1,720,979 research outputs found
The Geodesics for Poincaré’s Half-Plane: a Nonstandard Derivation
No full textConstants of motion in Mechanics are usually inferred from groups of symmetry transformations of the given system, as, for example, a Lagrangian function that is time-invariant implies the conservation of energy. Here we wish to show that useful properties of a mechanical system can sometimes be deduced from a family of Noether-like transformations that are not inspired by any symmetry whatsoever. The sample system we concentrate on is the Lagrangian interpretation of Poincaré’s half plane of hyperbolic geometry, and the properties we will derive in a new way are the shape and the time parameterization of its geodesics
Time reversibility and energy conservation for Lagrangian systems with nonlinear nonholonomic constraints
No full textWhen is a nonholonomic Lagrangian system
time-reversible? We prove that a simple sufficient condition is
that (skipping over some minor technicalities) both the Lagrangian
and the set of the triples that
satisfy the constraints are invariant by exchange of into . Another question is: when is energy
conserved in a nonholonomic autonomous Lagrangian system?
A likewise easy sufficient condition is that the set of the
couples satisfying the constraints is a cone
with respect to~ (meaning that if is admissible
then is admissible too for all ).
Time-reversibility and energy conservation are independent
properties, in the sense that neither one implies the other.
Both properties hold at the same time for any autonomous system
with a ``natural'' Lagrangian and with constraints that are
homogenous in
Nonlocal constants of motion in Lagrangian Dynamics of any order
No full textWe describe a recipe to generate “nonlocal” constants of motion for ODE Lagrangian systems. As a sample application, we recall a nonlocal constant of motion for dissipative mechanical systems, from which we can deduce global existence and estimates of solutions under fairly general assumptions. Then we review a generalization to Euler–Lagrange ODEs of order higher than two, leading to first integrals for the Pais–Uhlenbeck oscillator and other systems. Future developments may include adaptations of the theory to Euler–Lagrange PDEs
Druzkowski matrix search and D-nilpotent automorphisms
No full textIn 1939 Keller conjectured that any polynomial mapping
f\colon\C^n\to\C^n with constant nonvanishing Jacobian determinant,
should be invertible. This open problem bears the name of Jacobian
conjecture. Druzkowski proved that cubic-linear mappings are
sufficient to decide the conjecture. For this important class we develop
an algorithm that translates the constant Jacobian condition into
algebraic equations in the matrix of parameters. We also single out a
natural special case of these conditions, that we call D-nilpotency.
The class of D-nilpotent matrices turns out to coincide with set of
matrices that are permutation-similar to upper-triangular matrices. The
corresponding cubic-linear maps are always invertible
Anti-VEGF Drugs Dynamics: Relevance for Clinical Practice
Full text linkBackground: A drug and disease assessment model was used to evaluate the impact of different treatment regimens on intravitreal ranibizumab, bevacizumab, aflibercept, and brolucizumab concentrations and the proportion of free vascular endothelial growth factor (VEGF) to total VEGF. Methods: A time-dependent mathematical model using Wolfram Mathematica software was used. The pharmacokinetic and pharmacodynamic data for anti-VEGFs were obtained from published reports. The model simulated drug concentration after single and multiple doses of ranibizumab, bevacizumab, aflibercept, and brolucizumab, and it extrapolated time-dependent intraocular free VEGF proportion values. Various fixed treatment regimens (q4, q8, q10, q12) were simulated and evaluated as candidates for clinical utilization. Results: Our mathematical model shows good correlation between intraocular VEGF proportion values and clinical data. Simulations suggest that each anti-VEGF agent would allow for distinct treatment intervals to keep the proportion of free VEGF under threshold levels. Regimens scheduling q8 ranibizumab, q8 bevacizumab, q12 aflibercept, and q10 brolucizumab administration permit to maintain the proportion of unbound VEGF below 0.001%. Conclusions: Fixed q8 ranibizumab, q8 bevacizumab, q12 aflibercept, or q10 brolucizumab regimens may produce adequate intraocular VEGF inhibition
Optical multi/demultiplexer device, optical wavelength selective filter and method of making filter
No full textOn cubic-linear polynomial mappings
No full textAbstractIn the field of the Jacobian conjecture it is well-known after Drużkowski that from a polynomial ‘cubic-homogeneous’ mapping we can build a higher-dimensional ‘cubic-linear’ mapping and the other way round, so that one of them is invertible if and only if the other one is. We make this point clearer through the concept of ‘pairing’ and apply it to the related conjugability problem: one of the two maps is conjugable if and only if the other one is; moreover, we find simple formulas expressing the inverse or the conjugations of one in terms of the inverse or conjugations of the other. Two nontrivial examples of conjugable cubic-linear mappings are provided as an application
Complete integrability for Hamiltonian systems with a cone potential
No full textAbstractIt is known that, if a point in Rn is driven by a bounded below potential V, whose gradient is always in a closed convex cone which contains no lines, then the velocity has a finite limit as time goes to +∞. The components of the asymptotic velocity, as functions of the initial data, are trivially constants of motion. We find sufficient conditions for these functions to be Ck (2 ⩽ k ⩽ + ∞) first integrals, independent and pairwise in involution. In this way we construct a large class of completely integrable systems. We can deal with very different asymptotic behaviours of the potential and we have persistence of the integrability under any small perturbation of the potential in an arbitrary compact set
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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