Multiplication operators on Cesàro second order function spaces

Positivity - In this article, we investigate bounded, invertible and compact multiplication operators on the second order Cesàro function spaces.     

On Two Equivalent Dilation Theorems in VH-Spaces

We prove that a generalized version, essentially obtained by R.M. Loynes, of the B. Sz.-Nagy??s Dilation Theorem for ${\mathcal{B}^*(\mathcal{H})}$ -valued (here ${\mathcal{H}}$ is a VH-space in the sense of Loynes) positive semidefinite maps on *-semigroups is equivalent with a generalized version of the W.F. Stinespring??s Dilation Theorem for ${\mathcal{B}^*(\mathcal{H})}$ -valued completely positive linear maps on B ^*-algebras. This equivalence result is a generalization of a theorem of F.H. Szafraniec, originally proved for the case of operator valued maps (that is, when ${\mathcal{H}}$ is a Hilbert space).     

Ammonia adsorption on iron phthalocyanine on Au(111): influence on adsorbate-substrate coupling and molecular spin

The adsorption of ammonia on Au(111)-supported monolayers of iron phthalocyanine has been investigated by x-ray photoelectron spectroscopy, x-ray absorption spectroscopy, and density functional theory calculations. The ammonia-induced changes of the x-ray photoemission lines show that a dative bond is formed between ammonia and the iron center of the phthalocyanine molecules, and that the local spin on the iron atom is quenched. This is confirmed by density functional theory, which also shows that the bond between the iron center of the metalorganic complex and the Au(111) substrate is weakened upon adsorption of ammonia. The experimental results further show that additional adsorption sites exist for ammonia on the iron phthalocyanine monolayer.     

Kinetic approach for the purification of nucleotides with magnetic separation

The isolation of β‐nicotinamide adenine dinucleotide is of great importance since it is widely used in different scientific and technologic fields such as biofuel cells, sensor technology, and hydrogen production. In order to isolate β‐nicotinamide adenine dinucleotide, first 3‐aminophenyboronic acid functionalized magnetic nanoparticles were prepared to serve as a magnetic solid support and subsequently they were used for reversible adsorption/desorption of β‐nicotinamide adenine dinucleotide in a batch fashion. The loading capacity of the 3‐aminophenyboronic acid functionalized nanoparticles for β‐nicotinamide adenine dinucleotide adsorption was 13.0 μmol/g. Adsorption kinetic and isotherm studies showed that the adsorption process followed a pseudo‐second‐order kinetic model and the experimental data can be represented using Langmuir isotherm model. The 3‐aminophenyboronic acid functionalized magnetic nanoparticles were proposed as an alternative support for the β‐nicotinamide adenine dinucleotide purification. The results elucidated the significance of magnetic separation as a fast, relatively simple, and low‐cost technique. Furthermore, the magnetic supports can be reused at least five times for purification processes.     

In vitro incorporation studies of 99mTc–alendronate sodium at different bone cell lines

Bisphosphonates can be labeled with Technetium-99m (^99mTc) and are used for bone imaging because of their good localization in the skeleton and rapid clearance from soft tissues. Over the last decades bone scintigraphy has been used extensively in the evaluation of oncological patients to provide information about the sites of bone lesions, their prognosis and the effectiveness of therapy by showing the sequential changes in tracer uptake. Since the lesion visualization and lesion/bone ratio are important utilities for a bone scanning radiopharmaceutic; in this study incorporation of ^99mTc labeled alendronate sodium (^99mTc–ALD) was evaluated in U₂OS (human bone osteosarcoma) and NCI-H209 (human bone carcinoma) cell lines. ALD was directly labeled by ^99mTc, radiochemical purity and stability of the complex were analyzed by radioactive thin layer chromatography and radioactive high performance liquid chromatography studies. For cell incorporation study, NCI-H209 and U₂OS cell lines were used with standard cell culture methods. The six well plates were used for all experiments and the integrity of each cell monolayer was checked by measuring its transepithelial electrical resistance (TEER) with an epithelial voltammeter. Results confirmed that ALD was successfully radiolabeled with ^99mTc. ^99mTc–ALD incorporated with NCI-H209 and U₂OS cells. The uptake percentages of ^99mTc–ALD in NCI-H209 and U₂OS cell lines were found significantly different. Since ^99mTc–ALD highly uptake in cancer cell line, the results demonstrated that radiolabeled ALD may be a promising agent for bone cancer diagnosis.     

Multi-period supplier selection under price uncertainty

We consider a problem faced by a procurement manager who needs to purchase a large volume of multiple items over multiple periods from multiple suppliers that provide base prices and discounts. Discounts are contingent on meeting various conditions on total volume or spend, and some are tied to future realizations of random events that can be mutually verified. We formulate a scenario-based multi-stage stochastic optimization model that allows us to consider random events such as a drop in price because of the most favoured customer clauses, a price change in the spot market or a new discount offer. We propose certainty-equivalent heuristics and evaluate the regret of using them. We use our model for three bidding events of a large manufacturing company. The results show that considering most favored customer clauses in supplier offers may create substantial savings that may surpass the savings from regular discount offers.     

Pore diameter mapping using double pulsed-field gradient MRI and its validation using a novel glass capillary array phantom

Double pulsed-field gradient (d-PFG) MRI can provide quantitative maps of microstructural quantities and features within porous media and tissues. We propose and describe a novel MRI phantom, consisting of wafers of highly ordered glass capillary arrays (GCA), and its use to validate and calibrate a d-PFG MRI method to measure and map the local pore diameter. Specifically, we employ d-PFG Spin-Echo Filtered MRI in conjunction with a recently introduced theoretical framework, to estimate a mean pore diameter in each voxel within the imaging volume. This simulation scheme accounts for all diffusion and imaging gradients within the diffusion weighted MRI (DWI) sequence, and admits the violation of the short gradient pulse approximation. These diameter maps agree well with pore sizes measured using both optical microscopy and single PFG diffusion diffraction NMR spectroscopy using the same phantom. Pixel-by-pixel analysis shows that the local pore diameter can be mapped precisely and accurately within a specimen using d-PFG MRI.     

Extensions and their Minimizations on the Sierpinski Gasket

We study the extension problem on the Sierpinski Gasket (SG). In the first part we consider minimizing the functional \(\mathcal {E}_{\lambda }(f) = \mathcal {E}(f,f) + \lambda \int f^{2} d \mu \) with prescribed values at a finite set of points where \(\mathcal {E}\) denotes the energy (the analog of \(\int |\nabla f|^{2}\) in Euclidean space) and μ denotes the standard self-similiar measure on SG. We explicitly construct the minimizer \(f(x) = \sum _{i} c_{i} G_{\lambda }(x_{i}, x)\) for some constants c _i , where G _λ is the resolvent for λ≥0. We minimize the energy over sets in SG by calculating the explicit quadratic form \(\mathcal {E}(f)\) of the minimizer f. We consider properties of this quadratic form for arbitrary sets and then analyze some specific sets. One such set we consider is the bottom row of a graph approximation of SG. We describe both the quadratic form and a discretized form in terms of Haar functions which corresponds to the continuous result established in a previous paper. In the second part, we study a similar problem this time minimizing \(\int _{SG} |\Delta f(x)|^{2} d \mu (x)\) for general measures. In both cases, by using standard methods we show the existence and uniqueness to the minimization problem. We then study properties of the unique minimizers.     

The Divisible Sandpile at Critical Density

The divisible sandpile starts with i.i.d. random variables (“masses”) at the vertices of an infinite, vertex-transitive graph, and redistributes mass by a local toppling rule in an attempt to make all masses ≤  1. The process stabilizes almost surely if m < 1 and it almost surely does not stabilize if m > 1, where m is the mean mass per vertex. The main result of this paper is that in the critical case m = 1, if the initial masses have finite variance, then the process almost surely does not stabilize. To give quantitative estimates on a finite graph, we relate the number of topplings to a discrete bi-Laplacian Gaussian field.