Related papers: On Z2 harmonic functions on $\mathbb{R}^2$ and the…
This paper is devoted to the study of the second-order variational analysis of spectral functions. It is well-known that spectral functions can be expressed as a composite function of symmetric functions and eigenvalue functions. We…
In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper,…
The paper studies the harmonic maps on a direction between a Riemannian space and a generalized Lagrange space. Also, it is proved there that the solutions of C^2 class of certain ODEs or PDEs are harmonic maps, in the sense of this paper.
We give a brief overview of the kinetic theory for spin-1/2 fermions in Wigner function formulism. The chiral and spin kinetic equations can be derived from equations for Wigner functions. A general Wigner function has 16 components which…
The authors prepared this booklet in order to make several useful topics from the theory of special functions, in particular the spherical harmonics and Legendre polynomials for any dimension, available to undergraduates studying physics or…
Solutions to Laplace's equation are called harmonic functions. Harmonic functions arise in many applications, such as physics and the theory of stochastic processes. Of interest classically are harmonic polynomials, which have a simple…
In this paper, we first give a convenient formula for bi-Laplacian on a sphere and the complete description of its eigenvalues, buckling eigenvalues, and their corresponding eigenfunctions. We then show that the radial (or rotationally…
I review the spin dependent structure functions which control dominant (twist-2) and sub-dominant (twist-3) phenomena in hard processes. Novel effects associated with chirally odd parton distributions and with transverse polarization are…
This paper is about a family of symmetric rational functions that form a one-parameter generalization of the classical Hall-Littlewood polynomials. We introduce two sets of (skew and non-skew) functions that are akin to P and Q…
By using Fubini theorem or Tonelli theorem, we find that the zeta function value at 2 is equal to a special integral. Furthermore, We find that this special integral is two times of another special integral. By using this fact we obtain the…
We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points…
In this note we investigate the behavior of harmonic functions at singular points of $\mathsf{RCD}(K,N)$ spaces. In particular we show that their gradient vanishes at all points where the tangent cone is isometric to a cone over a metric…
In this paper, we investigate some properties on harmonic functions and solutions to Poisson equations. First, we will discuss the Lipschitz type spaces on harmonic functions. Secondly, we establish the Schwarz-Pick lemma for harmonic…
We evaluate closed string disk amplitudes in the pure spinor formalism. We focus on low point functions (two- and one-point functions) but our analysis is also relevant for higher n-point functions. Amongst others we discuss issues arising…
We extend to the case l=2 the study of the new generalized spherical harmonics introduced recently, and worked out only for the case l=1. We present some of the properties of the new quantities and clarify how they are related to standard…
In this paper, we consider estimates for the two-dimensional oscillatory integrals. The phase function of the oscillatory integrals is the linear perturbation of a function having $D$ type singularities. We consider estimates for the…
Using an approach based on the Casimir operators of the de Sitter group, the conformal invariant equations for a fundamental spin-2 field are obtained, and their consistency discussed. It is shown that, only when the spin-2 field is…
In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…
We calculate the Mellin moments of the $O(\alpha_s^2)$ coefficient functions for the unpolarized and polarized fragmentation functions. They can be expressed in terms of multiple finite harmonic sums of maximal weight {\sf w = 4}. Using…
We study the minimal possible growth of harmonic functions on lamplighters. We find that $(\mathbb{Z}/2)\wr \mathbb{Z}$ has no sublinear harmonic functions, $(\mathbb{Z}/2)\wr \mathbb{Z}^2$ has no sublogarithmic harmonic functions, and…