Synthesis,characterization, and antioxidant and anticholinesterase activities of pyrazolo derivatives

Twenty-four pyrazolo derivatives (1–4)(a-f) were synthesized and characterized by FTIR, ¹H, and ¹³C NMR (Nuclear Magnetic Resonance), and elemental analysis. The synthesized compounds were also investigated for their antioxidant and anticholinesterase activities. The compounds (3–4)(a-f) carrying morpholine ring were more active than the piperidinyl containing compounds (1–2)(a-f) in both activities. The compound 4f showed higher activity in both assays as compared with the others. Additionally, the anticholinesterase activity test provided higher values than the galantamine in the BChE assay. Therefore, compound 4f can be used as anticholinesterase agent and/or anticholinesterase assay standard.     

A heat transfer problem with exponential memory and the associated thermal stresses

In this study, a heat transfer problem defined by the Caputo–Fabrizio derivative, which is known to behave by the exponential decaying law, is addressed in an axially symmetric cylindrical region. Thus, the fundamental solutions of the heat diffusion process and the associated thermal stresses are aimed to find. For this purpose, Laplace and finite Hankel integral transforms are applied according to the geometry of the region. To obtain the thermal stresses, constitutive relations of the classical thermoelasticity theory are used. The effects of fractional orders on the diffusion process are illustrated graphically using MATLAB.     

Neuroactive Peptide Nanofibers for Regeneration of Spinal Cord after Injury

The highly complex nature of spinal cord injuries (SCIs) requires design of novel biomaterials that can stimulate cellular regeneration and functional recovery. Promising SCI treatments use biomaterial scaffolds, which provide bioactive cues to the cells in order to trigger neural regeneration in the spinal cord. In this work, the use of peptide nanofibers is demonstrated, presenting protein binding and cellular adhesion epitopes in a rat model of SCI. The self‐assembling peptide molecules are designed to form nanofibers, which display heparan sulfate mimetic and laminin mimetic epitopes to the cells in the spinal cord. These neuroactive nanofibers are found to support adhesion and viability of dorsal root ganglion neurons as well as neurite outgrowth in vitro and enhance tissue integrity after 6 weeks of injury in vivo. Treatment with the peptide nanofiber scaffolds also show significant behavioral improvement. These results demonstrate that it is possible to facilitate regeneration especially in the white matter of the spinal cord, which is usually damaged during the accidents using bioactive 3D nanostructures displaying high densities of laminin and heparan sulfate‐mimetic epitopes on their surfaces.     

Search for the global minimum structures of AlB3H2n (n = 0 − 6) clusters

The global minimum structures of AlB₃H_2n (n = 0–6) clusters are determined using the stochastic search method at the B3LYP/6–31G level of theory. These initially specified geometries are recalculated using B3LYP and CCSD(T) methods using the 6–311++G^** basis set. The structural and electronic properties of the two lowest‐lying isomers are presented. The structural parameters obtained for aluminum borohydride are compared with the experimental and theoretical results. The H₂ fragmentation energies of the most stable isomers are investigated. Chemical bonding analyses for the global minimum of AlB₃H_2n (n = 0–6) clusters are performed using the adaptive natural density partitioning method. © 2014 Wiley Periodicals, Inc.     

Tauberian conditions for the $$(C, \alpha )$$ integrability of functions

For a real-valued continuous function f(x) on \([0,\infty )\), we define

$$\begin{aligned} s(x)=\int _{0}^{x} f(u)du\quad \text {and}\quad \sigma _{\alpha } (x)= \int _{0}^{x}\left( 1-\frac{u}{x}\right) ^{\alpha }f(u)du \end{aligned}$$

for \(x>0\). We say that \(\int _{0}^{\infty } f(u)du\) is \((C, \alpha )\) integrable to L for some \(\alpha >-1\) if the limit \(\lim _{x \rightarrow \infty } \sigma _{\alpha } (x)=L\) exists. It is known that \(\lim _{x \rightarrow \infty } s(x) =L\) implies \(\lim _{x \rightarrow \infty }\sigma _{\alpha } (x) =L\) for all \(\alpha >-1\). The aim of this paper is twofold. First, we introduce some new Tauberian conditions for the \((C, \alpha )\) integrability method under which the converse implication is satisfied, and improve classical Tauberian theorems for the \((C,\alpha )\) integrability method. Next we give short proofs of some classical Tauberian theorems as special cases of some of our results.

     

The Stochastic Encounter-Mating Model

We propose a new model of permanent monogamous pair formation in zoological populations with multiple types of females and males. According to this model, animals randomly encounter members of the opposite sex at their so-called firing times to form temporary pairs which then become permanent if mating happens. Given the distributions of the firing times and the mating preferences upon encounter, we analyze the contingency table of permanent pair types in three cases: (i) definite mating upon encounter; (ii) Poisson firing times; and (iii) Bernoulli firing times. In the first case, the contingency table has a multiple hypergeometric distribution which implies panmixia. The other two cases generalize the encounter-mating models of Gimelfarb (Am. Nat. 131(6):865–884, 1988) who gives conditions that he conjectures to be sufficient for panmixia. We formulate adaptations of his conditions and prove that they not only characterize panmixia but also allow us to reduce the model to the first case by changing its underlying parameters. Finally, when there are only two types of females and males, we provide a full characterization of panmixia, homogamy and heterogamy.