About uniformly Lindelöf spaces

The idea of Lindelöfness is one of the most important in General Topology. There have been some variants in defining uniformly Lindelöfness of uniform spaces. For example, uniform A-Lindelöfness in the sense of L.V. Aparina [1], uniform B-Lindelöfness in the sense of A.A. Borubaev [2], uniform I-Lindelöfness in the sense of D.R. Isbell [5]. In this paper we propose a new approach to the definition of a uniform analogue of Lindelöfness. We introduce and study uniformly Lindelöf spaces.

Some notes on complex symmetric operators

In this paper we show that every conjugation C on the Hardy-Hilbert space H 2 is of type C = T * 𝒥T, where T is an unitary operator and 𝒥 f ( z ) = f ( z ¯ ) ¯ \mathcal{J}f\left( z \right) = \overline {f\left( {\bar z} \right)} with f ∈ H 2. Moreover we prove some relations of complex symmetry between the operators T and |T|, where T = U |T| is the polar decomposition of bounded operator T ∈ ℒ(ℋ) on the separable Hilbert space ℋ.

On the non existence of periodic orbits for a class of two dimensional Kolmogorov systems

In this paper we characterize the integrability and the non-existence of limit cycles of Kolmogorov systems of the form x ′ = x ( B 1 ( x , y ) ln | A 3 ( x , y ) A 4 ( x , y ) | + B 3 ( x , y ) ln | A 1 ( x , y ) A 2 ( x , y ) | ) , y ′ = y ( B 2 ( x , y ) ln | A 5 ( x , y ) A 6 ( x , y ) | + B 3 ( x , y ) ln | A 1 ( x , y ) A 2 ( x , y ) | ) \matrix{{x' = x\left( {{B_1}\left( {x,y} \right)\ln \left| {{{{A_3}\left( {x,y} \right)} \over {{A_4}\left( {x,y} \right)}}} \right| + {B_3}\left( {x,y} \right)\ln \left| {{{{A_1}\left( {x,y} \right)} \over {{A_2}\left( {x,y} \right)}}} \right|} \right),} \hfill \cr {y' = y\left( {{B_2}\left( {x,y} \right)\ln \left| {{{{A_5}\left( {x,y} \right)} \over {{A_6}\left( {x,y} \right)}}} \right| + {B_3}\left( {x,y} \right)\ln \left| {{{{A_1}\left( {x,y} \right)} \over {{A_2}\left( {x,y} \right)}}} \right|} \right)} \hfill \cr } where A 1 (x, y), A 2 (x, y), A 3 (x, y), A 4 (x, y), A 5 (x, y), A 6 (x, y), B 1 (x, y), B 2 (x, y), B 3 (x, y) are homogeneous polynomials of degree a, a, b, b, c, c, n, n, m respectively. Concrete example exhibiting the applicability of our result is introduced.

Popoviciu’s type inequalities for h-MN-convex functions

In this work, Popoviciu type inequalities for h-MN-convex functions are proved. Some direct examples are pointed out.

Applications of differential subordination for certain subclasses of meromorphically univalent functions defined by rapid operator

In this work, we investigate some applications of differential subordination for the class of meromorphic univalent functions defined by rapid operator and obtained coefficient bounds, integral representations, weighted and arithmetic mean for the class Σ(A, B, µ, θ).

Common fixed point theorems in complex valued non-negative extended b-metric space

We introduce complex valued non-negative extended b-metric spaces and establish new fixed point results for mappings under some rational contractions. Our idea improves and extends corresponding fixed point theorems in the setting of b-metric, extended b-metric and classical metric spaces. Nontrivial examples are provided to support the hypotheses and usefulness of the main result obtained herein.

New solvability condition of 2-d nonlocal boundary value problem for Poisson’s operator on rectangle

Differential and difference interpretations of a nonlocal boundary value problem for Poisson’s equation in open rectangular domain are studied. New solvability conditions are obtained in respect of existence, uniqueness and a priori estimate of the classical solution. Second order of accuracy difference scheme is presented.

Time series analysis of radiant heat using 75 hours VIIRS satellite day and night band nightfire data

The nightfires illuminated on the earth surface are caught by the satellite. These are emitted by various sources such as gas flares, biomass burning, volcanoes, and industrial sites such as steel mills. Amount of nightfires in an area is a proxy indicator of fuel consumption and CO2 emission. In this paper the behavior of radiant heat (RH) data produced by nightfire is minutely analyzed over a period of 75 hour; the geographical coordinates of energy sources generating these values are not considered. Visible Infrared Imaging Radiometer Suite Day/Night Band (VIIRS DNB) satellite earth observation nightfire data were used. These 75 hours and 28252 observations time series RH (unit W) data is from 2 September 2018 to 6 September 2018. The dynamics of change in the overall behavior these data and with respect to time and irrespective of its geographical occurrence is studied and presented here. Different statistical methodologies are also used to identify hidden groups and patterns which are not obvious by remote sensing. Underlying groups and clusters are formed using Cluster Analysis and Discriminant Analysis. The behavior of RH for three consecutive days is studied with the technique Analysis of Variance. Cubic Spline Interpolation and merging has been done to create a time series data occurring at equal minute time interval. The time series data is decomposed to study the effect of various components. The behavior of this data is also analyzed in frequency domain by study of period, amplitude and the spectrum.

Influence of cross diffusions on natural convection flow through annulus region with Navier slip and convective boundaries

In this manuscript we present the influence of cross diffusions on incompressible natural convection laminar flow between concentric cylinders with slip and convective boundaries. In addition, the first order chemical reaction is also considered. The governing equations with boundary conditions are transformed to a non - dimensional form with suitable transformations. Homotopy Analysis Method (HAM) is used to solve the system of equations. The influence of the various parameters like Slip, Dufour, Soret, chemical reaction parameters and the Biot number on velocity, temperature and concentration are investigated and presented through plots. It is found from this study that the influence of slip parameter and Biot number, the velocity and temperature profiles increase, while there is a reverse tendency under the effect of chemical reaction parameter.

A modified proximal point algorithm for solving variational inclusion problem in real Hilbert spaces

The purpose of this paper is to use a modified proximal point algorithm for solving variational inclusion problem in real Hilbert spaces. It is proven that the sequence generated by the proposed iterative algorithm converges strongly to the common solution of the convex minimization and variational inclusion problems.