Results 41 to 50 of about 10,834,928 (363)
Ray casting implicit fractal surfaces with reduced affine arithmetic [PDF]
, 2007 A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray.
Gamito, M.N., Maddock, S.C.
core +2 more sources
Physical Review Research, 2023 Many computational problems can be formulated in terms of high-dimensional functions. Simple representations of such functions and resulting computations with them typically suffer from the “curse of dimensionality,” an exponential cost dependence on ...
Ruojing Peng +2 more
doaj +1 more source
Arithmetic of positive characteristic L-series values in Tate algebras [PDF]
, 2015 The second author has recently introduced a new class of L-series in the arithmetic theory of function fields over finite fields. We show that the value at one of these L-series encode arithmetic informations of certain Drinfeld modules defined over Tate
Angles, Bruno +2 more
core +2 more sources
Arithmetic properties of Ramanujan's general partition function for modulo 11
Kuwait Journal of Science, 2020 In the present work, for the general partition function $p_k(n)$, we establish five new infinite families of congruences. Our emphasis throughout this paper is to exhibit the use of $q$-identities to generate congruences for the general partition ...
Srivatsa Kumar Belakavadi Radhakrishna +2 more
doaj +1 more source
A Functional Equation in Arithmetic [PDF]
Transactions of the American Mathematical Society, 1936 which occurs in all theories of numerical functions hitherto considered. The two most highly developed theories of this kind are those in which multiplication in the ring of all numerical functions is abstractly identical with C (Cauchy) or D (Dirichlet) multiplication of infinite series.t Lehmer's five postulates are sufficient for the development of ...
openaire +2 more sources
The Riemann-zeta function on vertical arithmetic progressions [PDF]
, 2012 We show that the twisted second moments of the Riemann zeta function averaged over the arithmetic progression $1/2 + i(an + b)$ with $a > 0$, $b$ real, exhibits a remarkable correspondance with the analogous continuous average and derive several ...
Xiannan Li, Maksym Radziwill
semanticscholar +1 more source
On upper bounds of arithmetic degrees [PDF]
American Journal of Mathematics, 2016 :Let $X$ be a smooth projective variety defined over $\overline{\Bbb{Q}}$, and $f\colon X\dashrightarrow X$ be a dominant rational map. Let $\delta_f$ be the first dynamical degree of $f$ and $h_X\colon X(\overline{\Bbb{Q}})\rightarrow [1,\infty)$ be a ...
Yohsuke Matsuzawa
semanticscholar +1 more source
A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions [PDF]
Mathematica BohemicaA specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely $(a,b)$-Fibonacci sequences and ...
Emil Daniel Schwab, Gabriela Schwab
doaj +1 more source
Arithmetic properties of the Ramanujan function
, 2006 We study some arithmetic properties of the Ramanujan function $\tau(n)$, such as the largest prime divisor $P(\tau(n))$ and the number of distinct prime divisors $\omega(\tau(n))$ of $\tau(n)$ for various sequences of $n$.
Luca, Florian, Shparlinski, Igor E
core +1 more source
Bounds for the Neuman–Sándor Mean in Terms of the Arithmetic and Contra-Harmonic Means
Axioms, 2022 In this paper, the authors provide several sharp upper and lower bounds for the Neuman–Sándor mean in terms of the arithmetic and contra-harmonic means, and present some new sharp inequalities involving hyperbolic sine function and hyperbolic cosine ...
Wen-Hui Li, Peng Miao, Bai-Ni Guo
doaj +1 more source