On a quadratic fractional Hammerstein-Volterra integral equation with linear modification of the argument

We study the existence of monotonic solutions of a quadratic fractional Hammerstein-Volterra integral equation with linear modification of the argument. The quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases. We show that the quadratic fractional Hammerstein-Volterra integral equation with linear modification of the argument has a monotonic solution in the Banach space of all real functions defined and continuous on a bounded and closed interval. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.     

The role of hydrophobic surfaces in altering water-mediated peptide-peptide interactions in an aqueous environment

Using Born-Oppenheimer molecular dynamics within the density functional framework, we calculated the effective force acting on water-mediated peptide-peptide interaction between antiparallel β-sheets in an aqueous environment and also in the vicinity of a hydrophobic surface. From the magnitude of the effective force (corresponding to the slope of the free energy as a function of the interpeptide distance) and its sign (a negative value indicates an effective attraction, whereas a positive value indicates an effective repulsion) we can elucidate the fundamental differences of the water-mediated peptide-peptide interactions in those two environments. The computed effective forces indicate that the water-mediated interaction between peptides in an aqueous environment is attractive in the range of interpeptide distance d = 7-8 ? when hydrophobic surfaces are not nearby. Due to the stabilization of the water molecules bridging between the two β-sheets, a free energy barrier exists between the direct and indirect (water-mediated) interpeptide interactions. However, when the peptides are in the proximity of hydrophobic surfaces, this free energy barrier decreases because the hydrophobic surfaces enhance the interpeptide attraction by the destabilization and ease-to-libration of the bridging water molecules between them.     

Global existence for second order functional semilinear equations

In this paper we study the global existence of solutions for initial value problems for functional semilinear equations, where the linear operator in the differential equation is the infinitesimal generator of a strongly cosine family in a Banach spaceX. Using the Leray-Schauder Alternative, we derive conditions under which a solution exists globally.     

Monitoring Phase II Comparative Clinical Trials with Two Endpoints and Penalty for Adverse Events

Adverse events in Phase II comparative clinical trials have received limited attention in the literature. Bersimis et al. (Stat Med 34:197–214, 2014) in proposed a class of comparative sequential designs with bivariate endpoints, where as a special case, the termination of the clinical trial due to the occurrence of a severe adverse event is treated. In this paper, using the Markov chain embedding technique, we extend this class of designs proposing two new designs, which treat cases where the development of an adverse event does not immediately stop the clinical trial, but penalizes appropriately the treatment that caused it. In both designs the penalty can be chosen either by assessing the severity of the adverse event or by optimizing the power. The numerical results show an excellent performance, achieving small expected sample sizes in conjunction with large values for power, satisfying in this way the ethical requirement for small sample sizes and fast decisions in clinical practice. The formulation of the procedure as a stochastic process is elegantly accomplished while it offers the necessary mathematical framework for further generalizing the designs covering more cases such as group sequential designs, etc.     

On First Order Impulsive Dynamic Equations on Time Scales

In this paper, the nonlinear alternative of Leray-Schauder type is used to investigate the existence of solutions for first order impulsive dynamic equations on time scales.     

Boundary Value Problems for Riemann–Liouville Fractional Differential Inclusions with Nonlocal Hadamard Fractional Integral Conditions

In this paper, we study a new class of boundary value problems from a fractional differential inclusion of Riemann–Liouville type and nonlocal Hadamard fractional integral boundary conditions. Some new existence results for convex as well as non-convex multi-valued maps are obtained using standard fixed point theorems. The obtained results are illustrated by examples.     

Dissolution and storage stability of nanostructured calcium carbonates and phosphates for nutrition

Rapid calcium (Ca) dissolution from nanostructured Ca phosphate and carbonate (CaCO₃) powders may allow them to be absorbed in much higher fraction in humans. Nanosized Ca phosphate and CaCO₃ made by flame-assisted spray pyrolysis were characterized by nitrogen adsorption, X-ray diffraction (XRD), Raman spectroscopy, and transmission electron microscopy. As-prepared nanopowders contained both CaCO₃ and CaO, but storing them under ambient conditions over 130 days resulted in a complete transformation into CaCO₃, with an increase in both crystal and particle sizes. The small particle size could be stabilized against such aging by cation (Mg, Zn, Sr) and anion (P) doping, with P and Mg being most effective. Calcium phosphate nanopowders made at Ca:P ≤ 1.5 were XRD amorphous and contained γ-Ca₂P₂O₇ with increasing hydroxyapatite content at higher Ca:P. Aging of powders with Ca:P = 1.0 and 1.5 for over 500 days gradually increased particle size (but less than for CaCO₃) without a change in phase composition or crystallinity. In 0.01 M H₃PO₄ calcium phosphate nanopowders dissolved ≈4 times more Ca than micronsized compounds and about twice more Ca than CaCO₃ nanopowders, confirming that nanosizing and/or amorphous structuring sharply increases Ca powder dissolution. Because higher Ca solubility in vitro generally leads to greater absorption in vivo, these novel FASP-made Ca nanostructured compounds may prove useful for nutrition applications, including supplementation and/or food fortification.     

Study of NH stretching vibrations in small ammonia clusters by infrared spectroscopy in He droplets and ab initio calculations

Infrared spectra of the NH stretching vibrations of (NH3)n clusters (n = 2-4) have been obtained using the helium droplet isolation technique and first principles electronic structure anharmonic calculations. The measured spectra exhibit well-resolved bands, which have been assigned to the nu1, nu3, and 2nu4 modes of the ammonia fragments in the clusters. The formation of a hydrogen bond in ammonia dimers leads to an increase of the infrared intensity by about a factor of 4. In the larger clusters the infrared intensity per hydrogen bond is close to that found in dimers and approaches the value in the NH3 crystal. The intensity of the 2nu4 overtone band in the trimer and tetramer increases by a factor of 10 relative to that in the monomer and dimer, and is comparable to the intensity of the nu1 and nu3 fundamental bands in larger clusters. This indicates the onset of the strong anharmonic coupling of the 2nu4 and nu1 modes in larger clusters. The experimental assignments are compared to the ones obtained from first principles electronic structure anharmonic calculations for the dimer and trimer clusters. The anharmonic calculations were performed at the M?ller-Plesset (MP2) level of electronic structure theory and were based on a second-order perturbative evaluation of rovibrational parameters and their effects on the vibrational spectra and average structures. In general, there is excellent (<20 cm(-1)) agreement between the experimentally measured band origins for the N-H stretching frequencies and the calculated anharmonic vibrational frequencies. However, the calculations were found to overestimate the infrared intensities in clusters by about a factor of 4.     

Synthesis, structural characterization, and biological studies of new antimony(III) complexes with thiones. The influence of the solvent on the geometry of the complexes

Five new antimony(III) complexes with the heterocyclic thiones 2-mercapto-benzimidazole (MBZIM), 5-ethoxy-2-mercapto-benzimidazole (EtMBZIM), and 2-mercapto-thiazolidine (MTZD) of formulas {[SbCl(2)(MBZIM)4]+.Cl-.2H(2)O. (CH(3)OH)} (1), {[SbCl(2)(MBZIM)4]+.Cl-.3H(2)O.(CH3CN)} (2), [SbCl(3)(MBZIM)2] (3), [SbCl(3)(EtMBZIM)(2)] (4), and [SbCl(3)(MTZD)2] (5) have been synthesized and characterized by elemental analysis, FT-IR, far-FT-IR, differential thermal analysis-thermogravimetry, X-ray diffraction, and conductivity measurements. Complex {[SbCl2(tHPMT)(2)]+Cl-}, (tHPMT = 2-mercapto-3,4,5,6-tetrahydro-pyrimidine), already known, was also prepared, and its X-ray crystal structure was solved. It is shown that the complex is better described as {[SbCl3(tHPMT)(2)]} (6). Crystal structures of all other complexes (1-5) have also been determined by X-ray diffraction at ambient conditions. The crystal structure of the hydrated ligand, EtMBZIM.H2O is also reported. Compound [C(28)H(24)Cl(2)N(8)S(4)Sb.2H(2)O.Cl.(CH(3)OH)] (1) crystallizes in space group P2(1), with a = 7.7398(8) A, b = 16.724(3) A, c = 13.717(2) A, beta = 98.632(11) degrees, and Z = 2. Complex [C(28)H(24)Cl(2)N(8)S(4)S(b).Cl.3H(2)O.(CH(3)CN)] (2) corresponds to space group P2(1), with a = 7.8216(8) A, b = 16.7426(17) A, c = 13.9375(16) A, beta = 99.218(10) degrees , and Z = 2. In both 1 and 2 complexes, four sulfur atoms from thione ligands and two chloride ions form an octahedral (Oh) cationic [SbS(4)Cl(2)]+ complex ion, where chlorides lie at axial positions. A third chloride counteranion neutralizes it. Complexes 1 and 2 are the first examples of antimony(III) compounds with positively charged Oh geometries. Compound [C(14)H(12)Cl(3)N(4)S(2)S(b)] (3) crystallizes in space group P, with a = 7.3034(5) A, b = 11.2277(7) A, c = 12.0172(8) A, alpha = 76.772(5) degrees, beta = 77.101(6) degrees, gamma = 87.450(5) degrees, and Z = 2. Complex [C(18)H(20)Cl(3)N(4)O(2)S(2)S(b)] (4) crystallizes in space group P1, with a = 8.6682(6) A, b = 10.6005(7) A, c = 13.0177(9) A, alpha = 84.181(6) degrees, beta = 79.358(6) degrees, gamma = 84.882(6) degrees, and Z = 2, while complex [C(6)H(10)Cl(3)N(2)S(4)S(b)] (5) in space group P2(1)/c shows a = 8.3659(10) A, b = 14.8323(19) A, c = 12.0218(13) A, beta = 99.660(12) degrees, and Z = 4 and complex [C(8)H(16)Cl(3)N(4)S(2)S(b)] (6) in space group P1 shows a = 7.4975(6) A, b = 10.3220(7) A, c = 12.1094(11) A, alpha = 71.411(7) degrees, beta = 84.244(7) degrees, gamma = 73.588(6) degrees, and Z = 2. Crystals of complexes 3-6 grown from acetonitrile solutions adopt a square-pyramidal (SP) geometry, with two sulfur atoms from thione ligands and three chloride anions around Sb(III). The equatorial plane is formed by two sulfur and two chloride atoms in complexes 3-5, in a cis-S, cis-Cl arrangement in 3 and 5 and a trans-S, trans-Cl arrangement in 4. Finally, in the case of 6, the equatorial plane is formed by three chloride ions and one sulfur from the thione ligand while the second sulfur atom takes an axial position leading to a unique SP conformation. The complexes showed a moderate cytostatic activity against tumor cell lines.     

Novel organotin(IV) compounds derived from bis(organostannyl)methanes: Synthesis and crystal structures of bis[diphenyl(pyridin-2-onato)stannyl]methane and bis[bromophenyl(pyrimidine-2-thionato)stannyl]methane · C7H8

Reaction between bis(chlorodiphenylstanyl)methane and the sodium salt of 2-hydroxypyridine (pyONa) in the molar ratio of 1:2 provides the organotin hydroxide derivative [Ph₂(pyO)SnCH₂Sn(OH)Ph₂]₂ (1) (where pyO = anion of 2-hydroxypyridine), while reaction of bis(dibromophenylstanyl)methane with the sodium salt of pyrimidine-2-thione (pmtNa) in molar ratio of 1:4 gives the corresponding organotin thiolate derivative, as its toluene solvate [BrPh(pmt)Sn]₂CH₂ · C₇H₈ (2) (where pmt = anion of pyrimidine-2-thione). Both compounds were characterized by single crystal X-ray diffraction analysis and contain five-coordinate tin atoms. Compound 1 is a centrosymmetric head-to-tail dimmer with almost symmetrical Sn(1)-O(H)-Sn(2A) bridges.