scholarly journals Weighted Fractional-Order Transform Based on Periodic Matrix

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2073
Author(s):  
Tieyu Zhao ◽  
Yingying Chi
Keyword(s):  
Image Encryption ◽  
Fractional Order ◽  
Theoretical Framework ◽  
Security Risk ◽  
Linear Summation ◽  
Periodic Matrix ◽  
Multiple Parameter ◽  
The Matrix ◽  
Definition Of

Tao et al. proposed the definition of the linear summation of fractional-order matrices based on the theory of Yeh and Pei. This definition was further extended and applied to image encryption. In this paper, we propose a reformulation of the definitions of Yeh et al. and Tao et al. and analyze them theoretically. The results show that many weighted terms are invalid. Therefore, we use the proposed reformulation to prove that the effective weighted terms depend on the period of the matrix. This also shows that the image encryption methods based on the weighted fractional-order transform will lead to the security risk of key invalidation. Finally, our hypothesis is verified by the unified theoretical framework of multiple-parameter discrete fractional-order transforms.

scholarly journals Key Validity Using the Multiple-Parameter Fractional Fourier Transform for Image Encryption

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1803
Author(s):  
Tieyu Zhao ◽  
Yingying Chi
Keyword(s):  
Fourier Transform ◽  
Image Encryption ◽  
Fractional Fourier Transform ◽  
Reference Value ◽  
Basis Functions ◽  
Point Of View ◽  
Security Risk ◽  
Multiple Parameter ◽  
Eigen Decomposition ◽  
Weighted Type

As a symmetric encryption algorithm, multiple-parameter fractional Fourier transform (MPFRFT) is proposed and applied to image encryption. The MPFRFT with two vector parameters has better security, which becomes the main technical means to protect information security. However, our study found that many keys of the MPFRFT are invalid, which greatly reduces its security. In this paper, we propose a new reformulation of MPFRFT and analyze it using eigen-decomposition-type fractional Fourier transform (FRFT) and weighted-type FRFT as basis functions, respectively. The results show that the effective keys are extremely limited. Furthermore, we analyze the extended encryption methods based on MPFRFT, which also have the security risk of key invalidation. Theoretical analysis and numerical simulation verify our point of view. Our discovery has important reference value for a class of generalized FRFT image encryption methods.

Feminist Interpretations of Action and the Public in Hannah Arendt’s Theory

2020 ◽  
Vol 65 (Special Issue) ◽  
pp. 87-103
Author(s):  
Noémi Bíró
Keyword(s):  
Human Activity ◽  
Political Thought ◽  
Hannah Arendt ◽  
Political Action ◽  
Theoretical Framework ◽  
Public Realm ◽  
The Public ◽  
The Social ◽  
Social Feminism ◽  
Definition Of

"Feminist Interpretations of Action and the Public in Hannah Arendt’s Theory. Arendt’s typology of human activity and her arguments on the precondition of politics allow for a variety in interpretations for contemporary political thought. The feminist reception of Arendt’s work ranges from critical to conciliatory readings that attempt to find the points in which Arendt’s theory might inspire a feminist political project. In this paper I explore the ways in which feminist thought has responded to Arendt’s definition of action, freedom and politics, and whether her theoretical framework can be useful in a feminist rethinking of politics, power and the public realm. Keywords: Hannah Arendt, political action, the Public, the Social, feminism "

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

Diagramming discursive intentionality—A cognitive-pragmatic model of intentional verbs

2020 ◽  
Vol 13 (2) ◽  
Author(s):  
Joschka Briese
Keyword(s):  
Practical Reasoning ◽  
Theoretical Framework ◽  
Theory Of Language ◽  
Definition Of

AbstractThis article presents a sign- and usage-based model of intentionality following the works of Robert B. Brandom and T. L. Short. The concept of discursive intentionality is established within Brandom’s theory of language explains discursive and practical reasoning as well as attributive and ascriptive practices. Discursive intentionality is distinguished from other intentionalities of conceptual proximity. Because Brandom’s concept of signs is underdetermined in his works, it will be complemented with T. L. Short’s theory of intentional signs. This dual theoretical framework leads to an innovative analysis of verbs which locates discursive intentionality at the semantic/pragmatic interface. After giving a definition of discursive intentionality, it will be diagrammed by breaking it down into different components (relata, relations, and predicates). Finally, it is tested regarding the plausibility of the diagrammatics of discursive intentionality, using the intentional verb “to promise” to differentiate between the ascription of intentionality and intention.

scholarly journals A new image encryption algorithm based on the OF-LSTMS and chaotic sequences

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yi He ◽  
Ying-Qian Zhang ◽  
Xin He ◽  
Xing-Yuan Wang
Keyword(s):  
Image Encryption ◽  
Fractional Order ◽  
Chaotic System ◽  
Short Term Memory ◽  
Encryption Algorithm ◽  
Chaotic Sequences ◽  
Long Short Term Memory ◽  
Input Gate ◽  
And Diffusion ◽  
Image Encryption Algorithm

AbstractIn this paper, a novel image encryption algorithm based on the Once Forward Long Short Term Memory Structure (OF-LSTMS) and the Two-Dimensional Coupled Map Lattice (2DCML) fractional-order chaotic system is proposed. The original image is divided into several image blocks, each of which is input into the OF-LSTMS as a pixel sub-sequence. According to the chaotic sequences generated by the 2DCML fractional-order chaotic system, the parameters of the input gate, output gate and memory unit of the OF-LSTMS are initialized, and the pixel positions are changed at the same time of changing the pixel values, achieving the synchronization of permutation and diffusion operations, which greatly improves the efficiency of image encryption and reduces the time consumption. In addition the 2DCML fractional-order chaotic system has better chaotic ergodicity and the values of chaotic sequences are larger than the traditional chaotic system. Therefore, it is very suitable to image encryption. Many simulation results show that the proposed scheme has higher security and efficiency comparing with previous schemes.

scholarly journals Infinite Matrix Products and the Representation of the Matrix Gamma Function

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
J.-C. Cortés ◽  
L. Jódar ◽  
Francisco J. Solís ◽  
Roberto Ku-Carrillo
Keyword(s):  
Gamma Function ◽  
Infinite Product ◽  
Infinite Matrix ◽  
Convergence Results ◽  
Matrix Products ◽  
The Matrix ◽  
Definition Of

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.

Multiple coexisting analysis of a fractional-order coupled memristive system and its application in image encryption

2021 ◽  
Vol 152 ◽  
pp. 111334
Author(s):  
Yongbing Hu ◽  
Qian Li ◽  
Dawei Ding ◽  
Li Jiang ◽  
Zongli Yang ◽  
...  
Keyword(s):  
Image Encryption ◽  
Fractional Order ◽  
Memristive System

Diversity, Equity, and Inclusion (DEI) Statements in the U. S. Creative Sector: Progress, or More Bullshit?

2021 ◽  
Vol 5 (2) ◽  
pp. 33-46
Author(s):  
Antonio C. Cuyler
Keyword(s):  
Content Analysis ◽  
Research Question ◽  
Theoretical Framework ◽  
Status Quo ◽  
Arts Organizations ◽  
The Public ◽  
Cultural Organizations ◽  
The Status ◽  
Definition Of ◽  
Equity And Inclusion

This article represents a snapshot and analysis of U. S. service arts organizations’ DEI statements and activities in 2018. At that time, many primarily White-serving U. S. cultural organizations responded defensively to accusations of elitism and a harmful rigged funding system that maintained the status quo by awarding most cultural funding to these organizations while undermining the health and vitality of cultural organizations by and for historically oppressed communities (Sidford, 2011). Furthermore, Helicon Collaborative (2017) found that even with a host of cultural equity, “diversity” projects (Tseng 2016), and public-facing DEI statements, little had changed within six years. Therefore, this study uses directed and summative content analysis to investigate the research question “what do cultural equity and diversity statements communicate about cultural organizations’ positions on DEI?” This study also uses Frankfurt’s (2005) essay On Bullshit and Laing’s (2016) two-prong definition of accountability as a theoretical framework to examine if and how cultural organizations hold themselves accountable for achieving DEI in the creative sector. Lastly, readers should keep in mind that the public murder of Geor-ge Floyd in 2020 has hastened all of the service arts organizations’ access, diversity, equity, and inclusion (ADEI) work examined in this study.

The bouncing ball and the Grünwald-Letnikov definition of fractional derivative

2021 ◽  
Vol 24 (4) ◽  
pp. 1003-1014
Author(s):  
J. A. Tenreiro Machado
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Restitution Coefficient ◽  
Classical Physics ◽  
Bouncing Ball ◽  
Mechanical Experiment ◽  
Fractional Models ◽  
Definition Of

Abstract This paper proposes a conceptual experiment embedding the model of a bouncing ball and the Grünwald-Letnikov (GL) formulation for derivative of fractional order. The impacts of the ball with the surface are modeled by means of a restitution coefficient related to the coefficients of the GL fractional derivative. The results are straightforward to interpret under the light of the classical physics. The mechanical experiment leads to a physical perspective and allows a straightforward visualization. This strategy provides not only a motivational introduction to students of the fractional calculus, but also triggers possible discussion with regard to the use of fractional models in mechanics.

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