Results 1 to 10 of about 9,213 (131)
Functions for the $3n+1$-problem [PDF]
Researches in MathematicsWhat functions can represent the $3n+1$-problem? A number of such functions have been given during the past years. In this paper, a specific one is considered which has $1, 2, 3, \ldots$ as critical points and $1.5, 2.5, 3.5, \ldots$ as fixed points on ...
P. Kórus
doaj +2 more sources
Optimal (controlled) quantum state preparation and improved unitary synthesis by quantum circuits with any number of ancillary qubits [PDF]
Quantum, 2023 As a cornerstone for many quantum linear algebraic and quantum machine learning algorithms, controlled quantum state preparation (CQSP) aims to provide the transformation of $|i\rangle |0^n\rangle \to |i\rangle |\psi_i\rangle $ for all $i\in \{0,1\}^k ...
Pei Yuan, Shengyu Zhang
doaj +1 more source
Special Matrices, 2023 Denote by σn{\sigma }_{n} the n-th Stirling polynomial in the sense of the well-known book Concrete Mathematics by Graham, Knuth and Patashnik. We show that there exist developments xσn(x)=∑j=0n(2jj!)−1qn−j(j)xjx{\sigma }_{n}\left(x)={\sum }_{j=0}^{n ...
Kovačec Alexander +1 more
doaj +1 more source
A note on the generalized 3n+1 problem [PDF]
Acta Arithmetica, 1999 Let \(m>d\geq 2\) be two integers with \(\text{gcd}(d,m)=1\), let \(R_d\) be a complete set of non-zero residues mod \(d\), and denote by \(\varphi:{\mathbb N}\to R_d\) the natural projection. Then the Hasse function is given by \(H(x)=x/d\) if \(x\equiv 0\bmod d\), \(H(x)=(mx-\varphi(mx))/d\) otherwise.
Garcia, Manuel V. P., Tal, Fabio A.
openaire +2 more sources
Comparative Evaluation of Intron Prediction Methods and Detection of Plant Genome Annotation Using Intron Length Distributions [PDF]
Genomics & Informatics, 2012 Intron prediction is an important problem of the constantly updated genome annotation. Using two model plant (rice and Arabidopsis) genomes, we compared two well-known intron prediction tools: the Blast-Like Alignment Tool (BLAT) and Sim4cc.
Long Yang, Hwan-Gue Cho
doaj +1 more source
Труды по прикладной ботанике, генетике и селекции, 2022 Background. Clogging of tetraploid maize crops with triploid grains leads to a decrease in grain yield and the destruction of the genome’s stability. Searching for the reasons of the tetraploid genome’s decomposition as well as solving the problem of ...
E. B. Khatefov +2 more
doaj +1 more source
COLLATZ CONJECTURE 3n±1 AS A NEWTON BINOMIAL PROBLEM
Computer Design Systems. Theory and Practice, 2023 The power transformation of Newton's binomial forms two equal 3n±1 algorithms for transformations of numbers n belongs to N, each of which have one infinite cycle with a unit lower limit of oscillations. It is shown that in the reverse direction, the Kollatz sequence is formed by the lower limits of the corresponding cycles, and the last element goes ...
Petro Kosobutskyy, Dariia Rebot
openaire +2 more sources
Synthesis of space-time optimal systolic algorithms for the Choleskyfactorization [PDF]
Discrete Mathematics & Theoretical Computer Science, 2002 In this paper we study the synthesis of space-time optimal systolic arrays for the Cholesky Factorization (CF). First, we discuss previous allocation methods and their application to CF. Second, stemming from a new allocation method we derive a space-
Clémentin Tayou Djamegni
doaj +2 more sources
Advances in Mathematical Physics, 2021 In this note, in 2D and 3D smooth bounded domain, we show the existence of strong solution for generalized Navier-Stokes equation modeling by px-power law with Dirichlet boundary condition under the restriction 3n/n+2n ...
Cholmin Sin
doaj +1 more source
New 209Bi photodisintegration data and physical criteria of data reliability [PDF]
EPJ Web of Conferences, 2020 The well-known problem of noticeable disagreements between photoneutron cross sections from various experiments was discussed in detail for 209Bi. Data for partial photoneutron reactions cross sections obtained at Livermore (USA) using quasimonoenergetic
Belyshev Sergey +9 more
doaj +1 more source