Exponential stability of the solutions of singularly perturbed systems with impulse effect

AbstractIn the present paper the exponential stability of the solutions of singularly perturbed systems with impulse effect is investigated. In order to obtain the main results the comparison method and piecewise continuous auxiliary functions which are analogues of Lyapunov's functions are used

Exponential stability of the solutions of the initial-value problem for systems with impulse effect

AbstractIn the present paper conditions have been found under which the exponential stability of a given solution of a system with impulse effect follows from the exponential stability of the respective system in variations

Advancing biological understanding and therapeutics discovery with small-molecule probes

Small-molecule probes can illuminate biological processes and aid in the assessment of emerging therapeutic targets by perturbing biological systems in a manner distinct from other experimental approaches. Despite the tremendous promise of chemical tools for investigating biology and disease, small-molecule probes were unavailable for most targets and pathways as recently as a decade ago. In 2005, the NIH launched the decade-long Molecular Libraries Program with the intent of innovating in and broadening access to small-molecule science. This Perspective describes how novel small-molecule probes identified through the program are enabling the exploration of biological pathways and therapeutic hypotheses not otherwise testable. These experiences illustrate how small-molecule probes can help bridge the chasm between biological research and the development of medicines but also highlight the need to innovate the science of therapeutic discovery

First measurement of Ωc0 production in pp collisions at s=13 TeV

The inclusive production of the charm–strange baryon 0 c is measured for the first time via its hadronic √ decay into −π+ at midrapidity (|y| <0.5) in proton–proton (pp) collisions at the centre-of-mass energy s =13 TeV with the ALICE detector at the LHC. The transverse momentum (pT) differential cross section multiplied by the branching ratio is presented in the interval 2 < pT < 12 GeV/c. The pT dependence of the 0 c-baryon production relative to the prompt D0-meson and to the prompt 0 c-baryon production is compared to various models that take different hadronisation mechanisms into consideration. In the measured pT interval, the ratio of the pT-integrated cross sections of 0 c and prompt + c baryons multiplied by the −π+ branching ratio is found to be larger by a factor of about 20 with a significance of about 4σ when compared to e+e− collisions

Elliptic flow of charged particles at midrapidity relative to the spectator plane in Pb–Pb and Xe–Xe collisions

Measurements of the elliptic flow coefficient relative to the collision plane defined by the spectator neutrons v2{ SP} in collisions of Pb ions at center-of-mass energy per nucleon–nucleon pair √ 2.76 TeV and Xe ions at √ sNN = sNN =5.44 TeV are reported. The results are presented for charged particles produced at midrapidity as a function of centrality and transverse momentum for the 5–70% and 0.2–6 GeV/c ranges, respectively. The ratio between v2{ SP} and the elliptic flow coefficient relative to the participant plane v2{4}, estimated using four-particle correlations, deviates by up to 20% from unity depending on centrality. This observation differs strongly from the magnitude of the corresponding eccentricity ratios predicted by the TRENTo and the elliptic power models of initial state fluctuations that are tuned to describe the participant plane anisotropies. The differences can be interpreted as a decorrelation of the neutron spectator plane and the reaction plane because of fragmentation of the remnants from the colliding nuclei, which points to an incompleteness of current models describing the initial state fluctuations. A significant transverse momentum dependence of the ratio v2{ SP}/v2{4} is observed in all but the most central collisions, which may help to understand whether momentum anisotropies at low and intermediate transverse momentum have a common origin in initial state f luctuations. The ratios of v2{ SP} and v2{4} to the corresponding initial state eccentricities for Xe–Xe and Pb–Pb collisions at similar initial entropy density show a difference of (7.0 ±0.9)%with an additional variation of +1.8% when including RHIC data in the TRENTo parameter extraction. These observations provide new experimental constraints for viscous effects in the hydrodynamic modeling of the expanding quark–gluon plasma produced in heavy-ion collisions at the LHC

On the asymptotic equivalence of systems with impulse effect

AbstractIn the present paper sufficient conditions for asymptotic equivalence and restricted asymptotic equivalence of a linear system of differential equations with impulse effect and its respective perturbed non-linear system are found

Convergence to a constant of the solutions of differential equations with impulse effect

AbstractThis paper examines the necessary and sufficient conditions for which the solutions of a system with impulse effect tend exponentially to a constant as t → ∞

Stability under persistent disturbances for systems with impulse effect

AbstractProblems concerning the stability of the solution of systems of ordinary differential equations with impulse effect under persistent disturbances are investigated for the first time. Definitions for stability and unstability of the system considered are introduced. The main results are formulated in two theorems. In the proofs of the theorems a new analogue of the Gronwall-Belmann inequality for piecewise continuous functions is applied

Sufficient conditions for oscillation of the solutions of a class of impulsive differential equations with advanced argument

Sufficient conditions for oscillation of the solutions of first order linear impulsive differential equations with advanced argument are found