We are concerned with the structure of the operator corresponding to the Lax–Friedrichs method. At first, the phenomenae which may arise by the naive use of the Lax–Friedrichs scheme are analyzed. In particular, it turns out that the correct definition of the method has to include the details of the discretization of the initial condition and the computational domain. Based on the results of th...

Let X be a Banach space and T ? B(X). Cohen determined class of regular infinite matrices A = (ank) for which Ln := ?? k=1 ankTk converges strongly to an element invariant under T. In the present paper we study A-mean A-uniform ergodic type results when is matrix satisfying Cohen?s uniformity condition lim j k=j |an,k+1 ank| 0, uniformly in n.

In this note, we point out that the proximity condition proposed in [8] can be weakened. We reprove the “Proximity ⇒ Smoothness” theorem under the so-called weak proximity condition. This improvement is embarrassingly trivial; and appears to be just an artifact of the authors overlooking a detail during the writing of [8]. But this raises a question: the unnecessarily strong proximity condition...

is irreducible. Irreducibility here and throughout this paper refers to irreducibility over the rationals. Some condition, such as ja0j = janj = 1, on the integers aj is necessary; otherwise, the irreducibility of all polynomials of the form above would imply every polynomial inZ[x] is irreducible (which is clearly not the case). In this paper, we will mainly be interested in relaxing the condi...

Consider a $$d$$ -type supercritical branching process $$Z_n^i=(Z_n^i(1),\ldots,Z_n^i(d))$$ , $$n\geq 0$$ in an independent and identically distributed random environment $$\xi =(\xi_0,\xi_1,\ldots)$$ starting with one initial particle of type $$i$$ . In previous paper we have established Kesten–Stigum theorem for $$Z_n^i$$ which implies that any $$1\leq i,j\leq d$$ $$Z_n^i(j)/\mathbb E_\xi Z_n...

where the s{j are the partial sums of a double series EM»./> which remain bounded for all (i, j). The necessary and sufficient conditions for regularity of Norlund means in the case of such double series have been given by C. N. Moore in Theorem II of Chapter II of his book4 entitled Summable series and convergence factors which will be subsequently referred to as S.S.C.F. In the case where the...

An improved condition to come down from infinity for exchangeable coalescent processes with simultaneous multiple collisions of ancestral lineages is provided. For non-critical coalescents this leads to an improved necessary and sufficient condition for the coalescent to come down from infinity. An analog conjecture for the full class of exchangeable coalescents is presented. New examples of cr...

Let C?(E) be the graph C?-algebra of a row-finite E. We give complete description vertex sets gauge-invariant regular ideals C?(E). It is shown that when E satisfies condition (L), are class which preserve (L) under quotients. That is, we show if then ideal J?C?(E) necessarily gauge-invariant. Further, ideal, it C?(E)?J?C?(F), where F (L).

!! Ui // X The modules Mi are “restrictions“ or pullbacks of M along Ui → X, and are compatible in that if Mi,j is the pullback of Mi over Ui along Ui ×X Uj → Ui, then we have isomorphisms Mi,j ∼= Mj,i that satisfy a coherence condition known as the cocycle condition. We say that modules over affine schemes have the property of descent for a family {Ui → X} if any family of compatible modules M...