We introduce $$\mu $$ -scalar curvature for a Kähler metric with moment map and start up study on constant as generalization of both cscK Kähler–Ricci soliton continuity path to extremal metric. some fundamental constraints the existence by investigating volume functional Tian-Zhu’s work, which is closely related Perelman’s W-functional. A new K-energy studied an approach uniqueness problem pre...

Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

The subject of this talk is the role of equivariant KK ahler geometry in the G=G model or, in other words, that of its equivariant supersymmetry. This supersym-metry is somewhat unusual in that it does not model the innnitesimal action of the group of gauge transformations. Nevertheless, this supersymmetry is useful on, at least, two counts. Firstly, it allows one to localise the path integral....

It is shown that the normalized trace of Fedosov star product for quantum moment map depends only on path component in cohomology class symplectic form and closed formal 2-form required to define connections (Theorem 1.3). As an application we obtain a family obstructions existence products naturally attached manifolds 1.5) K\"ahler 1.6). These are integral invariants depending form. Restricted...

We consider the problem of solving equations over k-ary trees. Here an equation is a pair of labeled-ary trees, where is a function associating an arity to each label. A solution to an equation is a morphism from-ary trees to k-ary trees that maps the left and right hand side of the equation to the same k-ary tree. This problem is a generalization of the word uniication problem posed by A. Mark...

The double bracket dissipation approach is applied to the Vlasov kinetic equation. The Vlasov equation is then transformed by a Poisson map to moment dynamics, leading to a nonlocal form of Darcy’s law. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the double bracket dissipation form. The moment dynamics for these double bracket kinetic equ...

Throughout this paper, k will denote a commutative ring containing the rational numbers Q, and k = k[x{, . . . , xn] will be the polynomial ring over k . If ƒ : k —• k is a polynomial map (i.e., a fc-algebra homomorphism), then ƒ is a polynomial automorphism provided there is an inverse ƒ " which is also a polynomial map. Very little is known about the group of polynomial automorphisms, and ind...

We study the fluctuations of the diagonal matrix elements of the quantum cat map about their limit. We show that after suitable normalization, the fifth centered moment for the Hecke basis vanishes in the semiclassical limit, confirming in part a conjecture of Kurlberg and Rudnick. We also study sums of matrix elements lying in short windows. For observables with zero mean, the first moment of ...

Let G be a real form of a complex reductive group. Suppose that we are given involutions σ and θ of G. Let H = G denote the fixed group of σ and let K = G denote the fixed group of θ. We are interested in calculating the double coset space H\G/K. We use moment map and invariant theoretic techniques to calculate the double cosets, especially the ones that are closed. One salient point of our res...