Toeplitz Operators with Horizontal Symbols Acting on the Poly-Fock Spaces by Armando Sánchez-Nungaray, Carlos González-Flores, Raquiel Rufino López-Martínez, Jorge Luis Arroyo-Neri

“…The C⁎ algebra generated with this kind of symbols is isomorphic to the C⁎-algebra functions on extended reals with values on the matrices of dimension n×n, and the limits at y=-∞ and y=∞ are scalar multiples of the identity matrix.…”
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Approximability in the GPAC by Diogo Poças, Jeffery Zucker

“…In particular, the Shannon GPAC cannot be used to generate non-differentially algebraic functions which can be approximately computed in other models of computation. …”
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Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views by Shashua, Amnon

“…It is shown that three perspective views of an object are connected by certain algebraic functions of image coordinates alone (no structure or camera geometry needs to be involved).…”
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The Reformulated F-Index of Vertex and Edge F-Join of Graphs by Durbar Maji, Ganesh Ghorai, Faria Ahmed Shami

“…The valency based topological indices (TIs) are defined by algebraic functions as the chemical graph theory tools in which the structural parameters are used as input and the output is related with the topology of chemical species. …”
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Some Elementary Aspects of Means by Mowaffaq Hajja

“…The solutions are expected to require no more than simple tools from analysis, algebra, functional equations, and geometry.…”
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New directions in cryptanalysis of block ciphers. by RezaeiPour , Davood, Md Said, Mohamad Rushdan

“…This attack is useful for cryptanalysis using simple algebraic functions as S-boxes. Results: In this study, we presented an improved AES S-box with good properties to improve the complexity of AES S-box algebraic expression with terms increasing to 255. …”
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Complex binary algebra by Yu, Xin

“…Complex binary algebra can be defined as a type of algebra that use packed binary representation form to implement any quaternary algebra function. Complex binary algebra is quite closely related to Boolean algebra and can be used to convert any binary function into quaternary function without any significant modification. …”
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Ax's theorem with an additive character by Hrushovski, E

“…Then any element of this class can be approximated, uniformly in the variables and in the prime p, by a polynomial expression in Ψp(ξ) at certain algebraic functions ξ of the variables, where Ψ (n mod p) = exp(2πin/p) is the standard additive character.…”

The Orbit Problem for parametric linear dynamical systems by Baier, C, Jantsch, S, Lefaucheux, E, Ouaknine, J, Whiteland, MA, Funke, F, Karimov, T, Luca, F, Purser, D, Worrell, J

“…More precisely, consider a d-dimensional square matrix M whose entries are algebraic functions in one or more real variables. Given initial and target vectors u,v ∈ ℚ^d, the parametric point-to-point orbit problem asks whether there exist values of the parameters giving rise to a concrete matrix N ∈ ℝ^{d× d}, and a positive integer n ∈ ℕ, such that N^{n} u = v. …”

Exploring Soliton Solutions for Fractional Nonlinear Evolution Equations: A Focus on Regularized Long Wave and Shallow Water Wave Models with Beta Derivative by Sujoy Devnath, Maha M. Helmi, M. Ali Akbar

“…Consequently, the study establishes a variety of reliable and novel soliton solutions involving trigonometric, hyperbolic, rational, and algebraic functions. By setting appropriate values for the parameters, we obtained peakons, anti-peakon, kink, bell, anti-bell, singular periodic, and flat kink solitons. …”
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Synthesis of binary programs with predominance of branching commands by V.V. Zhukov

“…In this article, a model of binary programs that implement the logic algebra functions (Boolean functions) is considered. These programs consist of one or several modules, which include the following three types of commands: computational, branching, and procedure call commands. …”
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A new evaluation method for customer outage costs using long-term outage data and Monte Carlo simulation by Sajad Najafi-Shad, Mozhdeh Mollashahi, Seyyed Mohsen Sadr

“…The determined CCDFs are transformed into algebraic functions through curve fitting for any substation. …”
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D’un point de vue rigoureux et parfaitement général : pratique des mathématiques rigoureuses chez Richard Dedekind by Emmylou Haffner

“…The first part of the paper shows evidences of the tight links woven by Dedekind between generality and rigor in his theory of algebraic functions co-written with H. Weber, as well as in his foundational essays and his work on algebraic number theory. …”
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Mixed powerdomains for probability and nondeterminism by Klaus Keimel, Gordon D. Plotkin

“…So we define power Kegelspitzen, and consider free algebras, functional representations, and predicate transformers. …”
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Statistical analysis, ciphertext only attack, improvement of generic quasigroup string transformation and dynamic string transformation by Hassan Disina, Abdulkadir, Jamel, Sapiee, Abubakar Pindar, Zahraddeen, Mat Deris, Mustafa

“…Algebraic functions are the primitives that strengthen the cryptographic algorithms to ensure confidentiality of data and information. …”

Construction of an Integrated Social Vulnerability Index to Identify Spatial Variability of Exposure to Seismic Hazard in Pahang, Malaysia by Sauti, Noor Suhaiza, Daud, Mohd Effendi, Kaamin, Masiri

“…The classes of a social vulnerability index map were overlaid with a seismic hazard map that was proposed by JMG (Mineral and Geoscience Department Malaysia) through the use of map algebra functions in GIS tools. Results for social vulnerability map showed that, majority of the study area are in relatively low to moderate level except for Kuantan district, which is highly vulnerable. …”

Unsteady flow of nanofluid over a sheet of variable thickness with nonlinear kinematics by Nasir Ali, Dil Nawaz Khan Marwat, Naeem Ullah, Hala H. Abd El-Gawad

“…Furthermore, the simulation includes the particular cases of uniform and linear (polynomial & algebraic functions) stretching/shrinking and injection/suction velocities. …”
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Nonconvex robust optimization by Teo, Kwong Meng

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Enhancing the spatially distributed total bed material load prediction using correction factor grid for plane bedded mountain river / Amir Nazaruddin by Nazaruddin, Amir

“…TBML equation by Sinnakaudan (2010) was employed to formulate a spatial distribution prediction model to show the spatial discrete variability of the total load using the map algebra functions. Discrepancy Ratio (DR) analysis indicates that the prediction model fails to show the variability in the total load for the study reach. …”
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Simulation of Vertical Movements of Seawater in Stratified Reservoirs by N. V. Kudinov, A. A. Filina, A. V. Nikitina, D. V. Bondarenko, I. F. Razveeva

“…This is open-source software that provides not only the redefinition of empirical dependences (as algebraic functions), but also the connection of external simulating modules to display dependences algorithmically.Discussion and Conclusion. …”
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