We present a novel randomized algorithm to factor polynomials over a finite field Fq of odd characteristic using rank 2 Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial f ∈ Fq[x] to be factored) with respect to a random Drinfeld module φ with complex multiplication. Factors of f supported on prime ideals with supersin...

Consider the set B = [0, 1] endowed with the operations⊕ = max,∧ = min. This is a well-known distributive lattice, and like any distributive lattice it can be considered as a semiring equipped with addition ⊕ and multiplication ⊗ := ∧. Importantly, both operations are idempotent, a⊕a = a and a⊗a = a∧a = a, and closely related to the order: a⊕ b = b ⇔ a ≤ b ⇔ a∧ b = a. For standard literature on...

The paper presents the concepts behind the "Urdhva Tiryagbhyam Sutra" and "Nikhilam Sutra" multiplication techniques. It then shows the architecture for a 16×16 Vedic multiplier module using Urdhva Tiryagbhyam Sutra. The paper then extends multiplication to 16×16 Vedic multiplier using "Nikhilam Sutra" technique. The 16×16 Vedic multiplier module using Urdhva Tiryagbhyam Sutra uses four 8×8 Ved...

The thermal safety of lithium-ion traction batteries is a highly concerning issue in the field electric transportation. large amount gas emissions during runaway process has high hazards, such as fire and explosion. quantitative analysis one important challenges testing evaluating battery safety. Focusing on quantifying using large-scale propagation modules packs, based idea cell result multipl...

Bit-sequential multiplier is being studied in a (+1, -1) binary representation. The maximum length of multiplier for a fix point numbers consists of n module. Each module is a five bit adder which contains 5 inputs and 3 outputs. It also contains an additional pin at the input as well as at the output. Computation time for multiplication is of the order of O(n). Hardware realization of module i...

We further extend the model predictive control framework, which is very popular in the process industry due to its ability to handle constraints on inputs and outputs, to a class of discrete event systems that can be modeled using the operations maximization, minimization, addition and scalar multiplication. This class encompasses max-plus-linear systems, min-max-plus systems, bilinear max-plus...

Let H(S) be the Hardy space on the unit sphere S in C, n ≥ 2. Then H(S) is a natural Hilbert module over the ball algebra A(B). Let Mz1 , ..., Mzn be the module operators corresponding to the multiplication by the coordinated functions. Each submodule M ⊂ H(S) gives rise to the module operators ZM,j = Mzj |M, j = 1, ..., n, on M. In this paper we establish the following commonly believed, but n...

We define evaluation forms associated to objects in a module subcategory of Ext-symmetry generated by finitely many simple modules over a path algebra with relations and prove a multiplication formula for the product of two evaluation forms. It is analogous to a multiplication formula for the product of two evaluation forms associated to modules over a preprojective algebra given by Geiss, Lecl...

We classify weights which map strong reverse Hölder weight classes to weak reverse Hölder weight spaces under pointwise multiplication.