605 research outputs found
Self-Injective Jacobian Algebras from Postnikov Diagrams
No full textWe study a finite-dimensional algebra Lambda from a Postnikov diagram D in a disk, obtained from the dimer algebra of Baur-King-Marsh by factoring out the ideal generated by the boundary idempotent. Thus, Lambda is isomorphic to the stable endomorphism algebra of a cluster tilting module T is an element of CM(B) introduced by Jensen-King-Su in order to categorify the cluster algebra structure of C[Gr(k)(C-n)]. We show that Lambda is self-injective if and only if D has a certain rotational symmetry. In this case, Lambda is the Jacobian algebra of a self-injective quiver with potential, which implies that its truncated Jacobian algebras in the sense of Herschend-Iyama are 2-representation finite. We study cuts and mutations of such quivers with potential leading to some new 2-representation finite algebras.Title in Thesis List of papers: Self-injective algebras from Postnikov diagrams</p
Nonparametric study of the evolution of the cosmological equation of state with SNeIa, BAO, and high-redshift GRBs
No full textWe study the dark energy equation of state as a function of redshift in a nonparametric way, without imposing any a priori w (z) (ratio of pressure over energy density) functional form. As a check of the method, we test our scheme through the use of synthetic data sets produced from different input cosmological models that have the same relative errors and redshift distribution as the real data. Using the luminosity-time correlation for gamma-ray burst (GRB) X-ray afterglows (the Dainotti et al. correlation), we are able to utilize GRB samples from the Swift satellite as probes of the expansion history of the universe out to z 10. Within the assumption of a flat Friedmann-Lemaître-Robertson-Walker universe and combining supernovae type Ia (SNeIa) data with baryonic acoustic oscillation constraints, the resulting maximum likelihood solutions are close to a constant w = –1. If one imposes the restriction of a constant w , we obtain w = -0.99 0.06 (consistent with a cosmological constant) with the present-day Hubble constant as and density parameter as , while nonparametric w (z) solutions give us a probability map that is centered at and . Our chosen GRB data sample with a full correlation matrix allows us to estimate the amount, as well as quality (errors), of data needed to constrain w (z) in the redshift range extending an order of magnitude beyond the farthest SNeIa measured
Proof of a conjecture of Bergeron, Ceballos and Labbé
No full text© 2017, University at Albany. All rights reserved. The reduced expressions for a given element w of a Coxeter group (W, S) can be regarded as the vertices of a directed graph R(w); its arcs correspond to the braid moves. Specifically, an arc goes from a reduced expression a to a reduced expression b when b is obtained from a by replacing a contiguous subword of the form stst … (for some distinct s,t ∈ S) by tsts … (where both subwords have length m s,t , the order of st ∈ W). We prove a strong bipartiteness-type result for this graph R(w): Not only does every cycle of R(w) have even length; actually, the arcs of R(w) can be colored (with colors corresponding to the type of braid moves used), and to every color c corresponds an “opposite” color c op (corresponding to the reverses of the braid moves with color c), and for any color c, the number of arcs in any given cycle of R(w) having color in {c, c op } is even. This is a generalization and strengthening of a 2014 result by Bergeron, Ceballos and Labbé
Anick's conjecture for spaces with decomposable Postnikov invariants
No full textAn elliptic space is one whose rational homotopy and rational cohomology are both finite dimensional. David Anick conjectured that any simply connected finite CW-complex S can be realized as the k-skeleton of some elliptic complex as long as k > dim S, or, equivalently, that any simply connected finite Postinkov piece S can be realized as the base of a fibration F-->E-->S where E is elliptic and F is k-connected, as long as the k is larger than the dimension of any homotopy class of S. This conjecture is only known in a few eases, and here we show that in particular if the Postnikov invariants of S are decomposable, then the Anick conjecture holds for S. We also relate this conjecture with other finiteness properties of rational spaces
Schur Times Schubert via the Fomin-Kirillov Algebra
No full textWe study multiplication of any Schubert polynomial S[subscript w] by a Schur polynomial sλ (the Schubert polynomial of a Grassmannian permutation) and the expansion of this product in the ring of Schubert polynomials. We derive explicit nonnegative combinatorial expressions for the expansion coefficients for certain special partitions λ, including hooks and the 2×2 box. We also prove combinatorially the existence of such nonnegative expansion when the Young diagram of λ is a hook plus a box at the (2,2) corner. We achieve this by evaluating Schubert polynomials at the Dunkl elements of the Fomin-Kirillov algebra and proving special cases of the nonnegativity conjecture of Fomin and Kirillov.
This approach works in the more general setup of the (small) quantum cohomology ring of the complex flag manifold and the corresponding (3-point) Gromov-Witten invariants. We provide an algebro-combinatorial proof of the nonnegativity of the Gromov-Witten invariants in these cases, and present combinatorial expressions for these coefficients.National Science Foundation (U.S.) (Grant DMS-6923772
From Bruhat intervals to intersection lattices and a conjecture of Postnikov
No full textWe prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w ∈ S n is at most the number of elements below w in the Bruhat order, and (B) that equality holds if and only if w avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups.</p
Heating internal channels of a catalyst carrier with periodic structure by impinging supersonic jet
No full textMOD-<i>C</i> Postnikov Approximation of a 1-Connected Space
No full textDeleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context [4]. They have also shown that if the set of morphisms is saturated then the Adams completion of an object is characterized by a certain couniversai property. We want to prove a stronger version of this result by dropping the saturation assumption on the set of morphisms; we also prove that the canonical map from an object to its Adams completion is an element of the set of morphisms under very moderate assumptions. These two results are fairly general in nature and are applicable to most cases of interest. Further using these two results and introducing “modulo a Serre class C of abelian groups” [9] we have obtained the mod-C Postnikov approximation of a 1-connected based CW-complex, with the help of a suitable set of morphisms.</jats:p
Rational S¹-equivariant homotopy theory
No full textWe give an algebraicization of rational S¹-equivariant homotopy theory. There is an algebraic category of “T-systems” which is equivalent to the homotopy category of rational S¹-simply connected S¹-spaces. There is also a theory of “minimal models” for T-systems, analogous to Sullivan’s minimal algebras. Each S¹-space has an associated minimal T-system which encodes all of its rational homotopy information, including its rational equivariant cohomology and Postnikov decomposition
Diaryliodonium Tetracyanidometallates Self-Assemble into Halogen-Bonded Square-Like Arrays
No full textTwo diphenyliodonium tetracyanidometallates, [Ph2I](2)[M(CN)(4)] (M = Ni and Pd), were prepared through anion metathesis. Their X-ray structural analyses show that the structure-defining contact for both crystals is the charge-assisted I center dot center dot center dot N halogen bond (HaB) formed between the I atom of the iodonium cations and the N atoms of the CN- ligands. These HaBs assemble the bidentate and 90 degrees-orienting HaB donor Ph2I+ and the tetradentate, square planar, and 90/180 degrees-orienting HaB acceptors [M(CN)(4)](2-) into supramolecular rectangles, which further assemble into infinite chains by sharing the vertexes occupied by the [M(CN)(4)](2-) anions. The noncovalent nature of these contacts was confirmed by density functional theory calculations (M06/def2-TZVP) followed by combined topological analysis of the electron density distribution in the quantum theory of the atoms-in-molecules approach and noncovalent interaction analysis. The philicities of the HaB partners were further verified by the analysis of electron localization function projections, electron density/electrostatic potential profiles along the I center dot center dot center dot N bond paths, natural bond orbital analysis, and the natural population analysis or atoms-in-molecules charge sums in model systems
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