A family of (n−1)! Diagonal polynomial orders ofN n

Letn>0 be an element of the setN of nonnegative integers, and lets(x)=x ₁+...+x _n , forx=(x ₁, ...,x _n ) N _n . Adiagonal polynomial order inN _n is a bijective polynomialp:N _n N (with real coefficients) such that, for allx,y N _n ,p(x)<p(y) whenevers(x)<s(y). Two diagonal polynomial orders areequivalent if a relabeling of variables makes them identical. For eachn, Skolem (1937) found a diagonal polynomial order. Later, Morales and Lew (1992) generalized this polynomial order, obtaining a family of 2 ^n–2 (n>1) inequivalent diagonal polynomial orders. Here we present, for eachn>0, a family of (n – 1)! diagonal polynomial orders, up to equivalence, which contains the Morales and Lew diagonal orders.     

Synthesis of 4-aryl-2,3,6,7-tetrahydro-1H-pyrimido[4,5-b][1,4]-diazepin-6-ones from 4,5-diamino-1H-pyrimidin-6-ones and 1-aryl-3-(dimethylamino)-1-propanones

The reaction of 1-aryl-3-(dimethylamino)-1-propanones 1 with one equivalent of 4,5-diamino-1H-pyrimidin-6-ones 2 , in acidic medium, leads to the formation of 4-aryl-2,3,6,7-tetrahydro-1H-pyrimido[4,5-b]-[1,4]diazepin-6-ones 3 . The structure elucidation of the products is based on detail nmr analysis of experiments such as ¹³C, ¹H and DEPT including selective ¹³C{¹H} decoupling experiments.     

Charge heterogeneity of recombinant pro-urokinase and urinary urokinase, as revealed by isoelectric focusing in immobilized pH gradients

When analysing homogeneous preparations of recombinant pro-urokinase and urinary urokinase by isoelectric focusing (IEF) in immobilized pH gradients, an extreme charge heterogeneity was detected (at least ten major and ten minor bands in the pH range 7–10). This extensive polydispersity was not caused by different degrees of glycosylation, or by IEF artefacts, such as binding to carrier ampholytes or carbamylation by urea. A great part of this heterogeneity could be traced back to the existence of a multitude of protein molecules containing Cys residues at different oxidation levels (-SH, -S-S-, even cysteic acid). Owing to the very large number of Cys residues in pro-urokinase (24 out of a total of 411 amino acids) and to the relatively high pI of its native forms (pI 9.5–9.8; the native form is believed to contain all Cys residues as -S-S- bridges), the presence of SH or cysteic acid residues would increase the negative surface charge, as even SH groups would be extensively ionized. In pro-urokinase, part of the heterogeneity was also due to spontaneous degradation to urokinase and possibly also to cleavage into lower-molecular-mass fragments. When all these causes of heterogeneity were removed, the pI spectrum was reduced to only four, about equally intense, bands. The cause of this residual heterogeneity is unknown.     

Some new tests for multivariate normality

Summary A family of statistics is presented that can be used for testing goodness of fit to a parametric family. These statistics include Mardia's measure of multivariate kurtosis and Moore and Stubblebine's test for multivariate normality. The asymptotic distribution of the statistics is found under mild hypotheses on the parametric family and, in the case of multivariate normality, the distribution is shown to be independent of the true parameter. A class of tests for multivariate normality is presented and the performance of two such tests in the bivariate case is found in simulations.The research of this author was carried out in part while at M.I.T. and then at Bell Communications ResearchThe research of this author was partially supported by National Science Foundation Grants     

A Robust Algorithm for Roots Selection and Saturation Pressure Calculation for Cubic Equations of State

Journal of Solution Chemistry - In this work, a robust and rigorous procedure for roots calculation and selection for a Cubic Equation of State is presented. Roundoff errors are detected and...     

Synthesis and Antifungal Activity of New Valine-Azole Hybrids

Russian Journal of General Chemistry - Herein, the synthesis of six new derivatives via molecular hybridization of imidazole or triazole and valine methyl ester as a rational design for accessing...     

On a class of generalised Schmidt groups

Annali di Matematica Pura ed Applicata (1923 -) - In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An $$A_5$$ -free group...     

Current Status of COVID-19 (Pre)Clinical Vaccine Development

The current COVID-19 pandemic has a tremendous impact on daily life world-wide. Despite the ability to dampen the spread of SARS-CoV-2, the causative agent of the diseases, through restrictive interventions, it is believed that only effective vaccines will provide sufficient control over the disease and revert societal live back to normal. At present, a double-digit number of efforts are devoted to the development of a vaccine against COVID-19. Here, we provide an overview of these (pre)clinical efforts and provide background information on the technologies behind these vaccines. In addition, we discuss potential hurdles that need to be addressed prior to mass scale clinical translation of successful vaccine candidates.     

Classical and metallocene catalytic systems: Comparison between the stereochemical mechanisms of α-olefin polymerization

Classical Ziegler-Natta and Kaminsky-Ewen catalysts promoting polymerization of hydrocarbon monomers are compared considering the reactivity and the stereochemical mechanisms of polymerization. It is suggested that also the “active sites” of heterogeneous catalysts could be cationic.