Riemann Sphere Research Articles

Non-CSC Extremal Kähler Metrics on $${{\varvec{S}}}^2_{\{2,2,2\}}$$ S { 2 , 2 , 2 } 2

We often call an extremal Kahler metric with finite singularities on a compact Riemann surface an HCMU (the Curvature of the Metric is Umbilical) metric. In this paper, we construct all of the normalized non-CSC HCMU metrics on $$S^2_{\{2,2,2\}}$$ by proving the existence of some kind of meromorphic 1-forms on the Riemann sphere $$S^{2}$$ .

Towards the Evolution of Artificial Metalloenzymes-A Protein Engineer's Perspective.

Incorporating artificial metal-cofactors into protein scaffolds results in a new class of catalysts, termed biohybrid catalysts or artificial metalloenzymes. Biohybrid catalysts can be modified chemically at the first coordination sphere of the metal complex, as well as at the second coordination sphere provided by the protein scaffold. Protein-scaffold reengineering by directed evolution exploits the full power of nature's diversity, but requires validated screening and sophisticated metal cofactor conjugation to evolve biohybrid catalysts. In this Minireview, we summarize the recent efforts in this field to establish high-throughput screening methods for biohybrid catalysts and we show how non-chiral catalysts catalyze reactions enantioselectively by highlighting the first successes in this emerging field. Furthermore, we shed light on the potential of this field and challenges that need to be overcome to advance from biohybrid catalysts to true artificial metalloenzymes.

Rational families converging to a family of exponential maps

We analyze the dynamics of a sequence of families of non-polynomial rational maps, \{f_{a,d}\} , for a \in \mathbb C^*= \mathbb C \setminus \{0\}, d \geq 2 . For each d , \{f_{a,d}\} is a family of rational maps of degree d of the Riemann sphere parametrized by a \in \mathbb C^* . For each a \in \mathbb C^* , as d \to \infty , f_{a,d} converges uniformly on compact sets to a map f_a that is conformally conjugate to a transcendental entire map on \mathbb C . We study how properties of the families f_{a,d} contribute to our understanding of the dynamical properties of the limiting family of maps. We show all families have a common connectivity locus; moreover the rational maps contain some well-studied examples.

Bootstrapping solutions of scattering equations

The scattering equations are a set of algebraic equations connecting the kinematic space of massless particles and the moduli space of Riemann spheres with marked points. We present an efficient method for solving the scattering equations based on the numerical algebraic geometry. The cornerstone of our method is the concept of the physical homotopy between different points in the kinematic space, which naturally induces a homotopy of the scattering equations. As a result, the solutions of the scattering equations with different points in the kinematic space can be tracked from each other. Finally, with the help of soft limits, all solutions can be bootstrapped from the known solution for the four-particle scattering.

An Iterative SISO Improved Complex Sphere Detection and Decoder for Turbo-MIMO Systems

An Iterative SISO Improved Complex Sphere Detection and Decoder for Turbo-MIMO Systems

Relations between Schoenberg Coefficients on Real and Complex Spheres of Different Dimensions

Positive definite functions on spheres have received an increasing interest in many branches of mathematics and statistics. In particular, the Schoenberg sequences in the spectral representation of positive definite functions have been studied by several mathematicians in the last years. This paper provides a set of relations between Schoenberg sequences defined over real as well as complex spheres of different dimensions. We illustrate our findings describing an application to strict positive definiteness.

Hydrogenation reaction pathways in chemistry of white phosphorus

Abstract Approaches for preparation of P–H bond containing derivatives directly from white phosphorus are summarized in this microreview. Transfer hydrogenation of P4 involving the activation and reaction of white phosphorus in the coordination sphere of transition metal complexes is a convenient and powerful route to the hydrogenated compounds. Electrochemical methods have also become popular in modern synthetic chemistry; these provide easy access to highly reactive intermediates, which can be selectively generated in situ and used for subsequent synthetic processes. These electrochemical routes provide efficient and environmentally safe methods for preparation of phosphorus derivatives bearing P–H bond. The mechanisms of the proposed processes and the nature of the intermediates formed in the overall electrochemical process are disclosed. The methods elaborated operate under the principals of “green chemistry” and can be considered as efficient alternatives to some classical pathways.

Characterization of Strict Positive Definiteness on products of complex spheres

In this paper we consider Positive Definite functions on products $\Omega_{2q}\times\Omega_{2p}$ of complex spheres, and we obtain a condition, in terms of the coefficients in their disc polynomial expansions, which is necessary and sufficient for the function to be Strictly Positive Definite. The result includes also the more delicate cases in which $p$ and/or $q$ can be $1$ or $\infty$. The condition we obtain states that a suitable set in $\mathbb{Z}^2$, containing the indexes of the strictly positive coefficients in the expansion, must intersect every product of arithmetic progressions.

Average Discrete Energies of Spectra of Gaussian Random Matrices

We present exact formulas for the averages of various discrete energies of certain point processes in the plane and two-dimensional sphere. Specifically, we consider point processes defined by the spectra of gaussian random matrices and their inverse images under stereographic projection on the Riemann sphere. The main attention is given to the discrete Coulomb energy, discrete logarithmic energy, and their analogs involving geodesic distances on the Riemann sphere. It is shown that the average discrete energies are expressed by integrals of certain special type taken over the Riemann sphere. This enables us to estimate their values and asymptotics as the size of random matrix tends to infinity. Analogous results are obtained for the three-point energy function considered by M. Atiyah. We also present several related conjectures and possible generalizations.

Innovative projects and programmes for the strategic development of the municipality

The relevance of the matter is caused by the fact that the essence of strategic planning consists in the definition of the priority sphere of social-and-economic development of the city district taking into account the external environment factors and available resources. It is necessary to prove the organization of the chosen project or programme, including sources and mechanisms of resources attraction, applied technologies, technical means, etc. within strategic management. The main document in the sphere of complex social-and-economic development of the municipal unit is the strategic plan that allows formulating the perspective purposes of the development, choosing alternative options of the municipality, thereby attracting investments into the projects and programmes. The subject of the research is the “City district Podolsk”. Some problems of strategic planning of investment projects and programmes, which are necessary for the improvement of activity of the “city district Podolsk”, are studied. The objective of the research is to develop recommendations on the strategic planning of activity of the “City district Podolsk”. Calculations for three investment programmes are made for the identification of the most successful direction of strategic development of the “City district Podolsk” by the means of formulas of the indicator of efficiency and coefficient of competitiveness. The achieved results can be used for creation of the Draft of the strategic development plan for the “City district Podolsk” till 2022.

Modular bootstrap agrees with the path integral in the large moduli limit

Based on the rigorous path integral formulation of Liouville Conformal Field Theory initiated by David-Kupiainen-Rhodes-Vargas on the Riemann sphere and David-Rhodes-Vargas on the torus of modulus $\tau$, we give the exact asymptotic behaviour of the 1-point toric correlation function as $\mathrm{Im}\:\tau\to\infty$. In agreement with formulae predicted within the bootstrap formalism of theoretical physics, our results feature an $(\mathrm{Im}\:\tau)^{-3/2}$ decay rate and we identify the derivative of DOZZ formula in the limit.

Fundamental two-forms for isomonodromic deformations

Abstract We give a simple explicit description of the fundamental two-forms for the isomonodromic deformations of unramified compatibly framed meromorphic connections on the Riemann sphere with arbitrary complex reductive structure group and calculate their Hamiltonians.

Thurston's algorithm and rational maps from quadratic polynomial matings

Topological mating is a combination that takes two same-degree polynomials and produces a new map with dynamics inherited from this initial pair. This process frequently yields a map that is Thurston-equivalent to a rational map \begin{document}$ F $\end{document} on the Riemann sphere. Given a pair of polynomials of the form \begin{document}$ z^2+c $\end{document} that are postcritically finite, there is a fast test on the constant parameters to determine whether this map \begin{document}$ F $\end{document} exists-but this test does not give a construction of \begin{document}$ F $\end{document} . We present an iterative method that utilizes finite subdivision rules and Thurston's algorithm to approximate this rational map, \begin{document}$ F $\end{document} . This manuscript expands upon results given by the Medusa algorithm in [ 9 ]. We provide a proof of the algorithm's efficacy, details on its implementation, the settings in which it is most successful, and examples generated with the algorithm.

ТЕНДЕНЦІЇ РОЗВИТКУ МІЖНАРОДНОГО ТУРИЗМ

The sphere of international tourism for the period 2000–2018 has been explored and analyzed in the article. The dynamics of the world tourist flows development and income from international tourism are considered, the determinants of development are derived, the regional structure of the world market of tourist services is given. The development of the tourism industry in the world is analyzed by indicators: the number of tourist arrivals, tourism revenues at current prices, total contribution of tourism to GDP. The main tourist regions are analyzed in the context of the study, they are compared both in terms of the number of tourist visits, and a list of the TOP 10 countries by volume of foreign exchange earnings from tourism in recent years. It is concluded that in recent years, there is a continuing upward trend in demand for emerging markets, with old markets such as the European market, partially losing its popularity. In the process of research, it is determined that in the conditions of development of the world economy, expansion of volumes of international trade, improvement of means of transport, communication, increase of internationalization and globalization of the world economy the demand for tourist services increases. One of the peculiarities of the development of the international tourist services market is the globalization of the market, which has reached all sectors of the tourism industry. It is concluded that nowadays international tourism is an important area of international economic activity, a complex sphere that significantly affects both the structure and the situation in the world economy as well as the economies of most individual countries and regions of the world. Tourism development has a stimulating effect on such sectors of the economy as transport, communications, trade, construction, agriculture, production of consumer goods, and іt is one of the most promising areas of structural restructuring of the economy, confirming the amount of foreign exchange earnings from tourism in the world in general and in individual countries. It is the increasing demand for tourism services and the volume of foreign exchange earnings from tourism in the world makes the topic relevant for further research.

Evaluation of attractive interactions in the second coordination sphere of iron complexes containing pendant amines.

The interactions between pendant amines in the second coordination sphere and ligands in the first coordination sphere are important for understanding the structures and reactivity of complexes containing PR2NR'2 ligands, which have been shown to be highly active H2 oxidation/production catalysts. A series of [Fe(PPh2NBn2)2(X)(Y)]n+ complexes have been prepared and structurally characterized. These complexes have two different ligands with which the pendant amines of the diphosphine ligand can interact. The solid state structure of cis-Fe(PPh2NBn2)2Cl2 reveals that the six-membered rings adjacent to the P atoms are in a boat confirmation, resulting in close NP distances that suggests the P atoms have a greater affinity for the lone pair of electrons on the N atom than chloride ligands. Similarly, boat conformations are observed for both rings adjacent to the hydride ligands of trans-[HFe(PPh2NBn2)2(CH3CN)]+ and trans-HFe(PPh2NBn2)2Cl, resulting in short NH distances. Spectroscopic and computational studies of trans-[HFe(PPh2NBn2)2(CO)]+, trans-[HFe(PPh2NBn2)(PPh2NBn2H)(CO)]2+, and trans-[HFe(PPh2NBn2)2(H2)]+ indicate the complexes are more stable when the pendant amines in boat conformations are adjacent to the hydride ligand. These data suggest an attractor ordering of H- > CO > H2 > PR3 > Cl- ∼ CH3CN.

Інформаційно-правове забезпечення сфери агропромислового комплексу України

Інформаційно-правове забезпечення сфери агропромислового комплексу України

Systematization of the Main Administrative Supervision Measures in the Agroindustrial Complex of Ukraine: a Modern View

Problem setting. The article deals with the lack of legislative regulation of the supervision powers of public authorities in the field of agroindustrial complex of Ukraine. This is directly reflected in the lack of orderliness and declarative nature of the regulatory documents that would regulate these issues, regulate in detail the procedure for carrying out supervisory measures, and most of the existing rules are outdated. In this aspect, it is a question of devaluing the very essence of state surveillance and its appointment as one of the regulators of public relations. In this regard, it is important to determine the content of the category «supervision measures in the agroindustrial complex», to outline the main criteria of the categories «control» and «supervision» and to provide suggestions for improving the supervisory activities of controlling entities. Target of research. The purpose of the study is the generalization of theoretical developments related to supervisory activities in the agroindustrial complex, delimitation of related categories that have a significant impact on the regulation of public relations in the agro sphere, identifying possible areas of improvement of regulatory support in the context of supervisory competence. Analysis of recent researches and publications. The following scientists analyze separate aspects of the question in their researches: V. Averyanov, O. Bandurka, Y. Bytyak, V. Galunko, T. Kolomiyets, Sobakar A., V. Haraschuk, V. Lytovchenko and others. Article’s main body. Characterizing separate supervisory activities in the field of agriculture, it is properly to identify their main features. Firstly, these measures are not related to the interference with the business activities of the enterprise. Secondly, they are generally carried out on a sample basis and are not continuous in nature. Thirdly, they serve as the basis for regulatory support of the field of agriculture, since the primary purpose of supervision is to analyse the state of economic activity and on the basis of the conducted monitoring of the implementation of preventive measures in order to prevent further offenses. Thus, supervisory measures in the agroindustrial complex should be understood as the exercise by the supervisory authorities of their powers in the agroindustrial sphere, which is manifested in the systematic but not daily monitoring (including monitoring activities) of the activities of economic entities without direct intervention. Conclusions and prospects for the development. The prospect of further research on this topic is evident, as by dividing the categories of supervision and control, outlining the limits of authority and reforming supervisory entities in the agroindustrial complex, as well as authorizing the administrative supervision measures under which should be understood by the supervisory authorities of their powers in the agroindustrial field, which is not systematic (including monitoring measures) in the activity of economic entities without direct intervention in such activities, we consider it essential to direct development of modern agroindustrial complex in the field of innovation and supervisory technologies. A critical analysis of governmental innovations provided prerequisites for discussing the premature and over-radical nature of the government in the questions of administrative reform in the sphere of agroindustrial complex, emphasizing once again the importance of public opinion in public policy matters. In our view, the most optimal is the renewal of the Ministry of Agrarian Policy transferring some of its functions, which are clearly not within the competence of the Ministry, to other executive bodies implementing state policy in the field of agriculture.

Convergence of the Kähler–Ricci iteration

The Ricci iteration is a discrete analogue of the Ricci flow. According to Perelman, the Ricci flow converges to a Kahler-Einstein metric whenever one exists, and it has been conjectured that the Ricci iteration should behave similarly. This article confirms this conjecture. As a special case, this gives a new method of uniformization of the Riemann sphere.

Hidden Symmetries of Complex Analysis

We are dealing with domains of the complex plane which are not symmetric in common sense, but support fixed point free antianalytic involutions. They are fundamental domains of different classes of analytic functions and the respective involutions are obtained by composing their canonical projections onto the complex plane with the simplest antianalytic involution of the Riemann sphere. What we obtain are hidden symmetries of the complex plane. The list given here of these domains is far from exhaustive.

Selective Formation of an FeIVO or an FeIIIOOH Intermediate From Iron(II) and H2O2: Controlled Heterolytic versus Homolytic Oxygen–Oxygen Bond Cleavage by the Second Coordination Sphere

AbstractWe demonstrate that the devised incorporation of an alkylamine group into the second coordination sphere of an FeII complex allows to switch its reactivity with H2O2 from the usual formation of FeIII species towards the selective generation of an FeIV‐oxo intermediate. The FeIV‐oxo species was characterized by UV/Vis absorption and Mössbauer spectroscopy. Variable‐temperature kinetic analyses point towards a mechanism in which the heterolytic cleavage of the O−O bond is triggered by a proton transfer from the proximal to the distal oxygen atom in the FeII‐H2O2 complex with the assistance of the pendant amine. DFT studies reveal that this heterolytic cleavage is actually initiated by an homolytic O−O cleavage immediately followed by a proton‐coupled electron transfer (PCET) that leads to the formation of the FeIV‐oxo and release of water through a concerted mechanism.