A difference method of solving the differential equation y' = h(t, y, y, y')

On the Equation Y

Does Lipschitz with Respect to x Imply Uniqueness for the Differential Equation y′ = f(x, y)?

Of course, the answer to the question posed in the title is no, in general, but, surprisingly enough, yes in a significant situation to be detailed later. This paper aims to bring to the attention of the widest possible mathematical audience an elementary result, based on the theorem of differentiation of inverse functions, which extends the applicability of uniqueness theorems. Loosely speakin...

Connections between C(X) and C(Y), where Y is a subspace of X

In this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $C(Y)$ and the set of prime $z$-ideals of $C(X)$ not containing $f$. Moreover, c...

-Y, Y loss in leukemia

Note Loss of the Y chromosome from individual metaphases is common in metaphase cells from both PHAstimulated lymphocytes and spontaneously dividing bone marrow cells. The frequency of Y loss is greater in older men, and the size of the 45,X,-Y cell population probably increases gradually with advancing age. (In females, a corollary loss of one X chromosome also occurs with advancing age.) This...

local FMm,n-diffeomorphism f: Y → Y.

Let r, s, q,m, n ∈ N be such that s ≥ r ≤ q. Let Y be a fibered manifold with m-dimensional basis and n-dimensional fibers. All natural affinors on (J(Y,R)0) are classified. It is deduced that there is no natural generalized connection on (J(Y,R)0). Similar problems with (J(Y,R)0) instead of (J(Y,R)0) are solved.