Normal approximation and fourth moment theorems for monochromatic triangles

Given a graph sequence denote by T₃(G_n) the number of monochromatic triangles in a uniformly random coloring of the vertices of G_n with colors. In this paper we prove a central limit theorem (CLT) for T₃(G_n) with explicit error rates, using a quantitative version of the martingale CLT. We then relate this error term to the well-known fourth-moment phenomenon, which, interestingly, holds only when the number of colors satisfies . We also show that the convergence of the fourth moment is necessary to obtain a Gaussian limit for any , which, together with the above result, implies that the fourth-moment condition characterizes the limiting normal distribution of T₃(G_n), whenever . Finally, to illustrate the promise of our approach, we include an alternative proof of the CLT for the number of monochromatic edges, which provides quantitative rates for the results obtained in [7].     

On New Functional Characteristics of Domains $$\Omega\in\mathbb R^n$$

Mathematical Notes - A system of new differential-geometric notions as the result of an analysis of the Trudinger–Wang inequalities is proposed. Their naturalness in multivariate analysis and...     

Set-theoretical solutions of the Zamolodchikov tetrahedron equation on associative rings and Liouville integrability

Theoretical and Mathematical Physics - This paper is devoted to tetrahedron maps, which are set-theoretical solutions of the Zamolodchikov tetrahedron equation. We construct a family of tetrahedron...     

Three-Dimensional Structure of Recombinant Thermophilic Ribokinase from Thermus speсies 2.9 in Complex with Adenosine Diphosphate

Crystallography Reports - The three-dimensional structure of recombinant thermophilic ribokinase from Thermus speсies 2.9 was determined at 2.4 Å resolution using crystals, which were...     

Investigation of Thermal Gradient Mechanical Fatigue Test Methods for Nickel-based Superalloys

Experimental Mechanics - Temperature gradients significantly affect the material fatigue process. A reliable and robust test procedure is needed for quantifying the effects of temperature gradients...     

COMPENSATING ROLE OF SELF-EQUILIBRATED STRESS FIELDS IN CONSTRUCTING NON-SINGULAR SOLUTIONS USING A NON-EUCLIDEAN CONTINUUM MODEL FOR AN INCOMPRESSIBLE SPHERE

Journal of Applied Mechanics and Technical Physics - A self-equilibrated stress field for an incompressible sphere is constructed based on a non-Euclidean continuum model. The...     

Multiphoton Processes of Two Modes of Quantized Field Interaction with Interacting Asymmetric Two Two-Level Atoms

International Journal of Theoretical Physics - The interaction between two modes quantized field and asymmetric two atoms represents one of the important quantum models to study the nonclassical...     

Using an ANP performance management framework to manage the development of transversal competences in University degrees

Organisations are concerned about measuring the performance of the product/service they deliver to their customers. In all types of organisations, if a proper performance assessment is to be developed, it should be measured in different dimensions. At University, the new study programs include the development and assessment of transversal competences due to their importance in enhancing the abilities and improving the employability of students. The achievement of transversal competences can be assessed in different levels/stages; for example, the 1st and 2nd years of a Bachelor’s degree; the 3rd and 4th years of a Bachelor’s degree and at Master’s level. The purpose of this paper is to integrate the research into performance management in organisations to develop an approach consisting of four components (a methodology, a solid and integrated performance management framework, graphical diagrams and quantitative techniques) to assess and manage the achievement of transversal competences through the different levels of study using a consolidated approach. The proposal uses the Analytic Network Process (ANP) to model dependences and feedback among the elements of the competences.

     

Minkowski type theorems for convex sets in cones

Acta Mathematica Hungarica - Minkowski’s classical existence theorem provides necessary and sufficient conditions for a Borel measure on the unit sphere of Euclidean space to be the surface...     

Vacuum Conditions and the Lifetime of a Single-Charged Helium Ion Beam in the Booster Synchrotron of the NICA (First Run)

JETP Letters - The results of the first run (December 2020) for the commissioning of the new superconducting synchrotron Booster at the Joint Institute for Nuclear Research are presented. Vacuum...