53 research outputs found
Reply to "Comment on 'Inflation with a graceful exit and entrance driven by Hawking radiation' "
No full textThe Comment [J. T. Firouzjaee, preceding Comment, Phys. Rev. D 89, 068301 (2014)] raises two points in regard to our paper [S. K. Modak and D. Singleton, Phys. Rev. D 86, 123515 (2012)]. The first is that one cannot use the tunneling picture to obtain the temperature and particle production rate in the Friedman-Robertson-Walker space-time. The second comment raised by Firouzjaee is that the Hawking-like radiation model for inflation presented in [Modak and Singleton; S. K. Modak and D. Singleton, Int. J. Mod. Phys. D 21, 1242020 (2012)] is inconsistent with the observed scalar and tensor perturbation spectrum. We show that the first comment is beside the point-we do not use the tunneling method in our papers [Modak and Singleton; Modak and Singleton]. The second criticism by Firouzjaee comes from the author evaluating quantities at different times-he evaluates the parameters of our model at the beginning of inflation and then compares this with the scalar and tensor perturbations evaluated at the horizon exit point.From Physical Review D, Vol.89(6), 68302, available online: http://dx.doi.org/10.1103/PhysRevD.89.068302. Copyright ©2014 by American Physical Society.Publisher version: https://doi.org/10.1103/PhysRevD.89.06830
Originality for Copyright Protection in Literary Works: After EBC v DB Modak
No full text266-276Originality, can be termed as the grund norm (the basic norm) for copyrightability. However, no one-size-fits-all formula
is adopted by countries on this aspect, and this article first explores the position and benchmarks to determine original
literary work (because even for different ‘works’ the criteria differs). Pursuant to this inquiry of identifying the ambit of the
respective thresholds, the Indian perspective is analysed with special emphasis on the decision delivered by Indian Supreme
Court in DB Modak. The judgement is critiqued to identify lacunae and absurdity in determining the law laid down and its
application in the factual matrix. Finally, subsequent Indian decisions are looked upon by the author to find out the
underlying approach by the courts wrt interpretation of DB Modak and what common threads emerge from them
Minimal spaces with a mathematical structure
No full textAbstractThis paper will discuss, grill topological space which is not only a space for obtaining a new topology but generalized grill space also gives a new topology. This has been discussed with the help of two operators in minimal spaces
New operators in ideal topological spaces and their closure spaces
No full textIn this paper, we introduce two operators associated with ψ* and *ψ operators in ideal topological spaces and discuss the properties of these operators. We give further characterizations of Hayashi-Samuel spaces with the help of these two operators. We also give a brief discussion on homeomorphism of generalized closure spaces which were induced by these two operators
µ -k -Connectedness in GTS
No full textopen sets and µ -β -open sets in a GTS (X, µ). By using the µ -σ -closure, µ -π -closure, µ -α -closure and µ -β -closure in (X, µ), we introduce and investigate the notions µ -k -separated sets and µ -k -connected sets in (X, µ)
Algebra of frontier points via semi-kernels
No full textIn topological spaces, the study of interior and closure of a set are renowned concepts where the interior is defined as the union of open sets and the closure is defined as the intersection of closed sets. In literature, it is also a significant study while a set is defined as the intersection of open sets, and the union of closed sets. These respective ideas are known as the kernel of a set and its complementary function. Utilizing these ideas, some authors have introduced various kinds of results in topological spaces. Some mathematicians have extended these concepts via Levine’s semi-open sets to semi-kernel and its complementary function. The study of these notions is also a remarkable part of the field of topological spaces as the collection of semi-open sets does not form a topology again. In this paper, we have taken the semi-kernel and its complementary function into account to introduce new types of frontier points. After that we have studied and presented several characterizations of these new types of frontiers and established relationships among them. Finally, we have shown that semi-homeomorphic images of these new types of frontiers are invariant
Set operators and associated functions
No full textThe study of two operators local function and the set operator
ψ
on the ideal topological spaces are likely to be same to the study of closure and interior operator of the topological spaces. However, they are not exactly equal with the interior and closure operator of the topological spaces. In this context, we introduce two new set operators on the ideal topological spaces. Detail properties of these two operators are the part of this article. Furthermore, the operators interior (resp.
ψ
) and closure (local function) obey the relation
I
n
t
(
A
)
= X \
C
l
(X \ A) (resp.
ψ
(A) = X \(X \A)
∗
)
. We search the general method of these relations, through this manuscript.Trdizi
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