Existence and Global Asymptotic Behavior of Positive Solutions for Sublinear and Superlinear Fractional Boundary Value Problems

In this paper, the authors aim at proving two existence results of fractional differential boundary value problems of the form(P_(a,b)){D~αu(x) + f(x, u(x)) = 0, x ∈(0, 1),u(0) = u(1) = 0, D~(α-3)u(0) = a, u(1) =-b,where 3 α≤ 4, Dαis the standard Riemann-Liouville fractional derivative and a, b are nonnegative constants. First the authors suppose that f(x, t) =-p(x)t~σ, with σ∈(-1, 1)and p being a nonnegative continuous function that may be singular at x = 0 or x = 1and satisfies some conditions related to the Karamata regular variation theory. Combining sharp estimates on some potential functions and the Sch¨auder fixed point theorem, the authors prove the existence of a unique positive continuous solution to problem(P_(0,0)).Global estimates on such a solution are also obtained. To state the second existence result, the authors assume that a, b are nonnegative constants such that a + b 0 and f(x, t) = tφ(x, t), with φ(x, t) being a nonnegative continuous function in(0, 1)×[0, ∞) that is required to satisfy some suitable integrability condition. Using estimates on the Green's function and a perturbation argument, the authors prove the existence and uniqueness of a positive continuous solution u to problem(P_(a,b)), which behaves like the unique solution of the homogeneous problem corresponding to(P_(a,b)). Some examples are given to illustrate the existence results.     

Effect of Ar bombardment on the electrical and optical properties of low-density polyethylene films

The influence of low-energy Ar ion beam irradiation on both electrical and optical properties of low-density polyethylene (LDPE) films is presented. The polymer films were bombarded with 320 keV Ar ions with fuences up to 1×10¹⁵ cm^?2. Electrical properties of LDPE films were measured and the effect of ion bombardment on the DC conductivity, dielectric constant and loss was studied. Optically, the energy gap, the Urbach’s energy and the number of carbon atoms in a cluster were estimated for all polymer samples using the UV–Vis spectrophotometry technique. The obtained results showed slight enhancement in the conductivity and dielectric parameters due to the increase in ion fluence. Meanwhile, the energy gap and the Urbach’s energy values showed significant decrease by increasing the Ar ion fluence. It was found that the ion bombardment induced chain scission in the polymer chain causing some carbonization. An increase in the number of carbon atoms per cluster was also observed.     

Attaining control by design over the hydrolytic stability of Fe-TAML oxidation catalysts

The iron(III) complexes of tetra amidato macrocyclic ligands (TAMLs) ([Fe{1-X1-2-X2C6H2-4,5-(NCOCMe2NCO)2CR2}(OH2)]- , 1: X1 = X2 = H, R2 = Me2 (a), R2 = (CH2)2 (b); X1 = X2 = Cl, R2 = F2 (c), etc.), which the proton is known to demetalate at pH < 3, are also subject to catalyzed demetalation by Br?nsted acid buffer components at pH 4-9 such as H2PO4-, HSO3-, and CH3CO2H, HO2CCH2CO2-. Buffers based on pyridine (py) and tris(hydroxymethyl)aminomethane (TRIS) are catalytically inactive. Where reactions proceed, the products are demetalated TAMLs and iron species of variable composition. Pseudo-first-order rate constants for the demetalation (kobs) are linear functions of the acid concentrations, and the effective second-order rate constants k1,eff have a hyperbolic dependence on [H+] (k1,eff = a1[H+]/(b1+[H+]). The rate of demetalation of 1a in H2PO4-/HPO42- buffer is appreciable, but the kobs values for 1b and 1c are immeasurably low, showing that the rates are strongly affected by the CR2 or "tail" fragments, which are known to potently affect the TAML basicity. The reactivities of 1 depend insignificantly on the aromatic ring or "head" group of 1. The proposed mechanism involves precoordination of the acidic buffer species followed by hydrolysis. The demetalating abilities of buffer species depend on their structures and acidities. Thus, although pyridine-2-carboxylic (picolinic) acid catalyzes the demetalation, its 3- and 4-isomers (nicotinic and isonicotininc acids) are inactive. The difference is rationalized to result from the ability that only coordinated picolinic acid has to deliver a proton to an amidato nitrogen in an intramolecular manner. The reaction order in picolinic acid equals one for 1a and two for 1b. For 1b, "inactive" pyridine and nicotinic acid speed up the demetalation in the presence of picolinic acid, suggesting that the second order arises from the axial binding of two pyridine molecules, one of which must be picolinic acid. The binding of pyridine- and imidazole-type ligands was confirmed by UV/vis equilibrium measurements and X-ray crystallography. The implications of these mechanistic findings for designing superior Fe-TAML oxidation catalysts and catalyst formulations are discussed using the results of DFT calculations.     

A class of generalized Ornstein transformations with the weak mixing property

It is shown that there is a class of Ornstein transformations, distinct from the Ornstein mixing class, which are almost surely weak mixing     

Diode laser absorption measurements at the Hα-transition in laser induced plasmas on different targets

The diode laser atomic absorption spectroscopy (DLAAS) technique has been utilized to assess the degree of optical opacity of plasma at the wavelength of the H_α-line. The plasma is produced at atmospheric conditions by focusing a 6 ns Nd:YAG laser pulse at 1.064 μm on different solid target materials including aluminum, iron and titanium as major elements as well as flat pieces of plastic and wood characterized by a high content of hydrogen. The optical depth was investigated as a function of delay times ranging from 0 to 5 μs, and at laser fluences ranging from 7 to 19 J/cm², all at a fixed gate time of 1 μs. The results show that the plasma associated with metallic targets is almost optically thin at the H_α-line over all fluences and at delay times ≥ 1 μs, but rather thick for hydrogen-rich targets (plastic and wood) over all delay times and fluences.     

A Synthetic High‐Spin Oxoiron(IV) Complex: Generation,Spectroscopic Characterization,and Reactivity

High versus low : The high‐yield generation of a synthetic high‐spin oxoiron(IV) complex, [Fe^IV(O)(TMG₃tren)]²⁺ (see picture, TMG₃tren = 1,1,1‐tris{2‐[N2‐(1,1,3,3‐tetramethylguanidino)]ethyl}amine), has been achieved by using the very bulky tetradentate TMG₃tren ligand, in order to both sterically protect the oxoiron(IV) moiety and enforce a trigonal bipyramidal geometry at the iron center, for which an S=2 ground state is favored.

     

Synthesis and photoluminescent properties of a Schiff-base ligand and its mononuclear Zn(II), Cd(II), Cu(II), Ni(II) and Pd(II) metal complexes

Mononuclear Zn(II), Cd(II), Cu(II), Ni(II) and Pd(II) metal complexes of Schiff-base ligand(HL₁) derived from 8-acetyl-7-hydroxycoumarin and P-phenylenediamine were prepared and characterized by microanalytical, mass, UV–Vis, IR, ¹H NMR, ¹³C NMR, ESR, conductance and fluorescence studies. The measured low molar conductance values in DMSO indicate that the complexes are non-electrolytes. The structures of the solid complexes under study are established by using IR, electronic and ESR spectroscopy suggesting that Zn(II) and Ni(II) complexes are octahedral, Cd(II) complex is tetrahedral, Cu(II) and Pd(II) complexes are square planar. The ESR spectrum of the Cu(II) complex in DMSO at 298 and 150 K was recorded and its salient features are reported, it supports the mononuclear structure. The Schiff base exhibited photoluminescence originating from intraligand (π–π*) transitions. Metal-mediated enhancement is observed on complexation of HL with Zn(II) and Cd(II), whereas metal-mediated fluorescence quenching occurs in Cu(II), Ni(II) and Pd(II).     

The Rain on Underground Porous Media Part I: Analysis of a Richards Model

The Richards equation models the water flow in a partially saturated underground porous medium under the surface. When it rains on the surface, boundary conditions of Signorini type must be considered on this part of the boundary. The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler’s scheme in time and finite elements in space. The convergence of this discretization leads to the well-posedness of the problem.