$$\mathcal {H}^+$$-multivalued contractions and their application to homotopy theory

Kikkawa and Suzuki (Nonlinear Anal 69:2942–2949, 2008) and Kikkawa and Suzuki (Fixed Point Theory Appl, 2008, Art. ID 649749) proved some fixed point results that are generalizations of Kannan’s, Nadler’s and Suzuki’s fixed point theorems. Here, we present fixed point results of this kind for multivalued mappings in the setting of \(\mathcal {H}^+\)-metric spaces. The theorems provided allow upgrading of some known results which is shown by examples. Moreover, we give a homotopy result as an application of our main theorem.     

Meir–Keeler-type conditions in abstract metric spaces

Various Meir–Keeler-type conditions for mappings acting in abstract metric spaces are presented and their connections are discussed. Results about associated symmetric spaces, obtained in [S. Radenovi?, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (2011), 38–50] are used to show that the regularity condition for the underlying cone can be dropped in some fixed point results that have appeared recently.     

Intercompany Study to Evaluate the Robustness of Capillary Isoelectric Focusing Technology for the Analysis of Monoclonal Antibodies

Interlaboratory comparisons are essential to bringing emerging technologies into biopharmaceutical industry practice and regulatory acceptance. As a result, an international team including 12 laboratories from 10 independent biopharmaceutical companies in the United States and Switzerland was formed to evaluate the precision and robustness of capillary isoelectric focusing (CIEF) to assess the charge heterogeneity of monoclonal antibodies. The different laboratories determined the apparent pI and the relative distribution of the charge isoforms of a representative monoclonal antibody (rMAb) sample using the same CIEF method. Statistical evaluation of the data was performed to determine within and between-laboratory consistencies and outlying information. The apparent pI data generated for each charge variant peak showed very good precision between laboratories with percentage of RSD values of ??0.5%. Similarly, the percentage of RSD for the rMAb charge variants percent peak area values are ??4.4% across different laboratories with different analysts using different lots of ampholytes and multiple instruments. Taken together, these results validate the appropriate use of CIEF in the biopharmaceutical industry in support of regulatory submissions.     

Characterization of carboxylic acids in atmospheric aerosols using hydrophilic interaction liquid chromatography tandem mass spectrometry

A sensitive hydrophilic interaction liquid chromatography/electrospray ionization mass spectrometry (HILIC/ESI-MS/MS) method was developed for determination of selected aliphatic (i.e. malonic, succinic, glutaric, adipic, pimelic, suberic, azelaic, maleic, fumaric, glycolic and pyruvic acid), alicyclic (i.e. cis-pinonic and pinic acid) and aromatic (i.e. trimesic, phthalic acid and its isomers) carboxylic acids. Analytes were separated on an amide column using a gradient elution with a 10mM constant ionic strength mobile phase containing acetonitrile and aqueous ammonium acetate buffer (pH 5.0). The influence of the buffer type, pH, polar modifier and temperature on analyte retention under HILIC was studied. Static sonication-assisted solvent extraction was optimized for sample preparation prior to analysis. The recoveries obtained were higher than 90% for most analytes. The method was proven to be sensitive with limits of detection ranged from 0.03 to 16.0 μg/L in selected reaction monitoring mode (SRM). The repeatability and intermediate precision of the method, expressed as RSD (%) of the peak area ratio between analytes and their internal standards were generally lower than 5%. The method was successfully applied for determination of the studied acids in samples of ambient aerosol particles. A big advantage of the new method is also its ability to detect and separate the isobaric compounds of the selected carboxylic acids. Our results demonstrate that the method is specific and sensitive for the determination of a wider range of polar carboxylic acids at low concentrations in complex samples of aerosol particles.     

A probabilistic approach to a non‐local quadratic form and its connection to the Neumann boundary condition problem

In this paper we look at a probabilistic approach to a non‐local quadratic form that has lately attracted some interest. This form is related to a recently introduced non‐local normal derivative. The goal is to construct two Markov processes: one corresponding to that form and the other which is related to a probabilistic interpretation of the Neumann problem. We also study the Dirichlet‐to‐Neumann operator for non‐local operators.     

On the Generalized Strongly Nil-Clean Property of Matrix Rings

Let R be an associative unital ring and not necessarily commutative.We analyze conditions under which every n × n matrix A over R is expressible as a sum A =E1 +…+ Es + N of (commuting) idempotent matrices Ei and a nilpotent matrix N.