the Riemann sphere can be realized as a nerve of a circle packing. Reflections in the dual circles generate a Kleinian group H H whose limit set is a generalized Apollonian gasket Λ H \Lambda _H . We design a surgery that relates H H to a rational map g g whose Julia set J g \mathcal {J}_g is (non-quasiconformally) homeomorphic to Λ H \Lambda _H . We show for a large class of triangulations, however, the groups of quasisymmetries of Λ H \Lambda _H and J g \mathcal {J}_g are isomorphic and coincide with the corresponding groups of self-homeomorphisms. Moreover, in the case of H H , this group is equal to the group of Möbius symmetries of Λ H \Lambda _H , which is the semi-direct product of H H itself and the group of Möbius symmetries of the underlying circle packing. In the case of the tetrahedral triangulation (when Λ H \Lambda _H is the classical Apollonian gasket), we give a quasiregular model for the above actions which is quasiconformally equivalent to g g and produces H H by a David surgery. We also construct a mating between the group and the map coexisting in the same dynamical plane and show that it can be generated by Schwarz reflections in the deltoid and the inscribed circle.

Hydrogen bonds of a water molecule in the second coordination sphere of amino acid metal complexes: Influence of amino acid coordination

The hydrogen bonds of free and coordinated amino acids with water molecule were studied by analyzing data in the crystal structures from the Cambridge Structural Database (CSD) and by quantum chemical calculations. The CSD data indicate bifurcated NH/O hydrogen bonds and O1/HO hydrogen bonds of coordinated oxygen. The O/HO hydrogen bonds of free zwitterions and non-coordinated carbonyl oxygen (O2/HO) in metal complexes form primarily linear, non-bifurcated hydrogen bonds. Calculated M06L-GD3/def2-TZVPP interaction energies for free zwitterions (glycine, cysteine, phenylalanine and, serine) and water molecule are in the range from −5.1 to −9.6 kcal/mol for NH/O and from −6.9 to −7.6 kcal/mol for O/HO interactions. Coordinated amino acids in neutral octahedral cobalt(III) complexes have NH/O interaction energies ca. -7.4 kcal/mol, independent of the amino acid. The singly and doubly charged complexes have stronger NH/O interactions; the strongest has energy of −16.9 kcal/mol. In the case of O1/HO hydrogen bond, the interaction energy decreases upon coordination; interactions are quite weak for neutral complexes (−2.2 to −2.6 kcal/mol). For O2/HO hydrogen bonds, all amino acids except serine show slightly stronger interaction in singly negative complexes (−6.3 to −8.0 kcal/mol), while interactions are weaker for neutral complexes (−2.8 to −4.4 kcal/mol), comparing to zwitterions.

Equivariant Picard groups of the moduli spaces of some finite Abelian covers of the Riemann sphere

In this note, following Kordek's work we will compute the equivariant Picard groups of the moduli spaces of Riemann surfaces with certain finite abelian symmetries.

Weakly concave operators

We study a class of left-invertible operators which we call weakly concave operators. It includes the class of concave operators and some subclasses of expansive strict $m$-isometries with $m > 2$. We prove a Wold-type decomposition for weakly concave operators. We also obtain a Berger–Shaw-type theorem for analytic finitely cyclic weakly concave operators. The proofs of these results rely heavily on a spectral dichotomy for left-invertible operators. It provides a fairly close relationship, written in terms of the reciprocal automorphism of the Riemann sphere, between the spectra of a left-invertible operator and any of its left inverses. We further place the class of weakly concave operators, as the term $\mathcal {A}_1$, in the chain $\mathcal {A}_0 \subseteq \mathcal {A}_1 \subseteq \ldots \subseteq \mathcal {A}_{\infty }$ of collections of left-invertible operators. We show that most of the aforementioned results can be proved for members of these classes. Subtleties arise depending on whether the index $k$ of the class $\mathcal {A}_k$ is finite or not. In particular, a Berger–Shaw-type theorem fails to be true for members of $\mathcal {A}_{\infty }$. This discrepancy is better revealed in the context of $C^*$- and $W^*$-algebras.

Numerical computation of a preimage domain for an infinite strip with rectilinear slits

Let Ω be the multiply connected domain in the extended complex plane \(\overline {\mathbb {C}}\) obtained by removing m non-overlapping rectilinear segments from the infinite strip \(S=\{z : \left |\text {Im} z\right |<\pi /2\}\). In this paper, we present an iterative method for numerical computation of a conformally equivalent bounded multiply connected domain G in the interior of the unit disk \(\mathbb {D}\) and the exterior of m non-overlapping smooth Jordan curves. We demonstrate the utility of the proposed method through two applications. First, we estimate the capacity of condensers of the form (S,E) where E ⊂ S is a union of disjoint segments. Second, we determine the streamlines associated with uniform incompressible, inviscid and irrotational flow past disjoint segments in the strip S.

Julia sets are quasicircles for rational maps of degree N

This research aims to study complex dynamics, where the complex dynamic is considered a branch of dynamical systems, which takes maps from the Riemann sphere to the Riemann sphere. The Julia sets are also examples of fractals and the most important of them, thus being a fractal set. This work aims to study the Julia sets of a family of rational maps are quasicircles and offer the boundaries of the immediate basin of attraction of zero and the infinity are quasi-circles. Now, we introduce the family of maps are defined as: Gb (z) = 2bn+1 z–n + z2n – b3n+1/zn (z2n – bn–1), (1) where n ≥ 2 and b ϵ ℂ\{0} also bn+1 ≠ 1 and b2n+2 ≠ 1.

Построение эффективного организационно-экономического механизма управления справедливой системой оплаты труда на предприятиях АПК

The article analyzes the activities of agricultural enterprises in the sphere of the agro-industrial complex of the Russian Federation, and also identifies the main problems of its unstable functioning, which made it possible to determine the influencing factors and principles for the formation of an effective wage mechanism at enterprises. The structure of optimal distribution of profits at agricultural enterprises is presented and recommendations are given on the formation of a fair wage system for workers in agricultural and processing enterprises for the short and long term development.