Search results for "Multiplication"
showing 10 items of 83 documents
On ergodic operator means in Banach spaces
2016
We consider a large class of operator means and prove that a number of ergodic theorems, as well as growth estimates known for particular cases, continue to hold in the general context under fairly mild regularity conditions. The methods developed in the paper not only yield a new approach based on a general point of view, but also lead to results that are new, even in the context of the classical Cesaro means.
On nilpotent Moufang loops with central associators
2007
Abstract In this paper, we investigate Moufang p-loops of nilpotency class at least three for p > 3 . The smallest examples have order p 5 and satisfy the following properties: (1) They are of maximal nilpotency class, (2) their associators lie in the center, and (3) they can be constructed using a general form of the semidirect product of a cyclic group and a group of maximal class. We present some results concerning loops with these properties. As an application, we classify proper Moufang loops of order p 5 , p > 3 , and collect information on their multiplication groups.
The periods of the generalized Jacobian of a complex elliptic curve
2015
Abstract We show that the toroidal Lie group G = ℂ2/Λ, where Λ is the lattice generated by (1, 0), (0, 1) and (τ̂, τ͂), with τ̂ ∉ ℝ, is isomorphic to the generalized Jacobian JL of the complex elliptic curve C with modulus τ̂, defined by any divisor class L ≡ (M) + (N) of C fulfilling M − N = [℘ (τ͂) : ℘´(τ͂) : 1] ∈ C. This follows from an apparently new relation between the Weierstrass sigma and elliptic functions.
Functions definable by numerical set-expressions
2011
A "numerical set-expression" is a term specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. If these operations are confined to the usual Boolean operations together with the result of lifting addition to the level of sets, we speak of "additive circuits". If they are confined to the usual Boolean operations together with the result of lifting addition and multiplication to the level of sets, we speak of "arithmetic circuits". In this paper, we investigate the definability of sets and functions by means of additive and arithmetic circuits, occasionally augmented with additional operations.
Quotients of Fermat curves and a Hecke character
2005
AbstractWe explicitly identify infinitely many curves which are quotients of Fermat curves. We show that some of these have simple Jacobians with complex multiplication by a non-cyclotomic field. For a particular case we determine the local zeta functions with two independent methods. The first uses Jacobi sums and the second applies the general theory of complex multiplication, we verify that both methods give the same result.
A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
2013
This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems are also discussed.
Micropropagation ofAgeratum houstonianumby nodal segments
2017
Ageratum houstonianum is a bedding and flowering potted plant originated from Central America which is generally propagate by seed. In this report a preliminary in vitro technique for propagation of A. houstonianum was investigated. In vitro germinated seeds were used to establish aseptic shoot cultures of several clones. Seedling stem segments bearing 3-4 nodes were placed on Murashige and Skoog (MS) basal medium plus 20 g L-1 sucrose, 8.0 g L-1 Agar to induce axillary shoot development. Axillary shoots were subcultured into the same medium and nodal segments were sectioned and subcultured to increase the stock of shoot cultures. Shoot cultures of the selected clone AG14 were used to accom…
Inductive synthesis of term rewriting systems
2005
Fast algorithm for inductive synthesis of term rewriting systems is described and proved to be correct. It is implemented and successfully applied for inductive synthesis of different algorithms, including the binary multiplication. The algorithm proposed supports automatic learning process and can be used for designing and implementation of ADT.
LightSpMV: Faster CSR-based sparse matrix-vector multiplication on CUDA-enabled GPUs
2015
Compressed sparse row (CSR) is a frequently used format for sparse matrix storage. However, the state-of-the-art CSR-based sparse matrix-vector multiplication (SpMV) implementations on CUDA-enabled GPUs do not exhibit very high efficiency. This has motivated the development of some alternative storage formats for GPU computing. Unfortunately, these alternatives are incompatible with most CPU-centric programs and require dynamic conversion from CSR at runtime, thus incurring significant computational and storage overheads. We present LightSpMV, a novel CUDA-compatible SpMV algorithm using the standard CSR format, which achieves high speed by benefiting from the fine-grained dynamic distribut…
On minimal ∗-identities of matrices∗
1995
Let Mn (F) be the algebra of n×n matrices (n≥2) over a field F of characteristic different from 2 and let ∗ be an involution in Mn (F) In case ∗ is the transpose involution, we construct a multilinear ∗ polynomial identify of Mn (F) of degree 2n−1, P 2n−1(k 1, s 2, … s 2n−1) in one skew variable and the remaining symmetric variables of minimal degree among all ∗-polynomial identities of this type. We also prove that any other multilinear ∗-polynomial identity of Mn (F) of this type of degree 2n−1 is a scalar multiple of P2n−1 . In case ∗ is the symplectic involution in Mn (F), we construct a ∗-polynomial identity of Mn (F) of degree 2n−1 in skew variables T2n−1 (k 1,…,k 2n−1) and we prove t…