Related papers: Du-Hwang Characteristic Area: Catch-22
Let $k$ be a local field with valuation ring $O_k$ and residue field $\overline{k}$. We extend Hahn--Banach theorem for the class of seminormed $k$-vector spaces to several classes of locally convex spaces and subspaces over $k$, $O_k$, and…
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
Recently, Hong and Li launched a systematic study of length-four pattern avoidance in inversion sequences, and in particular, they conjectured that the number of $0021$-avoiding inversion sequences can be enumerated by the OEIS entry…
Recently a paper by Lin and Ku \cite{lin} was posted, where the authors propose a very interesting idea to engineer the Dirac points in material which originally did not have such points by inducing a CDW state through introduction of…
This paper explores the dual space corresponding to p-Bergman space and examines the essential condition for the dual space to be a q-Bergman space. The investigation involves a detailed examination of the interpolation space of a Banach…
In this paper we give an example of a random perturbation of the Cat Map that produces a "global statistical attractor" in the form of a line segment. The transition probabilities for this random perturbation are smooth in some but not all…
This comment critically discusses certain aspects of a recent paper on parity doubling in the hadronic spectrum and its possible connection to chiral symmetry restoration.
We formulate a twisted version of the conjectured duality between heterotic and type I string theories. Our formulation relates the chiral part of the heterotic string with a type I topological B-model on a Calabi-Yau five-fold. We provide…
We formulate some refinements and complements to the categorical local Langlands conjecture of Fargues-Scholze. In particular, we state the expected compatibilities with Eisenstein series and duality, and explain some of their consequences.…
We calculate the charm-quark contribution to the decay K_L -> mu^+ mu^- in next-to-next-to-leading order of QCD. This new contribution reduces the theoretical uncertainty in the relevant parameter P_c from +/-22% down to +/-7%,…
I review recent estimates of the non-perturbative hadronic vacuum polarization contributions. Since these at present can only be evaluated in terms of experimental data of limited precision, the related uncertainties pose a serious…
Characters of $E_8\otimes E_8$ and SO(32) heterotic strings involving the full internal symmetry Cartan subalgebra generators are defined after circle compactification so that they are T dual. The novel point, as compared with an earlier…
Recently, F. Wang commented on our work "Scaling properties of background- and chiral-magnetically-driven charge separation in heavy ion collisions at $\sqrt{s}_{\rm NN} = 200$ GeV" and made several claims to support his conclusion that our…
The $\alpha'$-deformed frame-like Double Field Theory (DFT) is a T-duality and gauge invariant extension of DFT in which generalized Green-Schwarz transformations provide a gauge principle that fixes the higher-derivative corrections. It…
We explore topological defects in the 4-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. This theory has 1-form $\mathbb{Z}_{2}$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality…
The paper [1] by Liu, Madhavan, and Tegmark sought to use machine learning methods to elicit known conservation laws for several systems. However, in their example of a damped 1D harmonic oscillator they made seven serious errors, causing…
We address the problem of determining the Hausdorff dimension of sets consisting of complex irrationals whose complex continued fraction digits satisfy prescribed restrictions and growth conditions. For the Hurwitz continued fraction, we…
Quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a continuous set of generalised eigenfunctions of the wave operator, and directly in position…
Following the recent work [13] fulfilled in the discrete case, we pro- vide in this paper new intertwining relations for semigroups of one-dimensional diffusions. Various applications of these results are investigated, among them the famous…
Parametrizing the possible underlying theory or new physics' decoupling effects in the most general way we reexamined the validity of canonical trace relation and chiral symmetry in certain one-loop two-point functions. The anomalies and…