DFT study of the effect of substituents on the absorption and emission spectra of Indigo

ABSTRACT: BACKGROUND: Theoretical analyses of the indigo dye molecule and its derivatives with Chlorine (Cl), Sulfur (S), Selenium (Se) and Bromine (Br) substituents, as well as an analysis of the Hemi-Indigo molecule, were performed using the Gaussian 03 software package. RESULTS: Calculations were performed based on the framework of density functional theory (DFT) with the Becke 3- parameter-Lee-Yang-Parr (B3LYP) functional, where the 6-31 G(d,p) basis set was employed. The configuration interaction singles (CIS) method with the same basis set was employed for the analysis of excited states and for the acquisition of the emission spectra. CONCLUSIONS: The presented absorption and emission spectra were affected by the substitution position. When a hydrogen atom of the molecule was substituted by Cl or Br, practically no change in the absorbed and emitted energies relative to those of the indigo molecule were observed; however, when N was substituted by S or Se, the absorbed and emitted energies increased.     

Law of the iterated logarithm for random graphs

A milestone in probability theory is the law of the iterated logarithm (LIL), proved by Khinchin and independently by Kolmogorov in the 1920s, which asserts that for iid random variables with mean 0 and variance 1 In this paper we prove that LIL holds for various functionals of random graphs and hypergraphs models. We first prove LIL for the number of copies of a fixed subgraph H. Two harder results concern the number of global objects: perfect matchings and Hamiltonian cycles. The main new ingredient in these results is a large deviation bound, which may be of independent interest. For random k‐uniform hypergraphs, we obtain the Central Limit Theorem and LIL for the number of Hamilton cycles.     

The Lp dual Minkowski problem for p > 1 and q > 0

General $L_p$ dual curvature measures have recently been introduced by Lutwak, Yang and Zhang [24]. These new measures unify several other geometric measures of the Brunn–Minkowski theory and the dual Brunn–Minkowski theory. $L_p$ dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the $L_p$ dual Minkowski problem, which concerns the characterization of $L_p$ dual curvature measures. In this paper, we solve the existence part of the $L_p$ dual Minkowski problem for $p>1$ and $q>0$, and we also discuss the regularity of the solution.     

Universal deformation rings and self-injective Nakayama algebras

Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring $R(\mathrm{\Lambda },V)$ and we describe $R(\mathrm{\Lambda },V)$ explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups.     

On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

On percolation and ‐hardness

The edge‐percolation and vertex‐percolation random graph models start with an arbitrary graph G, and randomly delete edges or vertices of G with some fixed probability. We study the computational complexity of problems whose inputs are obtained by applying percolation to worst‐case instances. Specifically, we show that a number of classical ‐hard problems on graphs remain essentially as hard on percolated instances as they are in the worst‐case (assuming ). We also prove hardness results for other ‐hard problems such as Constraint Satisfaction Problems and Subset‐Sum, with suitable definitions of random deletions. Along the way, we establish that for any given graph G the independence number and the chromatic number are robust to percolation in the following sense. Given a graph G, let be the graph obtained by randomly deleting edges of G with some probability . We show that if is small, then remains small with probability at least 0.99. Similarly, we show that if is large, then remains large with probability at least 0.99. We believe these results are of independent interest.     

Composition of sulfated glycosaminoglycans and immunodistribution of chondroitin sulfate in deeply infiltrating endometriosis affecting the rectosigmoid

The composition of sulfated glycosaminoglycans (GAGs) and the tissue distribution of chondroitin sulfate (CS) were analyzed in deeply infiltrating endometriosis (DIE) of rectosigmoid, using metachromatic staining, and biochemical analysis employing electrophoresis before and after specific enzymatic or chemical degradations, and immunostaining with an antibody against CS. The sulfated GAGs were characterized as dermatan sulfate (DS), heparan sulfate (HS) and CS; and DS strongly predominated compared to HS and CS. Immunostaining procedures showed that CS was concentrated in the endometriosis foci, distributed throughout the stroma around the glands. This is the first report describing the composition of sulfated GAGs and the tissue location of CS in DIE by means of histochemical, biochemical and immunohistochemical analyses. These results confirmed that in DIE of rectosigmoid, as in eutopic endometrium [Nasciutti, L.E., Ferrari, R., Berardo, P.T., Souza, M.L.S., Takiya, C.M., Borojevic, R., Abrao, M.S., Silva, L.C.F., 2006. Distribution of chondroitin sulfate in human endometrium. Micron 37, 544–550], CS was the dominant sulfated GAG in stroma of the lesion foci.     

Non-quadratic defect energy: A comparison of gradient plasticity simulations to discrete dislocation dynamics results

A small-deformation strain gradient plasticity (GP) model for single-crystals has been proposed in [1], including a grain boundary (GB) yield condition without hardening. It has been extended by a hardening term for the GBs after a comparison to discrete dislocation dynamics (DDD) results in [2]. Differences between the strain gradients of the GP results and the DDD results motivate the consideration of a non-quadratic defect energy [3] in the GP model. It is shown that the gradients in the GP model can be improved using an exponent different from two. Remaining discrepancies in the strain profiles, compared to the DDD results, are attributed to the neglect of the individual gradients of plastic slip and due to the lack of a mechanism for the misorientation-dependent elastic interactions of dislocations across GBs [4] in the GP model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)