In this paper we derive a new algorithm for constructing a uni-tary decomposition of a sequence of matrices in product or quotient form. The unitary decomposition requires only unitary left and right transformations on the individual matrices and amounts to computing the generalized singular value decomposition of the sequence. The proposed algorithm is related to the classical Golub-Kahan proc...

In this paper we introduce techniques from complex harmonic analysis to prove a weaker version of the Geometric Arveson-Douglas Conjecture on the Bergman space for a complex analytic subset that is smooth on the boundary of the unit ball and intersects transversally with it. In fact, we prove that the projection operator onto the corresponding quotient module is in the Toeplitz algebra T (L∞), ...

A language L over an alphabet Σ is prefix-convex if, for any words x, y, z ∈ Σ, whenever x and xyz are in L, then so is xy. Prefix-convex languages include right-ideal, prefixclosed, and prefix-free languages. We study complexity properties of prefix-convex regular languages. In particular, we find the quotient/state complexity of boolean operations, product (concatenation), star, and reversal,...

 ‎In this article‎, ‎we first‎ ‎show that non-Noetherian Artinian uniserial modules over‎ ‎commutative rings‎, ‎duo rings‎, ‎finite $R$-algebras and right‎ ‎Noetherian rings are $1$-atomic exactly like $Bbb Z_{p^{infty}}$‎. ‎Consequently‎, ‎we show that if $R$ is a right duo (or‎, ‎a right‎ ‎Noetherian) ring‎, ‎then the Noetherian dimension of an Artinian‎ ‎module with homogeneous uniserial dim...

There are well-known characterizations of the hereditary quotient maps in the category of topological spaces, (that is, of quotient maps stable under pullback along embeddings), as well as of universal quotient maps (that is, of quotient maps stable under pullback). These are precisely the so-called pseudo-open maps, as shown by Arhangel’skii, and the bi-quotient maps of Michael, as shown by Da...

For self-orthogonal modules T , the quotient triangulated categories D(A)/K(addT ) are studied, in particular, their relations with the stable categories of some Frobenius categories are investigated. New descriptions of the singularity categories of Gorenstein algebras are obtained; and the derived categories of Gorenstein algebras are explicitly given, inside the stable categories of the grad...

Individuals with autism spectrum disorder (ASD) often have difficulty coordinated fine motor skills, but the degree of significantly varies from person to person. To elucidate cause this diversity, we monitored brain activity during movement tasks (tying bowknots) by near-infrared spectroscopy in 17 adults ASD and 18 typical development matched for age, gender, intelligence quotient (IQ). We al...

We explicitly describe the length minimizing geodesics for a sub-Riemannian structure of elliptic type defined on SL (2, ℝ). Our method uses symmetry reduction which translates problem into Riemannian two dimensional quotient space, projections can be easily visualized. As byproduct, we obtain an alternative derivation characterization cut-locus. use classification results three right invariant...

We show that every finite semigroup is a quotient of a finite semigroup in which every right stabilizer satisfies the identities x = x and xy = xyx. This result has several consequences. We first use it together with a result of I. Simon on congruences on paths to obtain a purely algebraic proof of a deep theorem of McNaughton on infinite words. Next, we give an algebraic proof of a theorem of ...