Search results for "complex analysis"
showing 10 items of 245 documents
Immunoassays for pyraclostrobin analysis in processed food products using novel monoclonal antibodies and QuEChERS-based extracts
2013
Strobilurins are a family of synthetic natural-derived pesticides widely used for fungi control in many crops. As part of a larger research project, a collection of monoclonal antibodies to one of the most relevant strobilurins, i.e. pyraclostrobin, has been generated using functionalized haptens with the spacer arm located at different sites. The toxophore aliphatic moiety, as observed with other strobilurins, and the planar aromatic two-ring system characteristic of this molecule were revealed as the best tethering sites for high-affinity monoclonal antibody production. A central derivatization position did not generate a good immune response, but such derivatives were useful as heterolog…
Elliptic problems with convection terms in Orlicz spaces
2021
Abstract The existence of a solution to a Dirichlet problem, for a class of nonlinear elliptic equations, with a convection term, is established. The main novelties of the paper stand on general growth conditions on the gradient variable, and on minimal assumptions on Ω. The approach is based on the method of sub and supersolutions. The solution is a zero of an auxiliary pseudomonotone operator build via truncation techniques. We present also some examples in which we highlight the generality of our growth conditions.
Multiple positive solutions for singularly perturbed elliptic problems in exterior domains
2003
Abstract The equation − e 2 Δ u + a e ( x ) u = u p −1 with boundary Dirichlet zero data is considered in an exterior domain Ω = R N ⧹ ω ( ω bounded and N ⩾2). Under the assumption that a e ⩾ a 0 >0 concentrates round a point of Ω as e →0, that p >2 and p N /( N −2) when N ⩾3, the existence of at least three positive distinct solutions is proved.
Existence of non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian
2021
The paper focuses on a Dirichlet problem driven by the (Formula presented.) -Laplacian. The existence of at least two non-zero solutions under suitable conditions on the nonlinear term is established. The approach is based on variational methods.
An elementary proof of Hilbertʼs theorem on ternary quartics
2012
Abstract In 1888, Hilbert proved that every nonnegative quartic form f = f ( x , y , z ) with real coefficients is a sum of three squares of quadratic forms. His proof was ahead of its time and used advanced methods from topology and algebraic geometry. Up to now, no elementary proof is known. Here we present a completely new approach. Although our proof is not easy, it uses only elementary techniques. As a by-product, it gives information on the number of representations f = p 1 2 + p 2 2 + p 3 2 of f up to orthogonal equivalence. We show that this number is 8 for generically chosen f, and that it is 4 when f is chosen generically with a real zero. Although these facts were known, there wa…
Subvarieties of the Varieties Generated by the SuperalgebraM1, 1(E) orM2(𝒦)
2003
Abstract Let 𝒦 be a field of characteristic zero, and let us consider the matrix algebra M 2(𝒦) endowed with the ℤ2-grading (𝒦e 11 ⊕ 𝒦e 22) ⊕ (𝒦e 12 ⊕ 𝒦e 21). We define two superalgebras, ℛ p and 𝒮 q , where p and q are positive integers. We show that if 𝒰 is a proper subvariety of the variety generated by the superalgebra M 2(𝒦), then the even-proper part of the T 2-ideal of graded polynomial identities of 𝒰 asymptotically coincides with the even-proper part of the graded polynomial identities of the variety generated by the superalgebra ℛ p ⊕ 𝒮 q . This description also affords an even-asymptotic desc…
Codimension growth of two-dimensional non-associative algebras
2007
Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c n (A), n =1,2,..., of codimensions of A is either bounded by n + 1 or grows exponentially as 2 n . We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n > 2.
Graded polynomial identities and codimensions: Computing the exponential growth
2010
Abstract Let G be a finite abelian group and A a G-graded algebra over a field of characteristic zero. This paper is devoted to a quantitative study of the graded polynomial identities satisfied by A. We study the asymptotic behavior of c n G ( A ) , n = 1 , 2 , … , the sequence of graded codimensions of A and we prove that if A satisfies an ordinary polynomial identity, lim n → ∞ c n G ( A ) n exists and is an integer. We give an explicit way of computing such integer by proving that it equals the dimension of a suitable finite dimension semisimple G × Z 2 -graded algebra related to A.
Probabilistic limit identification up to “small” sets
1996
In this paper we study limit identification of total recursive functions in the case when “small” sets of errors are allowed. Here the notion of “small” sets we formalize in a very general way, i.e. we define a notion of measure for subsets of natural numbers, and we consider as being small those sets, which are subsets of sets with zero measure.
Asymptotics for the Amitsur's Capelli - Type Polynomials and Verbally Prime PI-Algebras
2006
We consider associativePI-algebras over a field of characteristic zero. The main goal of the paper is to prove that the codimensions of a verbally prime algebra [11] are asymptotically equal to the codimensions of theT-ideal generated by some Amitsur's Capelli-type polynomialsEM,L* [1]. We recall that two sequencesan,bnare asymptotically equal, and we writean≃bn,if and only if limn→∞(an/bn)=1.In this paper we prove that\(c_n \left( {M_k \left( G \right)} \right) \simeq c_n \left( {E_{k^2 ,k^2 }^ * } \right) and c_n \left( {M_{k,l} \left( G \right)} \right) \simeq c_n \left( {E_{k^2 + l^2 ,2kl}^ * } \right) \)% MathType!End!2!1!, whereG is the Grassmann algebra. These results extend to all v…