How algebra spoiled recreational problems: A case study in the cross-cultural dissemination of mathematics

This paper deals with a sub-class of recreational problems which are solved by a simple memorized rule resulting from an elementary arithmetical or algebraic solution, called proto-algebraic rules. Their recreational aspect is derived from a surprise or trick solution which is not immediately obvious to the subjects involved. Around 1560 many such problems wane from arithmetic and algebra textbooks to reappear in the eighteenth century. Several hypotheses are investigated why popular Renaissance recreational problems lost their appeal. We arrive at the conclusion that the emergence of algebra as a general problem solving method changed the scope of what is considered recreational in mathematics.     

Development and validation of a simple solid‐phase extraction method coupled with liquid chromatography–triple quadrupole tandem mass spectrometry for simultaneous determination of lincomycin,tylosin A and tylosin B in royal jelly

We have developed an analytical method for the determination of lincomycin, tylosin A and tylosin B residues in royal jelly using liquid chromatography–triple quadrupole tandem mass spectrometry analysis. For extraction and purification, we employed 1% trifluoroacetic acid and 0.1 m Na₂EDTA solutions along with an Oasis HLB cartridge. The target antibiotics were well separated in a Kinetex EVO C₁₈ reversed‐phase analytical column using a combination of 0.1% formate acid in ultrapure water (A) and acetonitrile (B) as the mobile phase. Good linearity was achieved over the tested concentration range (5–50 μg/kg) in matrix‐matched standard calibration. The coefficients of determination (R²) were 0.9933, 0.9933 and 0.996, for tylosin A, tylosin B and lincomycin, respectively. Fortified royal jelly spiked with three different concentrations of the tested antibiotics (5, 10 and 20 μg/kg) yielded recoveries in the range 80.94–109.26% with relative standard deviations ≤4%. The proposed method was applied to monitor 11 brand of royal jelly collected from domestic markets and an imported brand from New Zealand; all the samples tested negative for lincomycin, tylosin A and tylosin B residues. In conclusion, 1% trifluoroacetic acid and 0.1 m Na₂EDTA aqueous solvents combined with solid‐phase extraction could effectively complete the sample preparation process for royal jelly before analysis. The developed approach can be applied for a routine analysis of lincomycin, tylosin A and tylosin B residues in royal jelly.     

Atomistic insights into the selective therapeutic activity of 6-(2,4-difluorophenoxy)-5-((ethylmethyl)pyridine-3-yl)-8-methylpyrrolo[1,2-a]pyrazin-1(2H)-one towards bromodomain-containing proteins

Cross-target effect has been one of the major mechanisms of drug toxicity, this has necessitated the design of inhibitors that are specifically tailored to target particular biomolecules. 6-(2,4-difluorophenoxy)-5-((ethylmethyl)pyridine-3-yl)-8-methylpyrrolo[1,2-a] pyrazin-1(2H)-one (Cpd38) is an inhibitor possessing high inhibition rate and tailored specificity towards bromodomain-containing protein 4 (BRD4). In this research, we used an array of computational techniques to provide insight at the atomistic level the specific targeting of BRD4 by Cpd38 relative to the binding of Cpd38 with E1A binding protein P300 (EP300); another bromodomain-containing protein (BCP). Comparatively, binding of Cpd38 improved the conformational stability and compactness of BRD4 protein when compared to the Cpd38 bound EP300. Also, Cpd38 induced a conformational change in the active site of BRD4 that facilitated a complementary pose between Cpd38 and BRD4 suitable for effective atomistic interactions. Expectedly, thermodynamic calculations revealed that the Cpd38-BRD4 system had higher binding energy (−36.11 Kcal/mol) than the Cpd38-EP300 system with a free binding energy of −15.86 Kcal/mol. Noteworthy is the opposing role Trp81 (acting as hydrogen bond acceptor) and Pro1074 (acting as hydrogen bond donor) found on the WPF and LPF loops respectively play in maintaining Cpd38 stability. Furthermore, the hydrogen bond acceptor/donator ratio was approximately 4:1 in Cpd38-BRD4 system compared with 2:1 in Cpd38-EP300 system. Taken together, atomistic insights and structural perspectives detailed in this report supplements the experimental report supporting the improved selectivity of Cpd38 for BRD4 ahead of other BCPs while providing leeway for the future design of BET selective agents with better pharmacological profile.     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

Medicinal Potential of Isoflavonoids: Polyphenols That May Cure Diabetes

In recent years, there is emerging evidence that isoflavonoids, either dietary or obtained from traditional medicinal plants, could play an important role as a supplementary drug in the management of type 2 diabetes mellitus (T2DM) due to their reported pronounced biological effects in relation to multiple metabolic factors associated with diabetes. Hence, in this regard, we have comprehensively reviewed the potential biological effects of isoflavonoids, particularly biochanin A, genistein, daidzein, glycitein, and formononetin on metabolic disorders and long-term complications induced by T2DM in order to understand whether they can be future candidates as a safe antidiabetic agent. Based on in-depth in vitro and in vivo studies evaluations, isoflavonoids have been found to activate gene expression through the stimulation of peroxisome proliferator-activated receptors (PPARs) (α, γ), modulate carbohydrate metabolism, regulate hyperglycemia, induce dyslipidemia, lessen insulin resistance, and modify adipocyte differentiation and tissue metabolism. Moreover, these natural compounds have also been found to attenuate oxidative stress through the oxidative signaling process and inflammatory mechanism. Hence, isoflavonoids have been envisioned to be able to prevent and slow down the progression of long-term diabetes complications including cardiovascular disease, nephropathy, neuropathy, and retinopathy. Further thoroughgoing investigations in human clinical studies are strongly recommended to obtain the optimum and specific dose and regimen required for supplementation with isoflavonoids and derivatives in diabetic patients.     

A bound on the Wasserstein-2 distance between linear combinations of independent random variables

We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ${?}^2\left({\mathbb{N}}^1\right)$. We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.     

A rapid and sensitive UHPLC–MS/MS method for the determination of celosin A in rat plasma with application to pharmacokinetic study

Celosin A (CA), a natural compound isolated from Celosia argentea L., has been shown significant hepatoprotective effect on AHNP‐induced liver injury. This study described a rapid and sensitive ultra‐high‐pressure liquid chromatography–tandem mass spectrometry (UHPLC–MS/MS) assay for determination of CA in rat plasma. Methanol‐mediated precipitation was used for sample pretreatment. Chromatographic separation was achieved on a T3 column with gradient elution using water and acetonitrile as mobile phase. Determination was obtained using an electrospray ionization source in negative selected reaction monitoring mode at the transitions of m/z 793.3 → m/z 661.2 and m/z 955.6 → m/z 793.2 for CA and IS, respectively. The assay was linear over the concentration range 0.25–2500 ng/mL (r > 0.995) with a lowest limit of quantification (LLOQ) of 0.25 ng/mL. The intra‐ and inter‐day precisions (RSD) were 1.65–9.84 and 2.46–13.49%, respectively, while accuracy (RR) ranged from 96.21 to 99.45%, respectively. The recovery ranged from 95.09 to 102.22% and the matrix effect from 98.29 to 100.13%. The analyte was stable under the tested storage conditions. The method has been successfully applied to a preclinical pharmacokinetic study in rats after a single intravenous (2 mg/kg) or oral (50 mg/kg) administration. The oral bioavailability of CA was ~1.94%; in addition, there was no difference between male and female rats. This is the first time of the use of an UHPLC–MS/MS method for determination of CA concentration in rat plasma and for evaluation of its pharmacokinetic behavior.     

On images of locally finite derivations and E-derivations

Some cases of the LFED Conjecture, proposed by the second author [15], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions $k(x)$ of the polynomial algebra $k[x]$, the formal power series algebra $k[[x]]$ and the Laurent formal power series algebra $k[[x]][x^{?1}]$, where $x=(x_1,x_2,\dots ,x_n)$ denotes n commutative free variables and k a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat–van der Kallen Theorem [3] is also discussed and emphasized.