Some algebraic aspects of mesoprimary decomposition

Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing “mesoprimary decompositions” determined by their underlying monoid congruences. Monoid congruences (and therefore, binomial ideals) can present many subtle behaviors that must be carefully accounted for in order to produce general results, and this makes the theory complicated. In this paper, we examine their results in the presence of a positive A-grading, where certain pathologies are avoided and the theory becomes more accessible. Our approach is algebraic: while key notions for mesoprimary decomposition are developed first from a combinatorial point of view, here we state definitions and results in algebraic terms, which are moreover significantly simplified due to our (slightly) restricted setting. In the case of toral components (which are well-behaved with respect to the A-grading), we are able to obtain further simplifications under additional assumptions. We also provide counterexamples to two open questions, identifying (i) a binomial ideal whose hull is not binomial, answering a question of Eisenbud and Sturmfels, and (ii) a binomial ideal I for which $I_{\mathrm{toral}}$ is not binomial, answering a question of Dickenstein, Miller and the first author.     

Formulation of Topical Dosage Forms Containing Synthetic and Natural Anti-Inflammatory Agents for the Treatment of Rheumatoid Arthritis

Topical anti-inflammatory and analgesic effect for the treatment of rheumatoid arthritis is of major interest because of their fewer side effects compared to oral therapy. The purpose of this study was to prepare different types of topical formulations (ointments and gels) containing synthetic and natural anti-inflammatory agents with different excipients (e.g.,: surfactants, gel-forming) for the treatment of rheumatoid arthritis. The combination of Non-Steroidal Anti-Inflammatory Drugs (NSAIDs), diclofenac sodium, a topical analgesic agent methyl salicylate, and a lyophilized extract of Calendula officinalis with antioxidant effect were used in our formulations. The aim was to select the appropriate excipients and dosage form for the formulation in order to enhance the diffusion of active substances and to certify the antioxidant, analgesic, and anti-inflammatory effects of these formulations. To characterize the physicochemical properties of the formulations, rheological studies, and texture profile analysis were carried out. Membrane diffusion and permeability studies were performed with Franz-diffusion method. The therapeutic properties of the formulations have been proven by an antioxidant assay and a randomized prospective study that was carried out on 115 patients with rheumatoid arthritis. The results showed that the treatment with the gel containing diclofenac sodium, methyl salicylate, and lyophilized Calendula officinalis as active ingredients, 2-propenoic acid homopolymer (Synthalen K) as gel-forming excipient, distilled water, triethanolamine, and glycerol had a beneficial analgesic and local anti-inflammatory effect.     

Rational design of a new one-step purification strategy for Candida antarctica lipase B by ion-exchange chromatography

A fast and efficient one-step method for purification of lipase B from Candida antarctica by ion-exchange chromatography was developed by rational design. The electrostatic properties of the enzyme were calculated and validated by isoelectric focusing and measurement of the titration curve. C. antarctica lipase B shows an unusual pH profile with a broad isoelectric region from pH 4 to 8. At pH 3 C. antarctica lipase B can be bound to a cation-exchange chromatography column and was purified to homogeneity with a purification factor of 2.4. It was stable at pH 3, the residual activity was still 80% after 6 days incubation at 20 degrees C. The broad isoelectric region of C. antarctica lipase B is unique as compared to almost all other alpha/beta-hydrolases which have a well-defined isoelectric point. A search in the lipase engineering database resulted in only one further alpha/beta-hydrolase, the Fusarium solani cutinase, which also has a broad isoelectric region.     

Improved Preparation of β‐d‐ManNAc‐(1→4)‐d‐Glc and β‐d‐TalNAc‐(1→4)‐d‐Glc Disaccharides and Evaluation of Their Activating Properties on the Natural Killer Cells NKR‐P1 and CD69 Receptors

This article has been retracted.     

Toward the quantification of the 13CO2/12CO2 ratio in exhaled mouse breath with mid-infrared hollow waveguide gas sensors

Mouse sepsis models are used to gain insight into the complex processes involved with patients suffering from glucose metabolism disorders. Measuring the expiratory release of ¹³CO₂ after administering stable labeled ¹³C₆-glucose enables assessment of the in vivo integrity and functionality of key metabolic processes. In the present study, we demonstrate that Fourier transform infrared spectroscopy operating in the mid-infrared spectral regime (2–20 μm) combined with hollow waveguide gas sensing modules simultaneously serving as a miniaturized gas cell and as a waveguide are capable of quantitatively monitoring ¹³CO₂ enrichment levels in low volume mouse breath samples.     

A new method for the synthesis of carba-sugar enones (gabosines) using a mercury(II)-mediated opening of 4,5-cyclopropanated pyranosides as the key-step

The stereoselective transformation of the cyclopropyl derivative 2, stereoselectively obtained with the Simmons-Smith reaction of methyl 2,6-di-O-benzyl-α-l-threo-hex-4-enopyranoside (1), into gabosines and deoxy-carbahexoses is described. The treatment of 2 with mercuric trifluoroacetate in dry methanol gives the organomercuric chloride 3, which by demercuration with lithium aluminum hydride affords the 4-C-deoxy-4-methyl-1,5-bis-glycoside 4. The acid hydrolysis of 4 produces a mixture of the two diastereoisomeric 2-methyl-cyclohex-2-enones 6 and 7, catalytically reduced to carba-sugars 10 and 11. Structures and stereochemistry of all isolated compounds were determined by 1D and 2D NMR experiments.     

A viscosity iterative technique for split variational inclusion and fixed point problems between a Hilbert space and a Banach space

The main purpose of this paper is to introduce a viscosity-type iterative algorithm for approximating a common solution of a split variational inclusion problem and a fixed point problem. Using our algorithm, we state and prove a strong convergence theorem for approximating a common solution of a split variational inclusion problem and a fixed point problem for a multivalued quasi-nonexpansive mapping between a Hilbert space and a Banach space. Furthermore, we applied our results to study a split convex minimization problem. Also, a numerical example of our result is given. Our results extend and improve the results of Byrne et al. (J. Nonlinear Convex Anal. 13, 759–775, 2012), Moudafi (J. Optim. Theory Appl. 150, 275–283, 2011), Takahashi and Yao (Fixed Point Theory Appl. 2015, 87, 2015), and a host of other important results in this direction.     

A variational perturbation treatment of the hydrogen molecular ion using the green function method on the united atom

We calculated the second-order perturbed energy and the first-order perturbed wave function of the hydrogen molecular ion by the Green function method based on a united atom with effective nuclear charge, Z. Since the perturbation is given by (Z/r) — (1/r_A) — (1/r_B), its magnitude depends on the parameter Z. We obtain an analytical expression for the second-order perturbed energy as a function of Z and the internuclear distance R. We discuss a variety of methods to determine the best values for Z and to derive the potential energy curve and the force constant for H; these methods vary in the accuracy of their results.     

Carbon-carbon bond activation of R-CN (R = Me, Ar, iPr, tBu) using a cationic Rh(III) complex

Addition of 1.0 equiv of Ph3SiH to [Cp*(PMe3)Rh(Me)(CH2Cl2)]+BAr'4- (1) resulted in release of methane and quantitative formation of [Cp*(PMe3)Rh(SiPh3)(CH2Cl2)]+BAr'4- (2). Subsequent addition of 1.0 equiv of MeCN to 2 caused immediate displacement of dichloromethane to form the eta1-nitrile adduct [Cp*(PMe3)Rh(SiPh3)(NCMe)]+BAr'4- (3). Upon standing at room-temperature overnight, complex 3 converted quantitatively to another product which has been characterized as the C-C activation product, [Cp*(PMe3)Rh(Me)(CNSiPh3)]+BAr'4- (5). Addition of other nitrile substrates (R-CN, R = Ph, (4-CF3)Ph, (4-MeO)Ph, iPr, tBu) to 2 also resulted in C-C activation of the R-CN bond to form [Cp*(PMe3)Rh(R)(CNSiPh3)]+BAr'4-. Evidence for an eta2-iminoacyl intermediate complex, [Cp*(PMe3)Rh(eta2-C(R)=N(SiPh3)]+BAr'4-, is also presented.