The linear-algebraic λ -calculus and the algebraic λ -calculus are untyped λ -calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while the latter uses equalities. When given by rewrites, algebraic λ -calculi are not confluent unless further restrictions are added. We provide a type system for the linear...

In this paper we deal with the problem of computing Lyapunov functions for stability verification of differential systems. We concern on symbolic methods and start the discussion with a classical quantifier elimination model for computing Lyapunov functions in a given polynomial form, especially in quadratic forms. Then we propose a new semi-algebraic method by making advantage of the local pro...

We analyze the implementation of the time-reversal (TR) transformation in the algebraic approach to tetrahedral local molecules through the chain of groups U(5) ⊃ U(4) ⊃ K(4) = A(4) ∧ S(4) ⊃ S(4) ≈ Td. We determine the general form of the TR operation using a purely algebraic realization, based exclusively on the requirement that the irreducible representations must not be changed under the tim...

We present a functional analogue of the elimination of Φ-instructions from Static Single Assignment (SSA) code. Extending earlier work on the relationship between SSA and functional languages we show that transformations from A-normal form (ANF) into a more restrictive form called GNF require the same compensating instructions to be inserted as are commonly inserted during the translation from ...

Low degree annihilators for Boolean functions are of great interest in cryptology because of algebraic attacks on LFSR-based stream ciphers. Several polynomial algorithms for construction of low degree annihilators are introduced in this paper. The existence of such algorithms is studied for the following forms of the function representation: algebraic normal form (ANF), disjunctive normal form...

Tujuan penelitian ini adalah mendeskripsikan jenis dan faktor penyebab kesalahan yang dialami siswa kelas VII dalam bentuk aljabar berdasarkan Teori Nolting. Metode digunakan deskriptif kualitatif. Subyek terdiri dari 10 diambil secara acak, kemudian 2 memenuhi 6 indikator tipe Nolting diwawancarai. Berdasarkan hasil diketahui bahwa persentase 50% mengalami misread direction errors, 20% careles...

We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are sufficient to enable signal reconstruction for generic signals, and slightly more ge...

In this paper, I will prove that assuming Schanuel’s conjecture, an exponential polynomial with algebraic coefficients can have only finitely many algebraic roots. Furthermore, this proof demonstrates that there are no unexpected algebraic roots of any exponential polynomial. This implies a special case of Shapiro’s conjecture: if p(x) and q(x) are two exponential polynomials over the algebraic...

the principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (iae) by using the bernoulli polynomials and the residual correction method. after implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown bernoulli coefficients. thismethod gives an analytic solution when t...