ON CERTAIN POINTS RELATING TO CHOLERA.

On Certain Doubtful Points in the Pathology of Cholera

us in the treatment of cholera. With a strong share in this desire, I have been induced to give publicity to the following remarks and suggestions, in the hope that they may receive their full share of criticism, confident that if even they are found to exert no practical influence in themselves towards our knowedge of this important subject, jet that the discussion, which I am ambitious enough...

Cholera in Relation to Certain Physical Phenomena

On convergence of certain nonlinear Durrmeyer operators at Lebesgue points

The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators $ND_{n}f$ of the form $$(ND_{n}f)(x)=intlimits_{0}^{1}K_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{N}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% K_{n}left( x,t,uright) $ satisfies some suitable assumptions. Here we estimate the rate...

Rational Points on Certain Quintic Hypersurfaces

Let f(x) = x+ax+bx+cx ∈ Z[x] and consider the hypersurface of degree five given by the equation Vf : f(p) + f(q) = f(r) + f(s). Under the assumption b 6= 0 we show that there exists Q-unirational elliptic surface contained in Vf . If b = 0, a < 0 and −a 6≡ 2, 18, 34 (mod 48) then there exists Q-rational surface contained in Vf . Moreover, we prove that for each f of degree five there exists Q(i...

Rational Points on Certain Elliptic Surfaces

Let Ef : y 2 = x + f(t)x, where f ∈ Q[t] \ Q, and let us assume that deg f ≤ 4. In this paper we prove that if deg f ≤ 3, then there exists a rational base change t 7→ φ(t) such that there is a non-torsion section on the surface Ef◦φ. A similar theorem is valid in case when deg f = 4 and there exists t0 ∈ Q such that infinitely many rational points lie on the curve Et0 : y 2 = x + f(t0)x. In pa...