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].     

Enhanced thermoelectric performance of PEDOT:PSS films via ionic liquid post-treatment

Thermoelectric(TE)energy harvesting can effectively convert waste heat into electricity,which is a crucial technology to solve energy concerns.As a promising candidate for energy conversion,poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate)(PEDOT:PSS)has gained significant attention owing to its easy doping,high transparency,and solution processability.However,the TE performance of PEDOT:PSS still needs to be further enhanced.Herein,different approaches have been applied for tuning the TE properties:(i)direct dipping PEDOT:PSS thin films in ionic liquid;(ii)post-treatment of the films with concentrated sulfuric acid(H₂SO₄),and then dipping in ionic liquid.Besides,the same bis(trifluoromethanesulfonyl)amide(TFSI)anion and different cation salts,including 1-ethyl-3-methylimidazolium(EMIM+)and lithium(Li+),are selected to study the influence of varying cation types on the TE properties of PEDOT:PSS.The Seebeck coefficient and electrical conductivity of the PEDOT:PSS film treated with H2SO4EMIM:TFSI increase simultaneously,and the resulting maximum power factor is 46.7μW·m^-1·K^-2,which may be attributed to the ionic liquid facilitating the rearrangement of the molecular chain of PEDOT.The work provides a reference for the development of organic films with high TE properties.     

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...     

Output feedback regulation of large-scale feedforward systems with discrete and distributed delays

Nonlinear Dynamics - This paper proposes an output feedback control strategy to achieve the global regulation of a class of large-scale feedforward nonlinear systems with discrete and distributed...     

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...