•In this paper, we have presented triple color image encryption and decryption.•Proposed cryptosystem provides security of multiple color image data in time domain, frequency domain and co-ordinate ...domain.•Time complexity and space complexity are less in comparison to others techniques.•Presented cryptosystem is appropriate for secure transmission of multiple images by single algorithm.
This paper proposes a new encryption and decryption method for triple color images using 2D multiple parameter fractional discrete Fourier transform (MPFrDFT) and 3D Arnold transform (AT). The proposed method converts three color images into Bayer images, which are considered as the three components of a color image. These three Bayer images are combined vertically and then baker chaotic map is applied to permute rows and columns and a similar process is applied in the horizontal combination, the image then obtained is considered as the complex valued image (CVI). Then apply 2D MPFrDFT on this CVI. The output of 2D MPFrDFT is separated into three components. Apply 3D AT into the three components and the output is considered as the three color components of the encrypted image. The experimental results and the security analysis of the proposed method are given to validate the feasibility and robustness of the method. The statistical analyses like histogram, correlation and entropy confirm the robustness of the proposed method against statistical attacks and experimental results show that the method is resistant to occlusion attack. The mathematical analysis shows that the brute force attack is not possible in proposed method.
Flavones are present in a variety of medicines and natural products and are important structural motif due to their unique mode of physiological action. Hence the structural importance of flavone ...moiety has elicited a great deal of interest in the field of organic synthesis and chemical biology to develop some new and improved synthesis of this molecular skeleton. Herein, we have described an up to date overview on the recent advances in the diverse synthetic methodologies of flavones. The review covers the basic conceptual and practical catalytic synthesis like carbonylative annulation, cyclodehydration, Suzuki Miyaura coupling, Heck coupling, green methodologies, metal catalyzed reactions, organocatalytic transformations, microwave irradiation, etc. which are significant for constructing flavone skeleton. This review will satisfy the expectations of readers who are interested in the development of the field and looking for an update. It will stimulate researchers to develop new and creative synthetic access to this heterocyclic system, which will be instrumental in the advancement of flavone chemistry.
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There appear to be multifunctional artefacts of a type such that none of their functions can be attributed only to some proper part of the artefact. I use two examples of allegedly multifunctional ...artefacts of this kind in what follows, one due to Lynne Rudder Baker (aspirin) and another of my own (a spork). The two examples are meant to make the same point. I discuss her aspirin example, since its discussion has entered the literature, but without its being dealt with satisfactorily. My example is, I believe, more intuitive than that of aspirin, which Baker introduced in her response to a challenge to her views, and so I will mostly rely on my example of a spork, especially at the end of the paper, to make my case. I argue that in at least those two cases, if the standard arguments for distinguishing between an object and what constitutes it are sound, an argument showing that what we might have taken to be a single multifunctional object is in fact a case of multiple single-function artefacts which collocate. Or almost. There is one further assumption needed for these cases, beyond what the constitution cases require, and I produce reasons for accepting that assumption.
Injective modules over the Jacobson algebra Abrams, Gene; Mantese, Francesca; Tonolo, Alberto
Canadian mathematical bulletin,
06/2021, Letnik:
64, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Abstract
For a field
K
, let
$\mathcal {R}$
denote the Jacobson algebra
$K\langle X, Y \ | \ XY=1\rangle $
. We give an explicit construction of the injective envelope of each of the (infinitely ...many) simple left
$\mathcal {R}$
-modules. Consequently, we obtain an explicit description of a minimal injective cogenerator for
$\mathcal {R}$
. Our approach involves realizing
$\mathcal {R}$
up to isomorphism as the Leavitt path
K
-algebra of an appropriate graph
$\mathcal {T}$
, which thereby allows us to utilize important machinery developed for that class of algebras.
•An iterative analytical solution involving generalized continued fractions.•Computation of the arbitrary composition of elements of the corresponding Lie groups.•Computation of the arbitrary ...composition of squeezing and rotation operators.•Computation of the time evolution operator for time-dependent quantum systems.•Solution extremely well suited for numerical calculations.
In this work we demonstrate new BCH-like relations involving the generators of the su(1,1), su(2) and so(2,1) Lie algebras. We use our results to obtain in a straightforward way the composition of an arbitrary number of elements of the corresponding Lie groups. In order to make a self-consistent check of our results, as a first application we recover the non-trivial composition law of two arbitrary squeezing operators. As a second application, we show how our results can be used to compute the time evolution operator of physical systems described by time-dependent hamiltonians given by linear combinations of the generators of the aforementioned Lie algebras.
In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of ...algebraic numbers and some tools from Diophantine approximation.
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