Cyclic Codes over the Integers Modulop

The purpose of this paper is twofold. First, we generalize the results of Pless and Qian and those of Pless, Solé, and Qian for cyclic ₄-codes to cyclic _p^m-codes. Second, we establish connections between this new development and the results on cyclic _p^m-codes obtained by Calderbank and Sloane. We produce generators for the cyclic _p^m-codes which are analogs to those for cyclic ₄-codes. We show that these may be used to produce a single generator for such codes. In particular, this proves that the ringR_n= _p^m[x]/(xⁿ− 1) is principal, a result that had been previously announced with an incorrect proof. Generators for dual codes of cyclic _p^m-codes are produced from the generators of the corresponding cyclic _p^m-codes. In addition, we also obtain generators for the cyclicp^m-ary codes induced from the idempotent generators for cyclicp-ary codes.     

Quantum mechanical modeling of Zn-based spinel oxides: Assessing the structural,vibrational, and electronic properties

The structural, electronic, and vibrational properties of two leading representatives of the Zn-based spinel oxides class, normal ZnX₂O₄ (X = Al, Ga, In) and inverse Zn₂MO₄ (M = Si, Ge, Sn) crystals, were investigated. In particular, density functional theory (DFT) was combined with different exchange-correlation functionals: B3LYP, HSE06, PBE0, and PBESol. Our calculations showed good agreement with the available experimental data, showing a mean percentage error close to 3% for structural parameters. For the electronic structure, the obtained HSE06 band-gap values overcome previous theoretical results, exhibiting a mean percentage error smaller than 10.0%. In particular, the vibrational properties identify the significant differences between normal and inverse spinel configurations, offering compelling evidence of a structure-property relationship for the investigated materials. Therefore, the combined results confirm that the range-separated HSE06 hybrid functional performs the best in spinel oxides. Despite some points that cannot be directly compared to experimental results, we expect that future experimental work can confirm our predictions, thus opening a new avenue for understanding the structural, electronic, and vibrational properties in spinel oxides.     

Antibacterial activity of agave fructans against salmonella typhimurium

Abstract

The objective of this study was to evaluate the antimicrobial effect of Agave fructans against the Salmonella Typhimurium in “in vitro” experiments. The result of the antimicrobial activity was 263.89?±?0, 414.95?±?12.83, 494.54?±?13.88, 522.29?±?0, 580.41?±?14.92?AU for 10, 20, 30, 40 and 50% of Agave fructans (AF) respectively. In addition, there is a significant effect on the growth of the bacteria with all the percentages of AF evaluated (p?<?0.001, R2?=?0.859) with respect to the control. The growth rate of Salmonella with 25% AF was statistically significant compared to the control (?0.7353?±?0.586, 0.0079?±?0.002?D.O./h, respectively; p?>?0.01). Agave fructans could be an alternative to prevent the infections caused by Salmonella.     

Exchange interactions in BaFe12O19

In the scope of the mean field approximation the nine nearest neighbour exchange interactions existing among the ferric ions in BaFe₁₂O₁₉ hexagonal ferrite have been determined from the experimental sublattice magnetizations. It is shown that these exchange interactions are well explained by means of the superexchange theory. It is also concluded that some direct exchange interaction does exist among the octahedral 4f _VI ions. The calculated magnetization, paramagnetic susceptibility, and Curie temperature are in good agreement with the corresponding experimental values. The stability of the collinear Gorter-type magnetic structure of BaFe₁₂O₁₉ is discussed as well.     

Perturbation of resonances in quantum mechanics

Schrödinger operators on L²($\text{R}$³) of the form ?Δ + V_λ with potentials V_λ real-analytic in λ are discussed. The analytic structure in V_λ and k (with k² the energy variable) of the resolvent kernel, the eigenvalues and resonances is exhibited and we obtain in particular convergent perturbation expansions for the resonances and the corresponding resonance functions. The lower order expansion coefficients are computed explicitly. The resonances and the corresponding functions are also computed for a particle moving under the action of n point interactions. This gives asymptotic low energy information about Schrödinger Hamiltonians with short range potentials. The perturbation theory of resonances, eigenvalues and of the corresponding functions for Hamiltonians describing n point interactions perturbed by a potential is also given.     

On fractal properties of non-normal numbers with respect to Rényi f-expansions generated by piecewise linear functions

The paper is devoted to the study of fractal properties of subsets of the set of non-normal numbers with respect to Rényi f  -expansions generated by continuous increasing piecewise linear functions defined on [0,+∞)$[0,+\infty )$. All such expansions are expansions for real numbers generated by infinite linear IFS f={_f0,_f1,…,_fn,…}$f=\{f_0,f_1,\dots ,f_n,\dots \}$ with the following list of ratios _Q∞=(_q0,_q1,…,_qn,…)$Q_{\infty }=(q_0,q_1,\dots ,q_n,\dots )$.     

Stability properties of an inverse parabolic problem with unknown boundaries

We treat the stability issue for an inverse problem arising from non-destructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem. We obtain that when the unknown part of the boundary is a priori known to be smooth, the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed. Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given the exponential ill-posedness, the stability estimate obtained is optimal. AMS 2000 Mathematics Subject Classification. Primary 35R30, Secondary 35B60, 33C90     

New palladium (II) complexes containing phosphine‐nitrogen ligands and their use as catalysts in aminocarbonylation reaction

Aminocarbonylation of aryl halides, homogeneously catalysed by palladium, is an efficient method that can be employed for obtaining amides for pharmaceutical and synthetic applications. In this work, palladium (II) complexes containing P^N ligands were studied as catalysts in the aminocarbonylation of iodobenzene in the presence of diethylamine. Two types of systems were used: a palladium (II) complex formed in situ; and one prepared prior to the catalytic reaction. In general, the palladium complexes studied achieved high conversions in an average reaction time of less than 2 hr, which is less than that for the standard system (Pd (II)/PPh₃) used. The pre‐synthesized complexes were faster than their in situ counterparts, as the latter require an induction time to form the Pd/P^N species. The structure and electronic properties of the ligand P^N can influence both the activity and the selectivity of the reaction, stabilizing the acyl‐palladium intermediates formed in a better manner.     

Highly Enantioselective Construction of Tricyclic Derivatives by the Desymmetrization of Cyclohexadienones

The asymmetric synthesis of tricyclic compounds by the desymmetrization of cyclohexadienones is presented. The reaction tolerated a large variety of substituents at different positions of the cyclohexadienone, and heterocyclic rings of different sizes were accessible. Density functional theory calculations showed that the reaction proceeds through an asynchronous [4+2] cycloaddition.     

Synthesis,Characterization and Photocleavage of Bis-decyl Pteroic Acid: A Folate Derivative with Affinity to Biomembranes†

Here, we provide mechanistic insight to the photocleavage of a compound in the folate family, namely pteroic acid. A bis-decyl chain derivative of pteroic acid was synthesized, structurally characterized and photochemically investigated. We showed that, like folic acid, pteroic acid and the decylated derivative undergo a photocleavage reaction in the presence of H₂O, while no reaction was observed in methanol solution. Furthermore, density functional theory calculations were carried out to predict relative stabilities of hypothetical mono-, bis- and tris-decylated pteroic acid derivatives to help rationalize the regioselectivity of the bis-decyl pteroic acid product. Additionally, the lipophilicity of the bis-decyl pteroic acid appears to confer a hydrophobic property enabling an interaction with biomembranes.