Let μ be singular of uncountable cofinality. If μ > 2cf(μ), we prove that in P = ([μ],⊇) as a forcing notion we have a natural complete embedding of Levy(א0, μ+) (so P collapses μ+ to א0) and even Levy(א0,UJbd κ (μ)). The “natural” means that the forcing ({p ∈ [μ] : p closed},⊇) is naturally embedded and is equivalent to the Levy algebra. Moreover we prove more than conjectured: if P fails the ...

For any given polynomial f over the finite field Fq with degree at most q−1, we associate it with a q×q matrix A(f) = (aik) consisting of coefficients of its powers (f(x)) = ∑q−1 i=0 aikx i modulo x−x for k = 0, 1, . . . , q−1. This matrix has some interesting properties such as A(g◦f) = A(f)A(g) where (g◦f)(x) = g(f(x)) is the composition of the polynomial g with the polynomial f . In particul...

We work on the uniqueness [1] of representations of the holonomy-flux algebra in loop quantum gravity. We argue that for analytic diffeomorphisms, the flux operators can be only constants as functions on the configuration space in representations with no anomaly, which are zero in the standard representation. In loop quantum gravity, the configuration variables are holonomies he[A] of a connect...

The most authoritative description of the morphophonemic rules that apply at word boundaries (external sandhi) in Sanskrit is by the great grammarian Pān. ini (fl. 5th c. B. C. E.). These rules are stated formally in Pān. ini’s grammar, the As. t .ādhyāyı̄ ‘group of eight chapters’. The present paper summarizes Pān. ini’s handling of sandhi, his notational conventions, and formal properties of h...

In this paper we introduce a quotient class of pairs of convex bodies in which every member have convex union. The space of pairs of convex bodies has been investigated in a number of papers [3], [8], [9], and [12]. This space has found an application in quasidifferential calculus (cf. [1], [5], [7], [10]). A quasidifferential is represented as a pair of convex bodies and it is essential to fin...

A general Lagrangian formulation of integrably deformed G/H-coset models is given. We consider the G/H-coset model in terms of the gauged Wess-Zumino-Witten action and obtain an integrable deformation by adding a potential energy term Tr(gTgT̄ ), where algebra elements T, T̄ belong to the center of the algebra h associated with the subgroup H. We show that the classical equation of motion of the ...

We characterize the Murasugi polynomial of an equivariant slice knot by proving a conjecture of J. Davis and S. Naik. A knot K in S is called periodic of period p if there is an orientation preserving action of Z/p on S which preserves K setwise and its fixed point set A is a circle disjoint to K. A is called the axis. Two periodic knots K0 and K1 of period p are called equivariantly concordant...

In recent years there has been increasing interest in the study of structures that can be presented by automata. The underlying idea in this line of research consists of applying properties of automata and techniques of automata theory to decision problems that arise in logic and applications. A typical example of a decision problem is the model checking problem, stated as follows. For a struct...

We propose stochastic approximation based methods with randomization of samples in two different settings one for policy evaluation using the least squares temporal difference (LSTD) algorithm and the other for solving the least squares problem. We consider a “big data” regime where both the dimension, d, of the data and the number, T, of training samples are large. Through finite time analyses...