Results 31 to 40 of about 4,959 (254)
An adaptive cryptosystem on a Finite Field [PDF]
PeerJ Computer Science, 2021 Owing to mathematical theory and computational power evolution, modern cryptosystems demand ingenious trapdoor functions as their foundation to extend the gap between an enthusiastic interceptor and sensitive information.
Awnon Bhowmik, Unnikrishnan Menon
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Local analytic solutions to some nonhomogeneous problems with $p$-Laplacian
Electronic Journal of Qualitative Theory of Differential Equations, 2008 Applying the Briot-Bouquet theorem we show that there exists an unique analytic solution to the equation $\left( t^{n-1}\Phi _{p}\left( y^{\prime}\right) \right) ^{\prime }+(-1)^{i}t^{n-1}\Phi _{q}(y)=0$, on $(0,~a)$, where $\Phi _{r}(y):=\left\vert y ...
Gabriella Bognár
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Combinatorial Models of the Distribution of Prime Numbers
Mathematics, 2021 This work is divided into two parts. In the first one, the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial ...
Vito Barbarani
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Weighted Prime Number Theorem on Arithmetic Progressions with Refinements
MathematicsWe present an extension of the Dirichlet-type prime number theorem to weighted counting functions, the importance of which has recently been recognized for formulating Chebyshev’s bias.
Koji Shimada, Shin-ya Koyama
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Formalization of the prime number theorem and Dirichlet's theorem [PDF]
, 2016 We present the formalization of Dirichlet's theorem on the infinitude of primes in arithmetic progressions, and Selberg's elementary proof of the prime number theorem, which asserts that the number $π(x)$ of primes less than $x$ is asymptotic to $x/\log x$, within the proof system Metamath.
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A Joint Elliott Type Theorem for Twists of L-Functions of Elliptic Curves
Mathematical Modelling and Analysis, 2016 We consider a collection of L-functions of elliptic curves twisted by a Dirichlet character modulo q (q is a prime number), and prove for this collection a joint limit theorem for weakly convergent probability measures in the space of analytic functions ...
Virginija Garbaliauskienė +1 more
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MathematicsDetermining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev’s estimates, etc.) particularly valuable.
Timothy Ganesan
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Advanced Engineering Materials, EarlyView.A flexure‐based variable stiffness structure is developed by integrating phase‐change modulation and adhesive interfacial locking of gallium. The design enables a wide stiffness variability, transitioning from soft, flexible behavior to rigid, load‐supporting performance.
Sungjin Kim +2 more
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Multimodal Data‐Driven Microstructure Characterization
Advanced Engineering Materials, EarlyView.A self‐consistent autonomous workflow for EBSP‐based microstructure segmentation by integrating PCA, GMM clustering, and cNMF with information‐theoretic parameter selection, requiring no user input. An optimal ROI size related to characteristic grain size is identified.
Qi Zhang +4 more
wiley +1 more source
The Pjateckiĭ-S̆apiro prime number theorem
Journal of Number Theory, 1983 It is proved that the sequence [nc] contains the expected number of primes whenever 1 < c < 1.1404…, thus improving Kolesnik's range 1 < c < 1.1111…. An identity of Vaughan's type in five variables is needed.
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