On Perturbed Fractional Differential Inclusions with Nonlocal Multi-point Erdélyi–Kober Fractional Integral Boundary Conditions

In this paper, by using a nonlinear alternative for a sum of compact upper semicontinuous and contractive multivalued operators, we establish sufficient conditions for the existence of solutions for perturbed fractional differential inclusions with nonlocal multi-point Erdélyi–Kober fractional integral boundary conditions. For the applicability of the main result, we include an example.     

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.     

Optimal data gathering paths and energy-balance mechanisms in wireless networks

This paper studies the data gathering problem in wireless networks, where data generated at the nodes has to be collected at a single sink. We investigate the relationship between routing optimality and fair resource management. In particular, we prove that for energy-balanced data propagation, Pareto optimal routing and flow maximization are equivalent, and also prove that flow maximization is equivalent to maximizing the network lifetime. We algebraically characterize the network structures in which energy-balanced data flows are maximal. Moreover, we algebraically characterize communication links which are not used by an optimal flow. This leads to the characterization of minimal network structures supporting the maximal flows.We note that energy-balance, although implying global optimality, is a local property that can be computed efficiently and in a distributed manner. We suggest online distributed algorithms for energy-balance in different optimal network structures and numerically show their stability in particular setting. We remark that although the results obtained in this paper have a direct consequence in energy saving for wireless networks they do not limit themselves to this type of networks neither to energy as a resource. As a matter of fact, the results are much more general and can be used for any type of network and different types of resources.     

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.     

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.     

Salicylaldoxime in manganese(III) carboxylate chemistry: Synthesis, structural characterization and physical studies of hexanuclear and polymeric complexes

The use of salicylaldehyde oxime (H₂salox) in manganese(III) carboxylate chemistry has yielded new members of the family of hexanuclear compounds presenting the [Mn₆(μ₃-O)₂(μ₂-OR)₂]¹²⁺ core, complexes [Mn^III₆(μ₃-O)₂(O₂CPh)₂(salox)₆(L₁)₂(L₂)₂] (L₁ = py, L₂ = H₂O (1); L₁ = Me₂CO, L₂ = H₂O (2); L₁ = L₂ = MeOH (3)). Addition of NaOMe to the acetonitrile reaction mixture, afforded the 1D complex [Mn^III₃Na(μ₃-O)(O₂CPh)₂(salox)₃(MeCN)]_n (4), whereas addition of NaClO₄ to the acetone reaction mixture afforded an analogous 1D complex [Mn^III₃Na(μ₃-O)(O₂CPh)₂(salox)₃(Me₂CO)]_n (5). The structures of 1–3 present the [Mn₆(μ₃-O)₂(μ₂-OR)₂]¹²⁺ core and can be described as two [Mn₃(μ₃-O)]⁷⁺ triangular subunits linked by two μ₂-oximato oxygen atoms of the salox²⁻ ligands, which show the less common μ₃-κ²O:κO′:κN coordination mode. The benzoato ligands are coordinated through the usual syn,syn-μ₂-κO:κO′ mode. The 1D polymeric structures of 4 and 5 consist of alternating [Mn₃(μ₃-O)]⁷⁺ subunits and Na⁺ atoms linked through two μ₃-κ²O:κO′:κN and one μ₄-κ²O:κ²O′:κN salox²⁻ ligands as well as one syn,anti-μ₂-κO:κO′ benzoato ligand. DC and AC magnetic susceptibility studies on 1 revealed the stabilization of an S = 4 ground state, and indications of single-molecule magnetism behavior, whereas the DC experimental data from polycrystalline sample of 5 are indicative of antiferromagnetic interactions within the [Mn₃] subunit. Solid state ¹H NMR data of 1 were used to probe the spin-lattice relaxation of the system.     

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.