Log in

Relevant bibliographies by topics / Multilinear polynomial / Journal articles

To see the other types of publications on this topic, follow the link: Multilinear polynomial.

Journal articles on the topic 'Multilinear polynomial'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Multilinear polynomial.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Šiljak, Dragoslav D., and Matija D. Šiljak. "Nonnegativity of uncertain polynomials." Mathematical Problems in Engineering 4, no. 2 (1998): 135–63. http://dx.doi.org/10.1155/s1024123x98000763.

Full text

Abstract:

The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.

APA, Harvard, Vancouver, ISO, and other styles

2

Ghosal, Purnata, and B. V. Raghavendra Rao. "On Proving Parameterized Size Lower Bounds for Multilinear Algebraic Models." Fundamenta Informaticae 177, no. 1 (December 18, 2020): 69–93. http://dx.doi.org/10.3233/fi-2020-1980.

Full text

Abstract:

We consider the problem of obtaining parameterized lower bounds for the size of arithmetic circuits computing polynomials with the degree of the polynomial as the parameter. We consider the following special classes of multilinear algebraic branching programs: 1) Read Once Oblivious Branching Programs (ROABPs), 2) Strict interval branching programs, 3) Sum of read once formulas with restricted ordering. We obtain parameterized lower bounds (i.e., nΩ(t(k)) lower bound for some function t of k) on the size of the above models computing a multilinear polynomial that can be computed by a depth four circuit of size g(k)nO(1) for some computable function g. Further, we obtain a parameterized separation between ROABPs and read-2 ABPs. This is obtained by constructing a degree k polynomial that can be computed by a read-2 ABP of small size such that the rank of the partial derivative matrix under any partition of the variables is large.

APA, Harvard, Vancouver, ISO, and other styles

3

GORDIENKO, ALEXEY, and GEOFFREY JANSSENS. "ℤSn-MODULES AND POLYNOMIAL IDENTITIES WITH INTEGER COEFFICIENTS." International Journal of Algebra and Computation 23, no. 08 (December 2013): 1925–43. http://dx.doi.org/10.1142/s0218196713500513.

Full text

Abstract:

We show that, like in the case of algebras over fields, the study of multilinear polynomial identities of unitary rings can be reduced to the study of proper polynomial identities. In particular, the factors of series of ℤSn-submodules in the ℤSn-modules of multilinear polynomial functions can be derived by the analog of Young's (or Pieri's) rule from the factors of series in the corresponding ℤSn-modules of proper polynomial functions. As an application, we calculate the codimensions and a basis of multilinear polynomial identities of unitary rings of upper triangular 2 × 2 matrices and infinitely generated Grassmann algebras over unitary rings. In addition, we calculate the factors of series of ℤSn-submodules for these algebras. Also we establish relations between codimensions of rings and codimensions of algebras and show that the analog of Amitsur's conjecture holds in all torsion-free rings, and all torsion-free rings with 1 satisfy the analog of Regev's conjecture.

APA, Harvard, Vancouver, ISO, and other styles

4

Latyshev, V. N. "Combinatorial generators of the multilinear polynomial identities." Journal of Mathematical Sciences 149, no. 2 (February 2008): 1107–12. http://dx.doi.org/10.1007/s10958-008-0049-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Giambruno, Antonio, and Mikhail Zaicev. "Codimension growth of central polynomials of Lie algebras." Forum Mathematicum 32, no. 1 (January 1, 2020): 201–6. http://dx.doi.org/10.1515/forum-2019-0130.

Full text

Abstract:

AbstractLet L be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic zero and let I be the T-ideal of polynomial identities of the adjoint representation of L. We prove that the number of multilinear central polynomials in n variables, linearly independent modulo I, grows exponentially like {(\dim L)^{n}}.

APA, Harvard, Vancouver, ISO, and other styles

6

CHEN, SHENSHI, YAQING CHEN, and QUANHAI YANG. "TOWARD RANDOMIZED TESTING OF q-MONOMIALS IN MULTIVARIATE POLYNOMIALS." Discrete Mathematics, Algorithms and Applications 06, no. 02 (March 19, 2014): 1450016. http://dx.doi.org/10.1142/s1793830914500165.

Full text

Abstract:

Given any fixed integer q ≥ 2, a q-monomial is of the format [Formula: see text] such that 1 ≤ sj ≤ q - 1, 1 ≤ j ≤ t. q-monomials are natural generalizations of multilinear monomials. Recent research on testing multilinear monomials and q-monomials for prime q in multivariate polynomials relies on the property that Zq is a field when q ≥ 2 is prime. When q > 2 is not prime, it remains open whether the problem of testing q-monomials can be solved in some compatible complexity. In this paper, we present a randomized O*(7.15k) algorithm for testing q-monomials of degree k that are found in a multivariate polynomial that is represented by a tree-like circuit with a polynomial size, thus giving a positive, affirming answer to the above question. Our algorithm works regardless of the primality of q and improves upon the time complexity of the previously known algorithm for testing q-monomials for prime q > 7.

APA, Harvard, Vancouver, ISO, and other styles

7

Belaada, Abdelaziz, Khalil Saadi, and Abdelmoumen Tiaiba. "On the Composition Ideals of Schatten Class Type Mappings." Journal of Mathematics 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/3492934.

Full text

Abstract:

We study the composition ideals of multilinear and polynomial mappings generated by Schatten classes. We give some coincidence theorems for Cohen strongly 2-summing multilinear operators and factorization results like that given by Lindenstrauss-Pełczński for Hilbert Schmidt linear operators.

APA, Harvard, Vancouver, ISO, and other styles

8

Chillara, Suryajith. "On Computing Multilinear Polynomials Using Multi- r -ic Depth Four Circuits." ACM Transactions on Computation Theory 13, no. 3 (September 30, 2021): 1–21. http://dx.doi.org/10.1145/3460952.

Full text

Abstract:

In this article, we are interested in understanding the complexity of computing multilinear polynomials using depth four circuits in which the polynomial computed at every node has a bound on the individual degree of r ≥ 1 with respect to all its variables (referred to as multi- r -ic circuits). The goal of this study is to make progress towards proving superpolynomial lower bounds for general depth four circuits computing multilinear polynomials, by proving better bounds as the value of r increases. Recently, Kayal, Saha and Tavenas (Theory of Computing, 2018) showed that any depth four arithmetic circuit of bounded individual degree r computing an explicit multilinear polynomial on n O (1) variables and degree d must have size at least ( n / r 1.1 ) Ω(√ d / r ) . This bound, however, deteriorates as the value of r increases. It is a natural question to ask if we can prove a bound that does not deteriorate as the value of r increases, or a bound that holds for a larger regime of r . In this article, we prove a lower bound that does not deteriorate with increasing values of r , albeit for a specific instance of d = d ( n ) but for a wider range of r . Formally, for all large enough integers n and a small constant η, we show that there exists an explicit polynomial on n O (1) variables and degree Θ (log 2 n ) such that any depth four circuit of bounded individual degree r ≤ n η must have size at least exp(Ω(log 2 n )). This improvement is obtained by suitably adapting the complexity measure of Kayal et al. (Theory of Computing, 2018). This adaptation of the measure is inspired by the complexity measure used by Kayal et al. (SIAM J. Computing, 2017).

APA, Harvard, Vancouver, ISO, and other styles

9

Pınar Eroglu, Münevver, and Nurcan Argaç. "On Identities with Composition of Generalized Derivations." Canadian Mathematical Bulletin 60, no. 4 (December 1, 2017): 721–35. http://dx.doi.org/10.4153/cmb-2016-072-4.

Full text

Abstract:

AbstractLet R be a prime ring with extended centroid C, Q maximal right ring of quotients of R, RC central closure of R such that dim C(RC) > , ƒ (X1, . . . , Xn) a multilinear polynomial over C that is not central-valued on R, and f (R) the set of all evaluations of the multilinear polynomial f (X1 , . . . , Xn) in R. Suppose that G is a nonzero generalized derivation of R such that G2(u)u ∈ C for all u ∈ ƒ(R).

APA, Harvard, Vancouver, ISO, and other styles

10

Filippis, Vincenzo De, Onofrio Mario Di Vincenzo, and Ching-Yueh Pan. "Quadratic Central Differential Identities on a Multilinear Polynomial." Communications in Algebra 36, no. 10 (October 13, 2008): 3671–81. http://dx.doi.org/10.1080/00927870802157962.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Lee, Tsiu Kwen. "Derivations with invertible values on a multilinear polynomial." Proceedings of the American Mathematical Society 119, no. 4 (April 1, 1993): 1077. http://dx.doi.org/10.1090/s0002-9939-1993-1156472-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Christ, Michael, and Jean-Lin Journé. "Polynomial growth estimates for multilinear singular integral operators." Acta Mathematica 159 (1987): 51–80. http://dx.doi.org/10.1007/bf02392554.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Del Pia, Alberto, and Aida Khajavirad. "The Running Intersection Relaxation of the Multilinear Polytope." Mathematics of Operations Research 46, no. 3 (August 2021): 1008–37. http://dx.doi.org/10.1287/moor.2021.1121.

Full text

Abstract:

The multilinear polytope of a hypergraph is the convex hull of a set of binary points satisfying a collection of multilinear equations. We introduce the running intersection inequalities, a new class of facet-defining inequalities for the multilinear polytope. Accordingly, we define a new polyhedral relaxation of the multilinear polytope, referred to as the running intersection relaxation, and identify conditions under which this relaxation is tight. Namely, we show that for kite-free beta-acyclic hypergraphs, a class that lies between gamma-acyclic and beta-acyclic hypergraphs, the running intersection relaxation coincides with the multilinear polytope and it admits a polynomial size extended formulation.

APA, Harvard, Vancouver, ISO, and other styles

14

Gutiérrez, Joaquín M., and Ignacio Villanueva. "Extensions of multilinear operators and Banach space properties." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 133, no. 3 (June 2003): 549–66. http://dx.doi.org/10.1017/s0308210500002535.

Full text

Abstract:

A new characterization of the Dunford–Pettis property in terms of the extensions of multilinear operators to the biduals is obtained. For the first time, multilinear characterizations of the reciprocal Dunford–Pettis property and Pełczyński's property (V) are also found. Polynomial and holomorphic versions of these properties are given as well.

APA, Harvard, Vancouver, ISO, and other styles

15

Anderson, Matthew, Dieter van Melkebeek, and Ilya Volkovich. "Deterministic polynomial identity tests for multilinear bounded-read formulae." computational complexity 24, no. 4 (April 25, 2015): 695–776. http://dx.doi.org/10.1007/s00037-015-0097-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Choi, Yun Sung, Domingo Garcia, Sung Guen Kim, and Manuel Maestre. "THE POLYNOMIAL NUMERICAL INDEX OF A BANACH SPACE." Proceedings of the Edinburgh Mathematical Society 49, no. 1 (February 2006): 39–52. http://dx.doi.org/10.1017/s0013091502000810.

Full text

Abstract:

AbstractIn this paper, we introduce the polynomial numerical index of order $k$ of a Banach space, generalizing to $k$-homogeneous polynomials the ‘classical’ numerical index defined by Lumer in the 1970s for linear operators. We also prove some results. Let $k$ be a positive integer. We then have the following:(i) $n^{(k)}(C(K))=1$ for every scattered compact space $K$.(ii) The inequality $n^{(k)}(E)\geq k^{k/(1-k)}$ for every complex Banach space $E$ and the constant $k^{k/(1-k)}$ is sharp.(iii) The inequalities$$ n^{(k)}(E)\leq n^{(k-1)}(E)\leq\frac{k^{(k+(1/(k-1)))}}{(k-1)^{k-1}}n^{(k)}(E) $$for every Banach space $E$.(iv) The relation between the polynomial numerical index of $c_0$, $l_1$, $l_{\infty}$ sums of Banach spaces and the infimum of the polynomial numerical indices of them.(v) The relation between the polynomial numerical index of the space $C(K,E)$ and the polynomial numerical index of $E$.(vi) The inequality $n^{(k)}(E^{**})\leq n^{(k)}(E)$ for every Banach space $E$.Finally, some results about the numerical radius of multilinear maps and homogeneous polynomials on $C(K)$ and the disc algebra are given.

APA, Harvard, Vancouver, ISO, and other styles

17

Filippis, Vincenzo De, and Onofrio Mario Di Vincenzo. "Posner's second theorem, multilinear polynomials and vanishing derivations." Journal of the Australian Mathematical Society 76, no. 3 (June 2004): 357–68. http://dx.doi.org/10.1017/s1446788700009915.

Full text

Abstract:

AbstractLet K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, d and δ non-zero derivations of R, f (x1,…, xn) a multilinear polynomial over K.Ifthen f(x1,…,xnis central-valued on R.

APA, Harvard, Vancouver, ISO, and other styles

18

Tiwari, S. K., and B. Prajapati. "Centralizing b-generalized derivations on multilinear polynomials." Filomat 33, no. 19 (2019): 6251–66. http://dx.doi.org/10.2298/fil1919251t.

Full text

Abstract:

Let R be a prime ring of characteristic different from 2 and F a b-generalized derivation on R. Let U be Utumi quotient ring of R with extended centroid C and f (x1,..., xn) be a multilinear polynomial over C which is not central valued on R. Suppose that d is a non zero derivation on R such that d([F(f(r)), f(r)]) ? C for all r = (r1,..., rn) ? Rn, then one of the following holds: (1) there exist a ? U, ? ? C such that F(x) = ax + ?x + xa for all x ? R and f (x1,..., xn)2 is central valued on R, (2) there exists ? ? C such that F(x) = ?x for all x ? R.

APA, Harvard, Vancouver, ISO, and other styles

19

Bai, Shuyang, and Murad S. Taqqu. "Multivariate limits of multilinear polynomial-form processes with long memory." Statistics & Probability Letters 83, no. 11 (November 2013): 2473–85. http://dx.doi.org/10.1016/j.spl.2013.06.027.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Campos, Jamilson R., Wasthenny Cavalcante, Vinícius V. Fávaro, Daniel Pellegrino, and Diana M. Serrano-Rodríguez. "Polynomial and multilinear Hardy-Littlewood inequalities: analytical and numerical approaches." Mathematical Inequalities & Applications, no. 2 (2018): 329–44. http://dx.doi.org/10.7153/mia-2018-21-24.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Lee, Pjek-Hwee, and Tsai-Lien Wong. "Derivations with Invertible or Nilpotent Values on a Multilinear Polynomial." Algebra Colloquium 7, no. 1 (March 2000): 93–98. http://dx.doi.org/10.1007/s10011-000-0093-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Carini, Luisa, Vincenzo De Filippis, and Onofrio Mario Di Vincenzo. "On Some Generalized Identities with Derivations on Multilinear Polynomials." Algebra Colloquium 17, no. 02 (June 2010): 319–36. http://dx.doi.org/10.1142/s1005386710000325.

Full text

Abstract:

Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, Z(R) the center of R, f(x1,…,xn) a non-central multilinear polynomial over K, d and δ derivations of R, a and b fixed elements of R. Denote by f(R) the set of all evaluations of the polynomial f(x1,…,xn) in R. If a[d(u),u] + [δ (u),u]b = 0 for any u ∈ f(R), we prove that one of the following holds: (i) d = δ = 0; (ii) d = 0 and b = 0; (iii) δ = 0 and a = 0; (iv) a, b ∈ Z(R) and ad + bδ = 0. We also examine some consequences of this result related to generalized derivations and we prove that if d is a derivation of R and g a generalized derivation of R such that g([d(u),u]) = 0 for any u ∈ f(R), then either g = 0 or d = 0.

APA, Harvard, Vancouver, ISO, and other styles

23

Cheon, Jung Hee, Jinhyuck Jeong, and Changmin Lee. "An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without a low-level encoding of zero." LMS Journal of Computation and Mathematics 19, A (2016): 255–66. http://dx.doi.org/10.1112/s1461157016000371.

Full text

Abstract:

Let$\mathbf{f}$and$\mathbf{g}$be polynomials of a bounded Euclidean norm in the ring$\mathbb{Z}[X]/\langle X^{n}+1\rangle$. Given the polynomial$[\mathbf{f}/\mathbf{g}]_{q}\in \mathbb{Z}_{q}[X]/\langle X^{n}+1\rangle$, the NTRU problem is to find$\mathbf{a},\mathbf{b}\in \mathbb{Z}[X]/\langle X^{n}+1\rangle$with a small Euclidean norm such that$[\mathbf{a}/\mathbf{b}]_{q}=[\mathbf{f}/\mathbf{g}]_{q}$. We propose an algorithm to solve the NTRU problem, which runs in$2^{O(\log ^{2}\unicode[STIX]{x1D706})}$time when$\Vert \mathbf{g}\Vert ,\Vert \mathbf{f}\Vert$, and$\Vert \mathbf{g}^{-1}\Vert$are within some range. The main technique of our algorithm is the reduction of a problem on a field to one on a subfield. The GGH scheme, the first candidate of an (approximate) multilinear map, was recently found to be insecure by the Hu–Jia attack using low-level encodings of zero, but no polynomial-time attack was known without them. In the GGH scheme without low-level encodings of zero, our algorithm can be directly applied to attack this scheme if we have some top-level encodings of zero and a known pair of plaintext and ciphertext. Using our algorithm, we can construct a level-$0$encoding of zero and utilize it to attack a security ground of this scheme in the quasi-polynomial time of its security parameter using the parameters suggested by Garg, Gentry and Halevi [‘Candidate multilinear maps from ideal lattices’,Advances in cryptology — EUROCRYPT 2013(Springer, 2013) 1–17].

APA, Harvard, Vancouver, ISO, and other styles

24

Du, Yiqiu, and Yu Wang. "Annihilator Conditions with Generalized Derivations on Multilinear Polynomials." Algebra Colloquium 20, no. 04 (October 7, 2013): 613–22. http://dx.doi.org/10.1142/s1005386713000588.

Full text

Abstract:

Let R be a prime ring of characteristic different from 2 with right Utumi quotient ring U and extended centroid C. Let g be a generalized derivation of R, f(x1,…,xn) a multilinear polynomial over C, a ∈ R, and I a nonzero right ideal of R. Suppose that a[g(f(r1,…,rn)), f(r1,…,rn)]=0 for all ri∈ I and aI ≠ 0. Then either g(x)=a1x with (a1-γ)I=0 for some a1∈ U and γ ∈ C, or there exists an idempotent element e ∈ soc (RC) such that IC=eRC and one of the following holds: (i) f(x1,…,xn) is central-valued in eRe; (ii) g(x)=bx+xc, where b, c ∈ U with (c-b-α)e=0 for some α ∈ C and f(x1,…,xn) is central-valued in eRe.

APA, Harvard, Vancouver, ISO, and other styles

25

Mishchenko, S. P., and Y. R. Pestova. "BASIS OF MULTILINEAR PART OF LEIBNIZ ALGEBRAS MANIFOLDS \overbrace{V_1}." Vestnik of Samara University. Natural Science Series 20, no. 3 (May 31, 2017): 76–82. http://dx.doi.org/10.18287/2541-7525-2014-20-3-76-82.

Full text

Abstract:

In the case of trivial characteristic of base ﬁeld, Leibniz algebras manifolds deﬁned by the identity x_1(x_2x_3)(x_4x_5)\equiv 0. has almost polynomial growth. In the work we continue research of this manifold, in particular, we construct bases of multilinear parts.

APA, Harvard, Vancouver, ISO, and other styles

26

Jia, Zeya, Bilal Khan, Qiuxia Hu, and Dawei Niu. "Applications of Generalized q-Difference Equations for General q-Polynomials." Symmetry 13, no. 7 (July 7, 2021): 1222. http://dx.doi.org/10.3390/sym13071222.

Full text

Abstract:

Andrews gave a remarkable interpretation of the Rogers–Ramanujan identities with the polynomials ρe(N,y,x,q), and it was noted that ρe(∞,−1,1,q) is the generation of the fifth-order mock theta functions. In the present investigation, several interesting types of generating functions for this q-polynomial using q-difference equations is deduced. Besides that, a generalization of Andrew’s result in form of a multilinear generating function for q-polynomials is also given. Moreover, we build a transformation identity involving the q-polynomials and Bailey transformation. As an application, we give some new Hecke-type identities. We observe that most of the parameters involved in our results are symmetric to each other. Our results are shown to be connected with several earlier works related to the field of our present investigation.

APA, Harvard, Vancouver, ISO, and other styles

27

Akyar, Handan, Taner Büyükköroğlu, and Vakıf Dzhafarov. "On Stability of Parametrized Families of Polynomials and Matrices." Abstract and Applied Analysis 2010 (2010): 1–16. http://dx.doi.org/10.1155/2010/687951.

Full text

Abstract:

The Schur and Hurwitz stability problems for a parametric polynomial family as well as the Schur stability problem for a compact set of real matrix family are considered. It is established that the Schur stability of a family of real matrices is equivalent to the nonsingularity of the family if has at least one stable member. Based on the Bernstein expansion of a multivariable polynomial and extremal properties of a multilinear function, fast algorithms are suggested.

APA, Harvard, Vancouver, ISO, and other styles

28

Wang, Yu. "Generalized Derivations with Power-Central Values on Multilinear Polynomials." Algebra Colloquium 13, no. 03 (September 2006): 405–10. http://dx.doi.org/10.1142/s1005386706000344.

Full text

Abstract:

Let R be a prime algebra over a commutative ring K, Z and C the center and extended centroid of R, respectively, g a generalized derivation of R, and f (X1, …,Xt) a multilinear polynomial over K. If g(f (X1, …,Xt))n ∈ Z for all x1, …, xt ∈ R, then either there exists an element λ ∈ C such that g(x)= λx for all x ∈ R or f(x1, …,xt) is central-valued on R except when R satisfies s4, the standard identity in four variables.

APA, Harvard, Vancouver, ISO, and other styles

29

Albrecht, Martin R., Pooya Farshim, Shuai Han, Dennis Hofheinz, Enrique Larraia, and Kenneth G. Paterson. "Multilinear Maps from Obfuscation." Journal of Cryptology 33, no. 3 (January 2, 2020): 1080–113. http://dx.doi.org/10.1007/s00145-019-09340-0.

Full text

Abstract:

AbstractWe provide constructions of multilinear groups equipped with natural hard problems from indistinguishability obfuscation, homomorphic encryption, and NIZKs. This complements known results on the constructions of indistinguishability obfuscators from multilinear maps in the reverse direction. We provide two distinct, but closely related constructions and show that multilinear analogues of the $${\text {DDH}} $$DDH assumption hold for them. Our first construction is symmetric and comes with a $$\kappa $$κ-linear map $$\mathbf{e }: {{\mathbb {G}}}^\kappa \longrightarrow {\mathbb {G}}_T$$e:Gκ⟶GT for prime-order groups $${\mathbb {G}}$$G and $${\mathbb {G}}_T$$GT. To establish the hardness of the $$\kappa $$κ-linear $${\text {DDH}} $$DDH problem, we rely on the existence of a base group for which the $$\kappa $$κ-strong $${\text {DDH}} $$DDH assumption holds. Our second construction is for the asymmetric setting, where $$\mathbf{e }: {\mathbb {G}}_1 \times \cdots \times {\mathbb {G}}_{\kappa } \longrightarrow {\mathbb {G}}_T$$e:G1×⋯×Gκ⟶GT for a collection of $$\kappa +1$$κ+1 prime-order groups $${\mathbb {G}}_i$$Gi and $${\mathbb {G}}_T$$GT, and relies only on the 1-strong $${\text {DDH}} $$DDH assumption in its base group. In both constructions, the linearity $$\kappa $$κ can be set to any arbitrary but a priori fixed polynomial value in the security parameter. We rely on a number of powerful tools in our constructions: probabilistic indistinguishability obfuscation, dual-mode NIZK proof systems (with perfect soundness, witness-indistinguishability, and zero knowledge), and additively homomorphic encryption for the group $$\mathbb {Z}_N^{+}$$ZN+. At a high level, we enable “bootstrapping” multilinear assumptions from their simpler counterparts in standard cryptographic groups and show the equivalence of PIO and multilinear maps under the existence of the aforementioned primitives.

APA, Harvard, Vancouver, ISO, and other styles

30

O'Shea, P., and R. A. Wiltshire. "A New Class of Multilinear Functions for Polynomial Phase Signal Analysis." IEEE Transactions on Signal Processing 57, no. 6 (June 2009): 2096–109. http://dx.doi.org/10.1109/tsp.2009.2014811.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Malev, Sergey. "The images of non-commutative polynomials evaluated on 2 × 2 matrices over an arbitrary field." Journal of Algebra and Its Applications 13, no. 06 (April 20, 2014): 1450004. http://dx.doi.org/10.1142/s0219498814500042.

Full text

Abstract:

Let p be a multilinear polynomial in several non-commuting variables with coefficients in an arbitrary field K. Kaplansky conjectured that for any n, the image of p evaluated on the set Mn(K) of n × n matrices is either zero, or the set of scalar matrices, or the set sl n(K) of matrices of trace 0, or all of Mn(K). This conjecture was proved for n = 2 when K is closed under quadratic extensions. In this paper, the conjecture is verified for K = ℝ and n = 2, also for semi-homogeneous polynomials p, with a partial solution for an arbitrary field K.

APA, Harvard, Vancouver, ISO, and other styles

32

Dhara, Basudeb, and Vincenzo De Filippis. "b-Generalized Derivations Acting on Multilinear Polynomials in Prime Rings." Algebra Colloquium 25, no. 04 (December 2018): 681–700. http://dx.doi.org/10.1142/s1005386718000482.

Full text

Abstract:

Let R be a prime ring of characteristic different from 2, Q be its maximal right ring of quotients, and C be its extended centroid. Suppose that [Formula: see text] is a non-central multilinear polynomial over C, [Formula: see text], and F, G are two b-generalized derivations of R. In this paper we describe all possible forms of F and G in the case [Formula: see text] for all [Formula: see text] in Rn.

APA, Harvard, Vancouver, ISO, and other styles

33

DE FILIPPIS, VINCENZO. "ANNIHILATORS OF POWER VALUES OF GENERALIZED DERIVATIONS ON MULTILINEAR POLYNOMIALS." Bulletin of the Australian Mathematical Society 80, no. 2 (June 19, 2009): 217–32. http://dx.doi.org/10.1017/s0004972709000203.

Full text

Abstract:

AbstractLet R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, I a nonzero right ideal of R. Let f(x1,…,xn) be a noncentral multilinear polynomial over C, m≥1 a fixed integer, a a fixed element of R, g a generalized derivation of R. If ag(f(r1,…,rn))m=0 for all r1,…,rn∈I, then one of the following holds: (1)aI=ag(I)=(0);(2)g(x)=qx, for some q∈U and aqI=0;(3)[f(x1,…,xn),xn+1]xn+2 is an identity for I;(4)g(x)=cx+[q,x] for all x∈R, where c,q∈U such that cI=0 and [q,I]I=0.

APA, Harvard, Vancouver, ISO, and other styles

34

De Filippis, V., G. Scudo, and L. Sorrenti. "Two-Sided Annihilator Condition with Generalized Derivations on Multilinear Polynomials." International Scholarly Research Notices 2014 (October 28, 2014): 1–9. http://dx.doi.org/10.1155/2014/563284.

Full text

Abstract:

Let R be a prime ring of characteristic different from 2, with extended centroid C, U its two-sided Utumi quotient ring, F a nonzero generalized derivation of R, f(x1,…,xn) a noncentral multilinear polynomial over C in n noncommuting variables, and a,b∈R such that a[F(f(r1,…,rn)),f(r1,…,rn)]b=0 for any r1,…,rn∈R. Then one of the following holds: (1) a=0; (2) b=0; (3) there exists λ∈C such that F(x)=λx, for all x∈R; (4) there exist q∈U and λ∈C such that F(x)=(q+λ)x+xq, for all x∈R, and f(x1,…,xn)2 is central valued on R; (5) there exist q∈U and λ,μ∈C such that F(x)=(q+λ)x+xq, for all x∈R, and aq=μa, qb=μb.

APA, Harvard, Vancouver, ISO, and other styles

35

Boyen, Xavier, and Thomas Haines. "Forward-Secure Linkable Ring Signatures from Bilinear Maps." Cryptography 2, no. 4 (November 8, 2018): 35. http://dx.doi.org/10.3390/cryptography2040035.

Full text

Abstract:

We present the first linkable ring signature scheme with both unconditional anonymity and forward-secure key update: a powerful tool which has direct applications in elegantly addressing a number of simultaneous constraints in remote electronic voting. We propose a comprehensive security model, and construct a scheme based on the hardness of finding discrete logarithms, and (for forward security) inverting bilinear or multilinear maps of moderate degree to match the time granularity of forward security. We prove efficient security reductions—which, of independent interest, apply to, and are much tighter than, linkable ring signatures without forward security, thereby vastly improving the provable security of these legacy schemes. If efficient multilinear maps should ever admit a secure realisation, our contribution would elegantly address a number of problems heretofore unsolved in the important application of (multi-election) practical Internet voting. Even if multilinear maps are never obtained, our minimal two-epoch construction instantiated from bilinear maps can be combinatorially boosted to synthesise a polynomial time granularity, which would be sufficient for Internet voting and more.

APA, Harvard, Vancouver, ISO, and other styles

36

Argaç, Nurcan, and Vincenzo De Filippis. "Actions of Generalized Derivations on Multilinear Polynomials in Prime Rings." Algebra Colloquium 18, spec01 (December 2011): 955–64. http://dx.doi.org/10.1142/s1005386711000836.

Full text

Abstract:

Let K be a commutative ring with unity, R a non-commutative prime K-algebra with center Z(R), U the Utumi quotient ring of R, C=Z(U) the extended centroid of R, I a non-zero two-sided ideal of R, H and G non-zero generalized derivations of R. Suppose that f(x1,…,xn) is a non-central multilinear polynomial over K such that H(f(X))f(X)-f(X)G(f(X))=0 for all X=(x1,…,xn)∈ In. Then one of the following holds: (1) There exists a ∈ U such that H(x)=xa and G(x)=ax for all x ∈ R. (2) f(x1,…,xn)2 is central valued on R and there exist a, b ∈ U such that H(x)=ax+xb and G(x)=bx+xa for all x ∈ R. (3) char (R)=2 and R satisfies s4, the standard identity of degree 4.

APA, Harvard, Vancouver, ISO, and other styles

37

Brandão, Antonio Pereira, Dimas José Gonçalves, and Plamen Koshlukov. "Graded A-identities for the matrix algebra of order two." International Journal of Algebra and Computation 26, no. 08 (December 2016): 1617–31. http://dx.doi.org/10.1142/s0218196716500715.

Full text

Abstract:

Let [Formula: see text] be a field of characteristic 0 and let [Formula: see text]. The algebra [Formula: see text] admits a natural grading [Formula: see text] by the cyclic group [Formula: see text] of order 2. In this paper, we describe the [Formula: see text]-graded A-identities for [Formula: see text]. Recall that an A-identity for an algebra is a multilinear polynomial identity for that algebra which is a linear combination of the monomials [Formula: see text] where [Formula: see text] runs over all even permutations of [Formula: see text] that is [Formula: see text], the [Formula: see text]th alternating group. We first introduce the notion of an A-identity in the case of graded polynomials, then we describe the graded A-identities for [Formula: see text], and finally we compute the corresponding graded A-codimensions.

APA, Harvard, Vancouver, ISO, and other styles

38

GUPTA, C. K., and A. N. KRASIL’NIKOV. "SOME NON-FINITELY BASED VARIETIES OF GROUPS AND GROUP REPRESENTATIONS." International Journal of Algebra and Computation 05, no. 03 (June 1995): 343–65. http://dx.doi.org/10.1142/s0218196795000203.

Full text

Abstract:

The following results are established: (i) There exists a subvariety of the variety of centre-by-abelian -by- (nilpotent of class 2) groups which is not finitely based; (ii) There exists a variety of group representations (over a field of characteristic 2) which satisfies a multilinear polynomial identity but without any finite basis for its identities: (iii) Over fields of characteristic 2, a product of two Specht varieties of group representations need not be Specht.

APA, Harvard, Vancouver, ISO, and other styles

39

Liu, Kun-Shan. "Generalized Derivations with Periodic Values." Algebra Colloquium 22, no. 01 (January 7, 2015): 163–68. http://dx.doi.org/10.1142/s1005386715000140.

Full text

Abstract:

Let R be a prime ring and n > 1 be a fixed positive integer. If g is a nonzero generalized derivation of R such that g(x)n=g(x) for all x ∈ R, then R is commutative except when R is a subring of the 2 × 2 matrix ring over a field. Moreover, we generalize the result to the case g(f(xi))n = g(f(xi)) for all x1, x2, …, xt∈ R, where f(Xi) is a multilinear polynomial.

APA, Harvard, Vancouver, ISO, and other styles

40

GUO, L. Z., and S. A. BILLINGS. "IDENTIFICATION OF BINARY CELLULAR AUTOMATA FROM SPATIO-TEMPORAL BINARY PATTERNS USING A FOURIER REPRESENTATION." International Journal of Bifurcation and Chaos 17, no. 06 (June 2007): 1985–96. http://dx.doi.org/10.1142/s0218127407018166.

Full text

Abstract:

The identification of binary cellular automata from spatio-temporal binary patterns is investigated in this paper. Instead of using the usual Boolean or multilinear polynomial representation, the Fourier transform representation of Boolean functions is employed in terms of a Fourier basis. In this way, the orthogonal forward regression least-squares algorithm can be applied directly to detect the significant terms and to estimate the associated parameters. Compared with conventional methods, the new approach is much more robust to noise. Examples are provided to illustrate the effectiveness of the proposed approach.

APA, Harvard, Vancouver, ISO, and other styles

41

Purushothama, B. R., and B. B. Amberker. "Access control mechanisms for outsourced data in public cloud using polynomial interpolation and multilinear map." International Journal of Cloud Computing 6, no. 1 (2017): 1. http://dx.doi.org/10.1504/ijcc.2017.083901.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Purushothama, B. R., and B. B. Amberker. "Access control mechanisms for outsourced data in public cloud using polynomial interpolation and multilinear map." International Journal of Cloud Computing 6, no. 1 (2017): 1. http://dx.doi.org/10.1504/ijcc.2017.10004724.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Duncan, Jennifer. "An Algebraic Brascamp–Lieb Inequality." Journal of Geometric Analysis 31, no. 10 (March 29, 2021): 10136–63. http://dx.doi.org/10.1007/s12220-021-00638-9.

Full text

Abstract:

AbstractThe Brascamp–Lieb inequalities are a very general class of classical multilinear inequalities, well-known examples of which being Hölder’s inequality, Young’s convolution inequality, and the Loomis–Whitney inequality. Conventionally, a Brascamp–Lieb inequality is defined as a multilinear Lebesgue bound on the product of the pullbacks of a collection of functions $$f_j\in L^{q_j}(\mathbb {R}^{n_j})$$ f j ∈ L q j ( R n j ) , for $$j=1,\ldots ,m$$ j = 1 , … , m , under some corresponding linear maps $$B_j$$ B j . This regime is now fairly well understood (Bennett et al. in Geom Funct Anal 17(5):1343–1415, 2008), and moving forward there has been interest in nonlinear generalisations, where $$B_j$$ B j is now taken to belong to some suitable class of nonlinear maps. While there has been great recent progress on the question of local nonlinear Brascamp–Lieb inequalities (Bennett et al. in Duke Math J 169(17):3291–3338, 2020), there has been relatively little regarding global results; this paper represents some progress along this line of enquiry. We prove a global nonlinear Brascamp–Lieb inequality for ‘quasialgebraic’ maps, a class that encompasses polynomial and rational maps, as a consequence of the multilinear Kakeya-type inequalities of Zhang and Zorin-Kranich. We incorporate a natural affine-invariant weight that both compensates for local degeneracies and yields a constant with minimal dependence on the underlying maps. We then show that this inequality generalises Young’s convolution inequality on algebraic groups with suboptimal constant.

APA, Harvard, Vancouver, ISO, and other styles

44

Toffano, Zeno, and François Dubois. "Interpolating Binary and Multivalued Logical Quantum Gates." Proceedings 2, no. 4 (November 20, 2017): 152. http://dx.doi.org/10.3390/ecea-4-05006.

Full text

Abstract:

A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one obtains for arity-one a complete family of logical operators corresponding to all the one-argument logical connectives. Scaling-up to n-arity gates is obtained by using the Kronecker product and unitary transformations. The quantum version of the Fourier transform of Boolean functions is presented and a Reed-Muller decomposition for quantum logical gates is derived. The common control gates can be easily obtained by considering the logical correspondence between the control logic operator and the binary logic operator. A new polynomial and exponential formulation of the Toffoli gate is presented. The method has parallels to quantum gate-T optimization methods using powers of multilinear operator polynomials. The method is then applied naturally to alphabets greater than two for multi-valued logical gates used for quantum Fourier transform, min-max decision circuits and multivalued adders.

APA, Harvard, Vancouver, ISO, and other styles

45

Hwang, Chyi, and Shih-Feng Yang. "Plotting Robust Root Locus For Polynomial Families Of Multilinear Parameter Dependence Based On Zero Inclusion/Exclusion Tests." Asian Journal of Control 5, no. 2 (October 22, 2008): 293–300. http://dx.doi.org/10.1111/j.1934-6093.2003.tb00120.x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Kim, Youngsoo, and Byunghoon Lee. "Zero-Sum Coefficient Derivations in Three Variables of Triangular Algebras." Journal of Mathematics Research 8, no. 5 (September 20, 2016): 37. http://dx.doi.org/10.5539/jmr.v8n5p37.

Full text

Abstract:

Under mild assumptions Benkovi\v{c} showed that an $f$-derivation of a triangular algebra is a derivation when the sum of the coefficients of the multilinear polynomial $f$ is nonzero. We investigate the structure of $f$-derivations of triangular algebras when $f$ is of degree 3 and the coefficient sum is zero. The zero-sum coeffient derivations include Lie derivations (degree 2) and Lie triple derivations (degree 3), which have been previously shown to be not necessarily derivations but in standard form, i.e., the sum of a derivation and a central map. In this paper, we present sufficient conditions on the coefficients of $f$ to ensure that any $f$-derivations are derivations or are in standard form.<br /><br />

APA, Harvard, Vancouver, ISO, and other styles

47

Wang, Ji-Hong, and Philip K. Hopke. "Equation-oriented system: an efficient programming approach to solve multilinear and polynomial equations by the conjugate gradient algorithm." Chemometrics and Intelligent Laboratory Systems 55, no. 1-2 (January 2001): 13–22. http://dx.doi.org/10.1016/s0169-7439(00)00110-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

DE FILIPPIS, VINCENZO, and GIOVANNI SCUDO. "HYPERCOMMUTING VALUES IN ASSOCIATIVE RINGS WITH UNITY." Journal of the Australian Mathematical Society 94, no. 2 (March 8, 2013): 181–88. http://dx.doi.org/10.1017/s1446788712000511.

Full text

Abstract:

AbstractLet $K$ be a commutative ring with unity, $R$ an associative $K$-algebra of characteristic different from $2$ with unity element and no nonzero nil right ideal, and $f({x}_{1} , \ldots , {x}_{n} )$ a multilinear polynomial over $K$. Assume that, for all $x\in R$ and for all ${r}_{1} , \ldots , {r}_{n} \in R$ there exist integers $m= m(x, {r}_{1} , \ldots , {r}_{n} )\geq 1$ and $k= k(x, {r}_{1} , \ldots , {r}_{n} )\geq 1$ such that $\mathop{[{x}^{m} , f({r}_{1} , \ldots , {r}_{n} )] }\nolimits_{k} = 0$. We prove that: (1) if $\text{char} (R)= 0$ then $f({x}_{1} , \ldots , {x}_{n} )$ is central-valued on $R$; and (2) if $\text{char} (R)= p\gt 2$ and $f({x}_{1} , \ldots , {x}_{n} )$ is not a polynomial identity in $p\times p$ matrices of characteristic $p$, then $R$ satisfies ${s}_{n+ 2} ({x}_{1} , \ldots , {x}_{n+ 2} )$ and for any ${r}_{1} , \ldots , {r}_{n} \in R$ there exists $t= t({r}_{1} , \ldots , {r}_{n} )\geq 1$ such that ${f}^{{p}^{t} } ({r}_{1} , \ldots , {r}_{n} )\in Z(R)$, the center of $R$.

APA, Harvard, Vancouver, ISO, and other styles

49

Vergeer, Ineke, and John M. Hogg. "Coaches’ Decision Policies about the Participation of Injured Athletes in Competition." Sport Psychologist 13, no. 1 (March 1999): 42–56. http://dx.doi.org/10.1123/tsp.13.1.42.

Full text

Abstract:

This study aimed to examine the effects of four situational factors on coaches’ decisions about an injured athlete’s participation in competition. A telephone survey was conducted among 64 coaches training female gymnasts of various competitive levels. Coaches were presented with hypothetical scenarios depicting situations in which an athlete suffered an ankle injury prior to competition. Injury severity, the gymnast’s age and ability level, and importance of the competition were systematically varied in a total of 16 scenarios. Using a multilinear polynomial model (Louvière. 1988), decision policies were calculated at the individual and aggregate levels. The aggregate level analysis showed a four-way interaction effect. Cluster analysis on individual policies revealed two groups, membership of which was associated with personal injury history. Results suggest that in their decision making, coaches are sensitive to the unique situational characteristics surrounding the injury and are influenced by their personal experiences with competing while injured.

APA, Harvard, Vancouver, ISO, and other styles

50

Demir, Ç., and N. Argaç. "Prime Rings with Generalized Derivations on Right Ideals." Algebra Colloquium 18, spec01 (December 2011): 987–98. http://dx.doi.org/10.1142/s1005386711000861.

Full text

Abstract:

Let K be a commutative ring with unit, R be a prime K-algebra with center Z(R), right Utumi quotient ring U and extended centroid C, and I a nonzero right ideal of R. Let g be a nonzero generalized derivation of R and f(X1,…,Xn) a multilinear polynomial over K. If g(f(x1,…,xn)) f(x1,…,xn) ∈ C for all x1,…,xn ∈ I, then either f(x1,…,xn)xn+1 is an identity for I, or char (R)=2 and R satisfies the standard identity s4(x1,…,x4), unless when g(x)=ax+[x,b] for suitable a, b ∈ U and one of the following holds: (i) a, b ∈ C and f(x1,…,xn)2 is central valued on R; (ii) a ∈ C and f(x1,…,xn) is central valued on R; (iii) aI=0 and [f(x1,…,xn), xn+1]xn+2 is an identity for I; (iv) aI=0 and (b-β)I=0 for some β ∈ C.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!