Mackey-Glass type delay differential equations near the boundary of absolute stability

For equations $x'(t) = -x(t) + \zeta f(x(t-h)), x \in \R, f'(0)= -1, \zeta > 0,$ with $C^3$-nonlinearity $f$ which has negative Schwarzian derivative and satisfies $xf(x) < 0$ for $x\not=0$, we prove convergence of all solutions to zero when both $\zeta -1 >0$ and $h(\zeta-1)^{1/8}$ are less than some constant (independent on $h,\zeta$). This result gives additional insight to the conjecture about the equivalence between local and global asymptotical stabilities in the Mackey-Glass type delay differential equations.Comment: 16 pages, 1 figure, accepted for publication in the Journal of Mathematical Analysis and Application

Yorke and Wright 3/2-stability theorems from a unified point of view

We consider a family of scalar delay differential equations $x'(t)=f(t,x_t)$, with a nonlinearity $f$ satisfying a negative feedback condition combined with a boundedness condition. We present a global stability criterion for this family, which in particular unifies the celebrated 3/2-conditions given for the Yorke and the Wright type equations. We illustrate our results with some applications.Comment: 10 pages, accepted for publication in the Expanded Volume of DCDS, devoted to the fourth international conference on Dynamical Systems and Differential Equations, held at UNC at Wilmington, May 2002. Minor changes from the previous versio

Proton-conducting membrane with spatially heterogeneous structure based on polymer-silica nanocomposites

An original approach for the preparation of ternary proton-conducting membranes consisting of high density polyethylene (PE), silicon dioxide, and phosphoric acid for the intermediate temperature (140- 180 oC) fuel cell is presented. The base of this method is a template synthesis of silica phase using hyperbranched polyethoxysiloxane as a precursor by hydrolytic condensation reaction within the volume of the nanoporous polymer matrix with pore’s diameter of about 10 nm obtained via the mechanism of delocalized solvent-crazing. The received polymer-silica nanocomposites containing up to 40 wt.% of SiO2 were characterized by a structure of two interpenetrating networks, and silicon dioxide formed a rigid three- dimensional framework. Loading of composites by phosphoric acid was carried out by their heating in an environment of H3PO4 at 160 oC that was above the melting point of PE. In this case, the polyethylene melt migrated from inner volume to surfaces of the composite while emerged pores were filled with acid. The amount of introduced acid increased linearly with a growth of silica phase in the composite and maximum content of H3PO4 equaled to 50 wt.%. The proton-conducting membranes obtained are characterized by conductivity of 0.03 S/cm and the best performance of 0.4 V at current densities of 0.4 A/cm2 at 160 oC

ЛЮМИНЕСЦЕНТНОЕ ОПРЕДЕЛЕНИЕ МЕДИ, СЕРЕБРА, ЗОЛОТА И ПЛАТИНЫ С ИСПОЛЬЗОВАНИЕМ 2-МЕРКАПТО-5-БЕНЗИМИДАЗОЛСУЛЬФОКИСЛОТЫ, В ТОМ ЧИСЛЕ ЗАКРЕПЛЕННОЙ НА ПОВЕРХНОСТИ КРЕМНЕЗЕМА

Текст статьи не публикуется в открытом доступе в соответствии с политикой журнала.2-Mercapto-5-benzimidazolesulfonic acid (MBI), also noncovalently bound to a silica surface, is proposed as a reagent for the low-temperature luminescence determination of Cu(I), Ag(I), Au(I), and Pt(II). Luminescence excitation and luminescence spectra of metal complexes with MBI in solutions and on the adsorbent surface represent broad unstructured bands in the regions 250–400 and 450–700 nm, respectively. The developed procedures for the luminescence and sorption–luminescence determination of Cu, Ag, Au, and Pt with limits of detection at a level of 0.001–0.01 μg on 0.1 g of adsorbent are tested in the determination of metals in natural and industrial samples

Application of silica modified with polyhexamethylene guanidyne and 8-oxyquinolyne-5-sulfur acid for concentration and sorption-atomic emission determination of metals in natural waters

Рассмотрены особенности концентрирования ионов металлов кремнеземом, модифицированным полигексаметиленгуанидином и 8-оксихинолин-5-сульфокислотой (SiO2-ПГМГ-Oxin), и оксихинолинатов металлов кремнеземом, модифицированным полигексаметиленгуанидином (SiO2-ПГМГ). В статическом режиме количественное (более 99 %) извлечение Cu(II), Zn(II), Co(II), Ni(II), Cd(II), Fe(III) и Al(III) с помощью SiO2-ПГМГ-Oxin достигается из растворов с рН 4-7, Mn(II) - рН 5,5-7,0. При рН 5 в динамическом режиме достигается групповое концентрирование ионов металлов SiO2-ПГМГ-Oxin или их оксихинолинатов SiO2-ПГМГ. Сорбированные элементы десорбируют 1 М растворами HCl или HNO3 и определяют атомно-эмиссионным методом. Разработанная методика сорбционно-атомно-эмиссионного определения использована при определении содержания металлов в природных водах.Peculiarities of metal ions collection by silica, modified with polyhexamethylene guanidine and 8-oxyquinoline-5-sulfo-acid (SiO2-PHMG-Oxin), and metals' oxyquinolinates by silica, modified with polyhexamethylene guanidine (SiO2-PHMG), are considered. Quantitative (?99%) extraction of Cu(II), Zn(II), Co(II), Ni(II), Cd(II), Fe(III), Al(III) by SiO2-PHMG-Oxin from the solutions with pH 4-7, Mn(II) - рН 5,5-7,0 was observed at batch equilibrium conditions. Under pH 5 group collection of metal ions by SiO2-PHMG-Oxin or their oxyquinolinates by SiO2-PHMG was archived at flow-injection conditions. Sorbed elements were desorbed by 1M solutions of HCl or HNO3 and determined by atomic emission method. Developed technique of sorption-atomic-emission determination was used for determination of metals content in natural waters