Related papers: Levy-Khintchine type representation of Dirichlet g…
Similar to other heavy flavor mesons, the weak decays of $D^*_{(s)}$ mesons can provide a platform to verify the standard model, explore new physics, and understand the mechanisms of weak interactions. At present, the theoretical and…
In this paper, we shall first establish the theory of bivariate Revuz correspondence of positive additive functionals under a semi-Dirichlet form, which is associated with a right Markov process $X$ satisfying the sector condition but…
A Dirichlet $k$-partition of a domain $U \subseteq \mathbb{R}^d$ is a collection of $k$ pairwise disjoint open subsets such that the sum of their first Laplace-Dirichlet eigenvalues is minimal. A discrete version of Dirichlet partitions has…
Using data from a recent reanalysis of neutron structure functions extracted from inclusive proton and deuteron deep-inelastic scattering (DIS), we re-examine the constraints on the shape of the $\bar d-\bar u$ asymmetry in the proton at…
A unitary representation of a, possibly infinite dimensional, Lie group G is called semi-bounded if the corresponding operators id\pi(x) from the derived representations are uniformly bounded from above on some non-empty open subset of the…
Given a compact doubling metric measure space $X$ that supports a $2$-Poincar\'e inequality, we construct a Dirichlet form on $N^{1,2}(X)$ that is comparable to the upper gradient energy form on $N^{1,2}(X)$. Our approach is based on the…
An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical. Such a semi-reductive algebraic group naturally arises and also plays a key role in the study of modular…
The Peterson variety (which we denote by $Y$) is a subvariety of the flag variety, introduced by Dale Peterson to describe the quantum cohomology rings of all the partial flag varieties. Motivated by the mirror symmetry for partial flag…
Let $\chi$ be a primitive Dirichlet character whose conductor $q$ is a prime number. For the certain averages of values of $\log |L(s, \chi)|$ in $q$-aspect at a fixed $s=\sigma>1/2$, under Generalized Riemann Hypothesis (GRH), we explain…
We study the Knapp-Stein $R$--groups for inner forms of the split group $SL_n(F),$ with $F$ a $p$--adic field of characteristic zero. Thus, we consider the groups $SL_m(D),$ with $D$ a central division algebra over $F$ of dimension $d^2,$…
We explore positivity properties of the semigroup generated by the negative of the Dirichlet-to-Neumann operator with real potential $\lambda$, defined on a subset of the vertices of a quantum graph. We show that for rationally independent…
Let the abstract fractional space-time operator $(\partial_t + A)^s$ be given, where $s \in (0,\infty)$ and $-A \colon \mathsf{D}(A) \subseteq X \to X$ is a linear operator generating a uniformly bounded strongly measurable semigroup…
A well pronounced spin--grouping of baryon resonances to O(4) partial waves is found in baryon spectra and shown to be well interpreted in terms of Lorentz group representations of the type (1/2 +l', 1/2 +l')* [(1/2, 0)+(0,1/2)] with l'…
We study quantum transport properties of finite periodic quasi-one-dimensional waveguides whose classical dynamics is diffusive. The system we consider is a scattering configuration, composed of a finite periodic chain of $L$ identical…
The celebrated L\'evy--Khintchine theorem is a fundamental limiting law that describes the growth rate of the denominators of the convergents in the continued fraction expansion of a Lebesgue-typical real number. In a recent breakthrough,…
Let $L_t:=\Delta_t +Z_t $, $t\in [0,T_c)$ on a differential manifold equipped with time-depending complete Riemannian metric $(g_t)_{t\in [0,T_c)}$, where $\Delta_t$ is the Laplacian induced by $g_t$ and $(Z_t)_{t\in [0,T_c)}$ is a family…
A generalized version of Chernoff's theorem has been obtained. Namely, the version of Chernoff's theorem for semigroups obtained in a paper by Smolyanov, Weizsaecker, and Wittich is generalized for a time-inhomogeneous case. The main…
A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$. The following two results are shown:…
In a recent Letter, Zhao et al. [1] reported the origin of quasi-one-dimensional metal-insulator (MI) transitions in compound semiconductor surfaces. Based on a density-functional theory (DFT) calculation within the generalized gradient…
In the first part of the paper we prove various results on regularity of Feynman-Kac functionals of Hunt processes associated with time dependent semi-Dirichlet forms. In the second part we study the Cauchy problem for semilinear parabolic…