3,106 research outputs found
S-I-convergence of sequences
In this article, we use the notions of a semi-open set and topological ideal, in order to define and study a new variant of the classical concept of convergence of sequences in topological spaces, namely, the S-I-convergence. Some basic properties of S-I-convergent sequences and their preservation under certain types of functions are investigated. Also, we study the notions related to compactness and cluster points by using semi-open sets and ideals. Finally, we explore the Iconvergence of sequences in the cartesian product spac
Rough I-convergence
In this work, using the concept of I-convergence and using the concept of rough convergence, we introduced the notion of rough I-convergence and the set of rough I-limit points of a sequence and obtained two rough I-convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relations between the set of I-cluster points and the set of rough I-limit points of a sequenc
Migration and Growth of Protoplanetary Embryos I: Convergence of Embryos in Protoplanetary Disks
According to the core-accretion scenario, planets form in protostellar disks
through the condensation of dust, coagulation of planetesimals, and emergence
of protoplanetary embryos. At a few AU in a minimum mass nebula, embryos'
growth is quenched by dynamical isolation due to the depletion of planetesimals
in their feeding zone. However, embryos with masses () in the range of a
few Earth masses () migrate toward a transition radius between the
inner viscously heated and outer irradiated regions of their natal disk. Their
limiting isolation mass increases with the planetesimals surface density. When
, embryos efficiently accrete gas and evolve into cores of
gas giants. We use numerical simulation to show that, despite streamline
interference, convergent embryos essentially retain the strength of
non-interacting embryos' Lindblad and corotation torque by their natal disks.
In disks with modest surface density (or equivalently accretion rates), embryos
capture each other in their mutual mean motion resonances and form a convoy of
super Earths. In more massive disks, they could overcome these resonant
barriers to undergo repeated close encounters including cohesive collisions
which enable the formation of massive cores.Comment: 9 pages, 6 figures, accepted for publication in Ap
Tracking eigenvalues to the frontier of moduli space I: Convergence and spectral accumulation
We study the limiting behavior of eigenfunctions/eigenvalues of the Laplacian
of a family of Riemannian metrics that degenerates on a hypersurface. Our
results generalize earlier work concerning the degeneration of hyperbolic
surfaces
I–Convergence of Arithmetical Functions
Let
n
>
1
be an integer with its canonical representation,
n
=
p
1
α
1
p
2
α
2
⋯
p
k
α
k
. Put
H
n
=
max
α
1
…
α
k
,
h
n
=
min
α
1
…
α
k
,
ω
n
=
k
,
Ω
n
=
α
1
+
⋯
+
α
k
,
f
n
=
∏
d
∣
n
d
and
f
∗
n
=
f
n
n
. Many authors deal with the statistical convergence of these arithmetical functions. For instance, the notion of normal order is defined by means of statistical convergence. The statistical convergence is equivalent with
I
d
–convergence, where
I
d
is the ideal of all subsets of positive integers having the asymptotic density zero. In this part, we will study
I
–convergence of the well-known arithmetical functions, where
I
=
I
c
q
=
A
⊂
N
:
∑
a
∈
A
a
−
q
<
+
∞
is an admissible ideal on
N
such that for
q
∈
0
1
we have
I
c
q
⊊
I
d
, thus
I
c
q
–convergence is stronger than the statistical convergence (
I
d
–convergence)
On rough and -convergence of sequences in normed linear spaces
In this paper, we have introduced first the notion of rough -convergence
in a normed linear space as an extension work of rough -convergence and then
rough -convergence in more general way. Then we have studied some
properties on these two newly introduced ideas. We also examined the
relationship between rough -convergence with both of rough -convergence
and rough -convergence.Comment: 13 page
ON ROUGH AND -CONVERGENCE OF SEQUENCES IN NORMED LINEAR SPACES
In this paper, we have introduced first the notion of rough -convergence in a normed linear space as an extension work of rough -convergence and then rough -convergence in more general way. Then we have studied some properties on these two newly introduced ideas. We also examined the relationship between rough -convergence with both of rough -convergence and rough -convergence
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