The aim of this paper is to introduce and study a new class of Bazilevič p-valent function of order β by using the subordination concept between this function and a generalized derivative operator. Some interesting properties are also obtained

The theory of analytic functions and more specific p-valent functions, is one of the most fascinating topics in one complex variable. There are many remarkable theorems dealing with extremal problems for a class of p-valent functions on the unit disk U. Recently, many researchers have shown great interests in the study of differential operator. The objective of this paper is to define a new generalized derivative operator of p-valent analytic functions of fractional power in the open unit disk U. This operator generalized some well-known operators studied earlier, we mention some of them in the present paper. Motivation by the generalized derivative operator; we introduce and investigate two new subclasses of starlike p-valent analytic functions of fractional power with positive coefficients and starlike p-valent analytic functions of fractional power with negative coefficients, respectively. In addition, a sufficient condition will be obtained. Some corollaries are also pointed out. Moreover, we determine the extreme points of functions belong to the class.

Seed size is a key functional trait that affects plant fitness at the seedling stage and may

vary greatly with species fruit size, growth form and fecundity. Using structural equation

modelling (SEM) and correlated trait evolution analysis, we investigated the interaction network

between seed size and fecundity, postfire regeneration strategy, fruit size, plant height

and serotiny (on-plant seed storage) among 82 species of the woody shrub genus, Hakea,

with a wide spectrum of seed sizes (2–500 mg). Seed size is negatively correlated with fecundity,

while fire-killed species (nonsprouters) produce more seeds than resprouters

though they are of similar size. Seed size is unrelated to plant height and level of serotiny

while it scales allometrically with fruit size. A strong phylogenetic signal in seed size revealed

phylogenetic constraints on seed size variation in Hakea. Our analyses suggest a

causal relationship between seed size, fecundity and postfire regeneration strategy in

Hakea. These results demonstrate that fruit size, fecundity and evolutionary history have

had most control over seed size variation among Hakea species.

The aim of the article is to study a sufficient condition for the classes of starlike and convex harmonic univalent functions with respect to k- symmetric points. The necessary condition for f to be in the classes will be studied. In addition, growth bounds for functions will also be given.

In this paper, we study and introduce the majorization properties of a new class of analytic p-valent functions of complex order defined by the generalized hypergeometric function. Some known consequences of our main result will be given. Moreover, we investigate the coefficient

estimates for this class.

In the present investigation, new subclasses of analytic functions in the open unit disk which are defined using generalized derivative operator are introduced. Several interesting properties of these classes are obtained.

With the rapid development of the Internet and communication networks, the confidentiality of digital

images transmitted over public networks must be preserved by using encryption techniques. Advanced

Encryption Standard (AES) is one of the most commonly used encryption algorithms at present. Although

AES has several advantages, such as security in data encryption, it also has a number of drawbacks, such as

high computations, pattern problems when used for encrypting images, and fixed S-box weak points. This

paper proposes a method that overcomes the fixed S-box weak points and improves the performance of

AES when used for encrypting images, particularly when the image data are large. In addition, the

MixColumn stage is replaced by chaotic mapping and XOR operation to reduce the high computations in

MixColumn transform. The proposed method is tested on several images, and the results show that the

proposed method efficiently generated cipher images with very low correlation coefficients of adjacent

pixels and provided better encryption speed and high security as a result of the dependence of the S-box on

the key characteristics of the chaotic system

We provide a validation of a formal approximate solution to the problem of the evolution of a slowly varying harvested logistic population. Using a contraction mapping proof, we show that the initial value problem for the population has an exact solution lying in an appropriately small neighbourhood of this approximate solution, under quite general conditions.

Steganographic techniques with varying degrees of embedding capacity, perceptual transparency, and security are presented. These techniques have been developed to protect privileged or confidential information restricted to public access and to replace cryptography methods. In this study, three embedding algorithms, namely, least significant bit insertion, bit-plane complexity segmentation, and enhanced version of pixel value difference (EPVD) were implemented and analyzed in terms of the main steganography issues (payload, invisibility, and security) using a different proper performance metrics. This study was motivated by the minimal research focus accorded to hiding data in compression domain for the class of video-based embedding methods. Therefore, analyzing steganographic algorithms is generally based on hiding information in the quantized AC-Coefficients of the frames during the MPEG-2 compression process. Simulation results reveal that EPVD provides better embedded payload and acceptable visual quality, but lower PSNR value.