Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found

Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments

* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.Sufficient conditions are obtained for the existence of local integral manifolds of autonomous systems of differential equations with impulses at fixed moments. In case of perturbations of the nonlinear part an estimate of the difference between the manifolds is obtained

Existence and Exponential Stability of Positive Almost Periodic Solutions for a Model of Hematopoiesis

By employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.The research of Juan J. Nieto has been partially supported by Ministerio de Educacion y Ciencia and FEDER, project MTM2007-61724S

Asymmetry of a complex gap near the Fermi level, determined from measurements of the thermopower in La₁₋xCaxMn₁₋yFeyO₃

The experimental data are analysed quantitatively with a percolation model using results of our recent investigations of the Shklovskii–Efros-like variable-range hopping conductivity in the same set of La₁₋xCaxMn₁₋yFeyO₃ samples with evidence for a soft Coulomb gap and a rigid gap in the density of states near the Fermi levelyesBelgorod State Universit

Critical behavior of magnetoresistance near the metal-insulator transition of La₀₇Ca₀₃MnO₃

The resistivity, ρ(T), of thin film and bulk samples of La₀₇Ca₀₃MnO₃ is investigated in magnetic fields between 0-10 T and temperatures between 10-340 K. Metallic resistivity, ρlt(T)=ρr+ρ2T2+ρ4.5T4.5, is observed well below the metal–insulator transition (MIT) temperature TMI. For T>TMI, the resistivity is governed by the Shklovskii-Efros variable-range hopping mechanism, giving View the MathML sourceyesBelgorod State Universit

Disorder in (Zn₁₋ₓMnₓ)₃As₂ and its consequences on impurity conduction and magnetic properties

Special attention is paid to the remanent disorder at temperatures much below the order-disorder phase hansition temperature Tph. Dependences of Tph and the activation energy of hopping conductivity on composition are analysedyesBelgorod State Universit

Variable-range hopping conductivity in La₁₋ₓCaₓMnO₃

The temperature dependence of the local activation energy, Eloc (T ) = d ln ρ(T )/d(kT )⁻¹ gives evidence for a variable-range hopping conductivity over states of the Coulomb gapyesBelgorod State Universit

Simultaneous co-localized super-resolution fluorescence microscopy and atomic force microscopy: combined SIM and AFM platform for the life sciences

Correlating data from different microscopy techniques holds the potential to discover new facets of signaling events in cellular biology. Here we report for the first time a hardware set-up capable of achieving simultaneous co-localized imaging of spatially correlated far-field super-resolution fluorescence microscopy and atomic force microscopy, a feat only obtained until now by fluorescence microscopy set-ups with spatial resolution restricted by the Abbe diffraction limit. We detail system integration and demonstrate system performance using sub-resolution fluorescent beads and applied to a test sample consisting of human bone osteosarcoma epithelial cells, with plasma membrane transporter 1 (MCT1) tagged with an enhanced green fluorescent protein (EGFP) at the N-terminal.Ana I. Gomez Varela wishes to acknowledge support from the Xunta de Galicia, Conselleria de Cultura, Educacion e Ordenacion Universitaria e da Conselleria de Economia, Emprego e Industria (Programa de axudas de apoio a etapa de formacion posdoutoral 2017). Adelaide Miranda and Pieter De Beule acknowledge financial support from Norte's Regional Operational Programme 2014-2020-Norte2020 (NORTE-01-0145-FEDER-000019). Sandra Paiva and Rosana Alves thank Fulbright Commission Portugal and Luso-American Development Foundation (FLAD) for their financial support to perform research work at UC Berkeley, California, USA. We thank the U.S. Embassy in Portugal for supporting David Drubin's visit to Portugal. We thank Ann Fisher of the UC Berkeley Cell Culture Facility for help with cell culture. We thank Dr. Kartoosh Heydari of the Cancer Research Lab Flow Cytometry Core Facility of UC Berkeley. Rosana Alves and Claudia Barata-Antunes are recipients of PhD fellowships from the Portuguese Foundation for Science and Technology (PD/BD/113813/2015 and PD/BD/135208/2017, respectively). The authors want to thank Nikon and Izasa Scientific for their support to the experiment by providing a N SIM-E microscope set-up on loan. We also gratefully acknowledge Dr. Kees van der Oord from Nikon Instruments Europe B.V. for his assistance with the SIM microscope as well as Paulo Madureira and Carlos Pitaes from IZASA Portugal and Jordi Recasens from IZASA Spain for their assistance with the integration of the SIM and AFM microscopes. Finally, we want to thank Benjamin Holmes for fruitful discussions and relentless support