Abstract: We provide, with proofs, a complete description of the authors’ construction of state-sum invariants announced in [CY], and its generalization to an arbitrary (artinian) semisimple tortile category. We also discuss the relationship of these invariants to generalizations of Broda’s surgery invariants [Br1,Br2] using techniques developed in the case of the semi-simple sub-quotient of Re...

1. Introduction In the higher rank paper 17], we reduced Dwork's conjecture from higher rank case over any smooth aane variety X to the rank one case over the simplest aane space A n. In the present paper, we nish our proof by proving the rank one case of Dwork's conjecture over the aane space A n , which is called the key lemma in 17]. The key lemma had already been proved in 16] in the specia...

k=1 |ak|, in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ ...

In this paper, we study on direction-of-arrival (DOA) estimation error reduction by Khatri-Rao (KR) product extended array in the presence of correlated waves. Recently, a simple array signal processing technique called KR product extended array has been proposed. By using the technique, degrees-of-freedom of an array can be easily increased. However, DOA estimation accuracy deteriorates when c...

Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel drawn with the analysis of time band limiting signal processing. It shown that a tridiagonal matrix commuting entanglement Hamiltonian can be found using algebraic Heun operator construct instances when there an underlying bispectral problem. Cases corresponding to Lie algebras $\mathfrak{su}(2)$ $\mathfrak{su...

A Kac-Moody algebra is called hyperbolic if it corresponds to a generalized Cartan matrix of hyperbolic type. We study root subsystems of root systems of hyperbolic algebras. In this paper, we classify maximal rank regular hyperbolic subalgebras of hyperbolic Kac-Moody algebras. Introduction A generalized Cartan matrix A is called a matrix of hyperbolic type if it is indecomposable symmetrizabl...

This document consists of details to which the original submission article has made references. These include a list of symbols, some matrix identities and calculus rules, a list of VarPro derivatives, symmetry analysis of the un-regularized VarPro Gauss-Newton matrix and MTSS computation details. Symbol Meaning Rp×q The space of real matrices of size p× q S The space of symmetric real matrices...

Exceptional points~(EPs) appear as degeneracies in the spectrum of non-Hermitian matrices at which eigenvectors coalesce. In general, an EP order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed. Our results show that these can be expressed terms determinant and traces matrix. findings further reveal total number reduce presence unitary antiunitary symmetries. Additionally, ...

We describe the development of Analytic Perturbation Theory (APT) in QCD, called Fractional APT (FAPT), which has been suggested to apply the renormalization group evolution and QCD factorization technique in the framework of APT. 1 Basics of APT in QCD In the standard QCD Perturbation Theory (PT) we have: ✔ the Renormalization Group (RG) equation das(L)/dL = −as − c1 as − . . . for the effecti...