Extremal problems related to maximal dyadic-like operators

We obtain sharp estimates for the localized distribution function of the dyadic maximal function Md?, when ? belongs to Lp,∞. Using this we obtain sharp estimates for the quasi-norm of Md? in Lp,∞ given the localized L¹-norm and certain weak Lp-conditions.     

A Combined Renormalization Group‐Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms.     

Synthesis of 4(3H)-quinazolinones from derivatives of methyl 2-isothiocyanatobenzoate

Ethyl N-(2-methoxycarbonylphenyl)thiocarbamate ( 2), N -(2-ethoxycarbonylphenyl)-4-methoxythiobenz-amide ( 3b ), and 2-(4-methoxyphenyl)-4H-3,1-benzothiazin-4-one ( 4a ), react with nucleophilic reagents containing at least one primary amino group to yield a variety of 2-substituted and 2,4-disubstituted 4(3H)quinazolinones, as well as some tricyclic and tetracyclic products.     

Reactions of o-aminonitriles with isocyanates. 2. A facile synthesis of imidazo[1,2-c]quinazoline-2,5-(3H,6H)dione

Anthranilonitrile reacts with ethyl isocyanatoacetate to form 2-(3-ethoxycarbonylmethylureido)benzonitrile (3b) which, upon heating, or treatment with a base, undergoes a double cyclization to yield imidazo[1,2-c]-quinazoline-2,5-(3H,6H)dione ( 5 ) in excellent yield. In the presence of acid, 3b is converted into 1,4-dihydro-2,4-dioxo-3-(2H)quinazolineacetic acid ( 11 ), or its ethyl ester ( 10 ). The action of concentrated sulfuric acid converts the adduct 13 of anthranilic acid and ethyl isocyanatoacetate into 2-ethoxycarbonyl-methylamino-4H-3,1 -benzoxazin-4-one ( 14 ).     

Synthesis and mesomorphic behavior of a new series of side-chain liquid crystalline polymethacrylates bearing 2,6-naphthylene-based mesogen

A new homologous series of liquid crystalline (LC) polymethacrylates, the poly[ω-(2-phenoxycarbonyl-naphthalene-6-yloxy)alkyl methacrylate]s, in which the length of the alkyl spacer is varied between 3 and 12 methylene units, have been synthesized by free-radical polymerization. The prepared polymers were studied by IR and ¹H-NMR spectroscopy, viscosity measurements, differential scanning calorimetry (DSC), and polarized microscopy. Polymers with 3 or 4 methylene units spacer were glassy in nature, whereas those with 5–12 methylene units spacer exhibited smectic behavior. The glass transition temperatures decrease on increasing spacer length. The isotropization temperatures and the corresponding transition entropies showed an odd–even effect, with the odd members exhibiting the higher values. This effect attenuates on increasing spacer length. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2391–2399, 1999     

Some Weak Forms of the Axiom of Choice Restricted to the Real Line

It is shown that AC(ℝ), the axiom of choice for families of non‐empty subsets of the real line ℝ, does not imply the statement PW(ℝ), the powerset of ℝ can be well ordered. It is also shown that (1) the statement “the set of all denumerable subsets of ℝ has size 2 ${}^{\text{ℵ}{}_{\text{0}}}$ ” is strictly weaker than AC(ℝ) and (2) each of the statements (i) “if every member of an infinite set of cardinality 2 ${}^{\text{ℵ}{}_{\text{0}}}$ has power 2 ${}^{\text{ℵ}{}_{\text{0}}}$ , then the union has power 2 ${}^{\text{ℵ}{}_{\text{0}}}$ ” and (ii) “ℵ(2 ${}^{\text{ℵ}{}_{\text{0}}}$ ) ≠ ℵ_ω” (ℵ(2 ${}^{\text{ℵ}{}_{\text{0}}}$ ) is Hartogs' aleph, the least ℵ not ≤ 2 ${}^{\text{ℵ}{}_{\text{0}}}$ ), is strictly weaker than the full axiom of choice AC.     

Choice principles for special subsets of the real line

We study the role the axiom of choice plays in the existence of some special subsets of ? and its power set ?(?).     

Accelerating the simulation of brain tumor proliferation with many-core GPUs

Medical centers, such as hospitals, clinics and diagnostic centers, form a special category of facilities, where the need to perform demanding scientific simulations has to be combined with a reasonable deployment cost in order for such simulations to be applicable at a wide scale. Under these circumstances, the use of supercomputing clusters can not be considered as a universal solution. Nevertheless, we argue that the use of the newly introduced multi-core and many-core microprocessors – either at the local level or through cloud computing infrastructure – can lead to significant speedups if the necessary software development effort is expended.In the current paper, in order to give evidence of the feasibility of such an approach, we present a numerical method for the simulation of brain tumors proliferation and we demonstrate the acceleration of this method in the context of a state of the art many-core GPU. The numerical solution is based on the high-order discontinuous Galerkin (DG) method and the simulation is performed on the unstructured mesh that results from the space discretization of the brain volume. Two implementation schemes using CUDA and one multithreaded implementation using OpenMP are evaluated and they highlight the potential speedup that a diagnostic process can experience in a facility that is equipped with a single node multi-core or many-core microprocessor.     

On a variant of Rado’s selection lemma and its equivalence with the Boolean prime ideal theorem

We establish that, in ZF (i.e., Zermelo–Fraenkel set theory minus the Axiom of Choice AC), the statement RLT: Given a set I and a non-empty set \({\mathcal{F}}\) of non-empty elementary closed subsets of 2 ^I satisfying the fip, if \({\mathcal{F}}\) has a choice function, then \({\bigcap\mathcal{F} \ne \emptyset}\) , which was introduced in Morillon (Arch Math Logic 51(7–8):739–749, 2012), is equivalent to the Boolean Prime Ideal Theorem (see Sect. 1 for terminology). The result provides, on one hand, an affirmative answer to Morillon’s corresponding question in Morillon (2012) and, on the other hand, a negative answer—in the setting of ZFA (i.e., ZF with the axiom of extensionality weakened to permit the existence of atoms)—to the question in Morillon (2012) of whether RLT is equivalent to Rado’s selection lemma.     

A Molecular Tetrahedral Cobalt–Seleno-Based Complex as an Efficient Electrocatalyst for Water Splitting

The cobalt–seleno-based coordination complex, [Co{(SePⁱPr₂)₂N}₂], is reported with respect to its catalytic activity in oxygen evolution and hydrogen evolution reactions (OER and HER, respectively) in alkaline solutions. An overpotential of 320 and 630 mV was required to achieve 10 mA cm⁻² for OER and HER, respectively. The overpotential for OER of this CoSe₄-containing complex is one of the lowest that has been observed until now for molecular cobalt(II) systems, under the reported conditions. In addition, this cobalt–seleno-based complex exhibits a high mass activity (14.15 A g⁻¹) and a much higher turn-over frequency (TOF) value (0.032 s⁻¹) at an overpotential of 300 mV. These observations confirm analogous ones already reported in the literature pertaining to the potential of molecular cobalt–seleno systems as efficient OER electrocatalysts.