Hydrogen bonding interactions between α-, β-glucose,and methacrylic acid

Intermolecular interactions between α-, β-glucose, and methacrylic acid (MAA) have been investigated. Twenty-two possible conformations have been optimized at the DFT(B3LYP) level of theory with the 6-31G(d) basis set. The geometrical parameters for the most stable configurations of hydrogen bonding sites in the optimized systems have been determined. The binding energies ΔE _bind have been calculated at the MP2/6-311++G(d,p) level of approximation taking into account the basis set superposition error (BSSE) and the zero-point vibrational energies corrections. Results indicate that the most stabilized complexes form hydrogen bonds either through carboxylic and hemiacetal oxygen atoms acting as proton acceptors. Both, α- and β-anomers are studied in the pyranose six-membered ring. In all complexes, the nuclear quadrupole coupling constants (χ) for ¹⁷O nuclei were obtained about 10.0 MHz, while for the ²H atoms they vary from ≈200.0 to ≈350.0 kHz.     

Scalar field dynamics in a BTZ background with generic boundary conditions

We revisit the dynamics of a massive scalar field in a Banados, Teitelboim, and Zanelli background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window \(-3/4\le m_e^2\ell ^2<0\) can be well defined within a one-parametric family of distinct boundary conditions (\(-3/4\) being the conformally coupled case), while for \(m_e^2\ell ^2\ge 0\) the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for \(m_e^2\ell ^2<-1\), and also it is shown that in the range \(m_e^2\ell ^2 \in [-1,-3/4)\) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved.     

Structure correlation of silylated dicarboxylic acid monomer and its respective oligomeric polyamide-imide using experimental and theoretical vibrational spectra

Correlation between theoretical and experimental (infrared and Raman spectroscopies) vibrational spectra of two compounds, both with a silyl group present in their main chain and with an optically active structure (L-valine) as side group, was performed. These compounds are based in a chiral dicarboxylic acid monomer and its respective polyamide-imide, oligomer that was previously synthesized by a direct polycondensation. Spectra were recorded in the region comprised between 500 and 4000?cm^?1 for infrared and Raman analysis. The Raman spectra were obtained through a 1064?nm laser as excitation source.

Theoretical models were carried out in order to find the optimal molecular geometry of the analyzed systems, with a complete assignment of their vibrational spectra. The Raman experimental data obtained with a Nd:YAG laser for this kind of silylated organic compounds, and the comparison between these results with the theoretical data is a useful advance in the polymer synthesis field, which can be used as reference for subsequent studies.     

Super-exponential inflation from a dynamical foliation of a 5D vacuum state

We introduce super-exponential inflation (ω<−1) from a 5D Riemann-flat canonical metric on which we make a dynamical foliation. The resulting metric describes a super accelerated expansion for the early universe well known as super-exponential inflation that, for very large times, tends to an asymptotic de Sitter (vacuum dominated) expansion. The scalar field fluctuations are analyzed. The important result here obtained is that the spectral index for energy density fluctuations is not scale invariant, and for cosmological scales becomes ns(k<k_?)?1. However, for astrophysical scales this spectrum changes to negative values ns(k>k_?)<0.     

An approach to the synthesis of furanoheliangolides through Diels-Alder reactions

The core structure of the natural sesquiterpene lactones furanoheliangolides, an 11-oxabicyclo[6.2.1]undecane system, was synthesized through a pathway involving two Diels-Alder reactions.     

A Lower Bound for the Determinantal Complexity of a Hypersurface

We prove that the determinantal complexity of a hypersurface of degree \(d > 2\) is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least 5. As a result, we obtain that the determinantal complexity of the \(3 \times 3\) permanent is 7. We also prove that for \(n> 3\), there is no nonsingular hypersurface in \({\mathbb {P}}^n\) of degree d that has an expression as a determinant of a \(d \times d\) matrix of linear forms, while on the other hand for \(n \le 3\), a general determinantal expression is nonsingular. Finally, we answer a question of Ressayre by showing that the determinantal complexity of the unique (singular) cubic surface containing a single line is 5.     

GRASP with hybrid heuristic-subproblem optimization for the multi-level capacitated minimum spanning tree problem

We propose a GRASP using an hybrid heuristic-subproblem optimization approach for the Multi-Level Capacitated Minimum Spanning Tree (MLCMST) problem. The motivation behind such approach is that to evaluate moves rearranging the configuration of a subset of nodes may require to solve a smaller-sized MLCMST instance. We thus use heuristic rules to define, in both the construction and the local search phases, subproblems which are in turn solved exactly by employing an integer programming model. We report numerical results obtained on benchmark instances from the literature, showing the approach to be competitive in terms of solution quality. The proposed GRASP have in fact improved the best known upper bounds for almost all of the considered instances.     

A relax-and-cut algorithm for the prize-collecting Steiner problem in graphs

Given an undirected graph G with penalties associated with its vertices and costs associated with its edges, a Prize Collecting Steiner (PCS) tree is either an isolated vertex of G or else any tree of G, be it spanning or not. The weight of a PCS tree equals the sum of the costs for its edges plus the sum of the penalties for the vertices of G not spanned by the PCS tree. Accordingly, the Prize Collecting Steiner Problem in Graphs (PCSPG) is to find a PCS tree with the lowest weight. In this paper, after reformulating and re-interpreting a given PCSPG formulation, we use a Lagrangian Non Delayed Relax and Cut (NDRC) algorithm to generate primal and dual bounds to the problem. The algorithm is capable of adequately dealing with the exponentially many candidate inequalities to dualize. It incorporates ingredients such as a new PCSPG reduction test, an effective Lagrangian heuristic and a modification in the NDRC framework that allows duality gaps to be further reduced. The Lagrangian heuristic suggested here dominates their PCSPG counterparts in the literature. The NDRC PCSPG lower bounds, most of the time, nearly matched the corresponding Linear Programming relaxation bounds.     

Cluster Partition Function and Invariants of 3-Manifolds

The author reviews some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G.The author focuses on the case of G =SL(N,C) and M being a knot complement:M =S3 \ k.The main result presented in this note is the cluster partition function,a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral for G =SL(N,C).He also reviews various applications and open questions regarding the cluster partition function and some of its relation with string theory.