On generalized square-full numbers in an arithmetic progression

Czechoslovak Mathematical Journal - Let a and $$b \in \mathbb{N}$$ . Denote by Ra,b the set of all integers n > 1 whose canonical prime representation $$n = p_1^{{\alpha _1}}p_2^{{\alpha...     

Synthesis,Biological Evaluation,and In Silico Studies of New Acetylcholinesterase Inhibitors Based on Quinoxaline Scaffold

A quinoxaline scaffold exhibits various bioactivities in pharmacotherapeutic interests. In this research, twelve quinoxaline derivatives were synthesized and evaluated as new acetylcholinesterase inhibitors. We found all compounds showed potent inhibitory activity against acetylcholinesterase (AChE) with IC₅₀ values of 0.077 to 50.080 µM, along with promising predicted drug-likeness and blood–brain barrier (BBB) permeation. In addition, potent butyrylcholinesterase (BChE) inhibitory activity with IC₅₀ values of 14.91 to 60.95 µM was observed in some compounds. Enzyme kinetic study revealed the most potent compound (6c) as a mixed-type AChE inhibitor. No cytotoxicity from the quinoxaline derivatives was noticed in the human neuroblastoma cell line (SHSY5Y). In silico study suggested the compounds preferred the peripheral anionic site (PAS) to the catalytic anionic site (CAS), which was different from AChE inhibitors (tacrine and galanthamine). We had proposed the molecular design guided for quinoxaline derivatives targeting the PAS site. Therefore, the quinoxaline derivatives could offer the lead for the newly developed candidate as potential acetylcholinesterase inhibitors.     

The Mean-value of Meromorphic Functions with Respect to a Generalized Boolean Transformation

A formula for the mean-value distribution of certain meromorphic functions on a vertical line s = σ +iR under a generalized Boolean transformation, called rational Boolean transformation from R into itself, is derived using Birkhoff 's ergodic theorem. This formula is represented as a computable integral. Using the Cauchy's integral theorem, values of this integral corresponding to various possible cases are explicitly computed.     

Three dimensional microvascular measurements in human endometrium using optical slices from laser scanning confocal microscopy (LSCM)

There is increasing interest in the structure of the microvascular environment in human endometrium because of the recognition of the complexity and functional importance of this tissue. Endometrial microcirculatory networks and their relationships have rarely been studied in three-dimensions.Longitudinal uterine slices containing endometrial tissue were carefully selected from women undergoing a hysterectomy. Formalin-fixed endometrial sections (≤50 μm) representing the fundal and isthmic regions were immunofluorescently labeled with monoclonal antibody (CD34) to target the endothelium of microvessel and fluorescein isothiocyanate (FITC) labeled goat anti-mouse. Digital images were acquired using a Nikon Eclipse E800 microscope equipped with a Radiance 2000 confocal scanning laser attachment. ImarisBasic 4.1 visualization suite was utilized for qualitative interpretation. NeuronTracer 1.0 software was utilized to derive the length and numerical densities.There were significant changes across the phases of the menstrual cycle in functional and basal endometrial layers in vessel length density (LD_v) and branch point density (ND_v) within both fundal and isthmic regions of the uterus (P < 0.001). There was also a significant effect of menstrual cycle phase on mean vessel segment length (SL_v) within each region and within each of the layers (P < 0.001). The capillary radial diffusion distance r(diff) was negatively correlated with LD_v. In general, within each of the menstrual cycle phases, LD_v, ND_v were greater in the fundal than the isthmic regions while, in contrast, SL_v was found to be greatest in the isthmic region.Utilization of immunofluorescence and laser scanning confocal microscopy has enabled us to demonstrate significant vascular changes in human endometrial layers illustrating that in general, within each of the menstrual cycle phases, vessel length and branch point densities were greater in the fundal than the isthmic regions, while vessel segment lengths were found to be greatest in the isthmic region.     

X-ray crystallography and magnetic studies of a stable macrocyclic tetranitroxide. Intramolecular dimer of nitroxides in a constrained geometry of the upper rim of calix[4]arene

Synthesis, crystallography, and magnetic characterization of a stable macrocyclic tetranitroxide 1, a calix[4]arene, which is functionalized with four tert-butylnitroxides at the upper rim, is described. In solution, 1 has a 4-fold symmetric fixed cone conformation on the NMR time scale and small, but nonnegligible, exchange interactions between the radicals (30 K > /J/k/ >1.8 mK). In the solid state, dimerization of one diagonal pair of nitroxides leads to a pinched cone conformation for 1 with strong intradimer antiferromagnetic coupling with /J/k/ = 200-300 K (singlet-triplet energy gap, DeltaE(ST) approximately 1 kcal/mol).     

On the distribution of (k,r)-integers in Piatetski-Shapiro sequences

Czechoslovak Mathematical Journal - A natural number n is said to be a (k, r)-integer if n = akb, where k &gt; r &gt; 1 and b is not divisible by the rth power of any prime. We study the...     

On the distribution of square-full and cube-full primitive roots

Periodica Mathematica Hungarica - A positive integer n is called an r-full integer if for all primes $$p\mid n$$ we have $$p^r\mid n.$$ Let p be an odd prime. For $$\gcd (n,p)=1$$, the smallest...