Current Issue : January-March
Volume : 2023
Issue Number : 1
Articles : 5 Articles
A system of generalized fuzzy random differential equations with boundary conditions
is investigated, which is a fuzzy version of a system of general random differential equations.
We first present random fixed point (RFP) theorems in fuzzy metric space (FM). In the sequel, we
define the operators that are of integral type. Furthermore, these operators are related to a part
of random differential equations (RDE). For the desired system with boundary conditions, we study
the suitable integral operators associated with a large family of random differential equations. Finally,
we prove the existence of a unique random solution (EURS)....
A recursive method based on successive computations of perimeters of inscribed
regular polygons for estimating π is formulated by employing the Pythagorean
theorem alone without resorting to any trigonometric calculations.
The approach is classical but the formulation of coupled recursion relations is
new. Further, use of infinite series for computing π is explored by an improved
version of Leibniz’s series expansion. Finally, some remarks with reference
to π are made on a relatively recently rediscovered Sumerian tablet
depicting geometric figures....
Fisher-Tippet-Gnedenko classical theory shows that the normalized maximum
of n iid random variables with distribution F belonging to a very wide
class of functions, converges in law to an extremal distribution H, that is determined
by the tail of F. Extensions of this theory from the iid case to stationary
and weak dependent sequences are well known from the work of Leadbetter,
Lindgreen and Rootzén. In this paper, we present a very simple class of
random processes that runs from iid sequences to non-stationary and strongly
dependent processes, and we study the asymptotic behavior of its normalized
maximum. More interesting, we show that when the process is strongly
dependent, the asymptotic distribution is no longer an extremal one, but a
mixture of extremal distributions. We present very simple theoretical and simulated
examples of this result. This provides a simple framework to asymptotic
approximations of extremes values not covered by classical extremal
theory and its well-known extensions....
In this paper, we consider operators arising in the modeling of renewable
systems with elements that can be in different states. These operators are
functional operators with non-Carlemann shifts and they act in Holder spaces
with weight. The main attention was paid to non-linear equations relating
coefficients to operators with a shift. The solutions of these equations were
used to reduce the operators under consideration to operators with shift, the
invertibility conditions for which were found in previous articles of the authors.
To construct the solution of the non-linear equation, we consider the
coefficient factorization problem (the homogeneous equation with a zero
right-hand side) and the jump problem (the non-homogeneous equation with
a unit coefficient). The solution of the general equation is represented as a
composition of the solutions to these two problems....
In this paper, our focus is to introduce and investigate a class of mappings
called M-asymmetric irresolute multifunctions defined between bitopological
structural sets satisfying certain minimal properties. M-asymmetric irresolute
multifunctions are point-to-set mappings defined using M-asymmetric semiopen
and semiclosed sets. Some relations between M-asymmetric semicontinuous
multifunctions and M-asymmetric irresolute multifunctions are
established. This notion of M-asymmetric irresolute multifunctions is analog
to that of irresolute multifunctions in the general topological space and, upper
and lower M-asymmetric irresolute multifunctions in minimal bitopological
spaces, but mathematically behaves differently....
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