We study the solvability of special partial differential relations of the form Du(x) ∈ K for u ∈ W (Ω;R), where Ω ⊂ R is a bounded domain, Du(x) is the Jacobi matrix of u, and K is a given set of m × n matrices. In this note, we present some results obtained in the paper [16] on the W -reduction principles and a general existence theorem that generalize the similar reduction principles for Lips...

1 The general problem class We consider on the interval (−π, π) the singular non-symmetric differential equation Lu := iε d dx f (x) du dx + i du dx = λu, (1.1) in which f is a 2π-periodic function having the following properties: f (x + π) = −f (x) , f (−x) = −f (x) ; (1.2) * We are grateful to Brian Davies for attracting our interest to the problem, and for numerous useful discussions. We als...

— We study a nonlinear Neumann boundary value problem associated to a nonhomogeneous differential operator. Taking into account the competition between the nonlinearity and the bifurcation parameter, we establish sufficient conditions for the existence of nontrivial solutions in a related Orlicz–Sobolev space. Résumé. — On étudie un problème aux limites de Neumann associé à un opérateur différe...

Fluoresing photography has become a prominent branch in opthalmology. During the last few years, it gives us dynamic infor-of circulation of the EYE and its pathologieal disorders.By passing the fluoresein through the retinal and choroidal vessels we are able to record the different typesand stages of disease which these are not exactly diagno-sed by ophthalmoscopy and founds photography.By flu...

Since the introduction of Dale's principle of "one neuron releases one transmitter at all its synapses," a growing number of exceptions to this principle have been identified. While the concept of neurotransmitter co-release by a single neuron is now well accepted, the specific synaptic circuitry and functional advantage of co-neurotransmission remain poorly understood in general. Here we repor...

We study the phase space of Chazy’s equation. 0. Main results In 1979, K. Okamoto constructed the spaces of initial conditions of Painlevé equations, which can be considered as the parametrized spaces of all solutions, including the meromorphic solutions (see [2, 3, 4, 5]) In 1910, Chazy studied Painlevé type equation with third order (see [1]) explicitly given by du dt3 = 2u du dt2 − 3 ( du dt...

This article discusses a conjectural description of the Lie algebra of the differential Galois group attached to a linear differential equation as being the smallest algebraic Lie algebra whose reduction mod p contains, for almost all p, the p-curvature of the reduction mod p of the differential equation in question. RESUME. On discute une description conjecturale de Falgebre de Lie du groupe d...

Arainfall simulator for 5 10 mplotswasdesignedand testedwithin theEMIRE(EtudeetModeÂlisationde l'Infiltration, du Ruissellement et de l'Erosion) program. The simulator is intended to be used in the field and to reproduce natural tropical rain storms. The simulator is composed of fixed stand pipes. The nozzle (Spraying SystemsCo. 1H106SQ)mounted on the top of the pipes sprays square areas. At a ...

1. Problem and its background. Consider a C differential P(z)dxdy (z = x+iy) on an open Riemann surface R with P(z)*t0. We denote by PX(R) the set of C solutions on R of the elliptic equation Au=Pu, or more precisely, of d*du(z)—u(z)P(z)dxdy, with a certain property X. For P = 0 we use the traditional notation HX instead of OX. Let Opx be the set of pairs (R} P) such that PX(R) reduces to const...