Search results for "complex analysis"
showing 10 items of 245 documents
Binary Hamming codes and Boolean designs
2021
AbstractIn this paper we consider a finite-dimensional vector space $${\mathcal {P}}$$ P over the Galois field $${\text {GF}}(2),$$ GF ( 2 ) , and the family $${\mathcal {B}}_k$$ B k (respectively, $${\mathcal {B}}_k^*$$ B k ∗ ) of all the k-sets of elements of $$\mathcal {P}$$ P (respectively, of $${\mathcal {P}}^*= {\mathcal {P}} \setminus \{0\}$$ P ∗ = P \ { 0 } ) summing up to zero. We compute the parameters of the 3-design $$({\mathcal {P}},{\mathcal {B}}_k)$$ ( P , B k ) for any (necessarily even) k, and of the 2-design $$({\mathcal {P}}^{*},{\mathcal {B}}_k^{*})$$ ( P ∗ , B k ∗ ) for any k. Also, we find a new proof for the weight distribution of the binary Hamming code. Moreover, we…
Stress concentration for closely located inclusions in nonlinear perfect conductivity problems
2019
We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium. The governing equation may be degenerate of $p-$Laplace type, with $1<p \leq N$. We prove optimal $L^\infty$ estimates for the blow-up of the gradient of the solution as the distance between the inclusions tends to zero.
Nonlinear nonhomogeneous Neumann eigenvalue problems
2015
We consider a nonlinear parametric Neumann problem driven by a nonhomogeneous differential operator with a reaction which is $(p-1)$-superlinear near $\pm\infty$ and exhibits concave terms near zero. We show that for all small values of the parameter, the problem has at least five solutions, four of constant sign and the fifth nodal. We also show the existence of extremal constant sign solutions.
Blocks with Equal Height Zero Degrees
2009
We study blocks all of whose height zero ordinary characters have the same degree. We suspect that these might be the Broue-Puig nilpotent blocks.
Local behaviour of singular solutions for nonlinear elliptic equations in divergence form
2012
We consider the following class of nonlinear elliptic equations $$\begin{array}{ll}{-}{\rm div}(\mathcal{A}(|x|)\nabla u) +u^q=0\quad {\rm in}\; B_1(0)\setminus\{0\}, \end{array}$$ where q > 1 and $${\mathcal{A}}$$ is a positive C 1(0,1] function which is regularly varying at zero with index $${\vartheta}$$ in (2−N,2). We prove that all isolated singularities at zero for the positive solutions are removable if and only if $${\Phi\not\in L^q(B_1(0))}$$ , where $${\Phi}$$ denotes the fundamental solution of $${-{\rm div}(\mathcal{A}(|x|)\nabla u)=\delta_0}$$ in $${\mathcal D'(B_1(0))}$$ and δ0 is the Dirac mass at 0. Moreover, we give a complete classification of the behaviour near zero of al…
On vibrating thin membranes with mass concentrated near the boundary: an asymptotic analysis
2018
We consider the spectral problem \begin{equation*} \left\{\begin{array}{ll} -\Delta u_{\varepsilon}=\lambda(\varepsilon)\rho_{\varepsilon}u_{\varepsilon} & {\rm in}\ \Omega\\ \frac{\partial u_{\varepsilon}}{\partial\nu}=0 & {\rm on}\ \partial\Omega \end{array}\right. \end{equation*} in a smooth bounded domain $\Omega$ of $\mathbb R^2$. The factor $\rho_{\varepsilon}$ which appears in the first equation plays the role of a mass density and it is equal to a constant of order $\varepsilon^{-1}$ in an $\varepsilon$-neighborhood of the boundary and to a constant of order $\varepsilon$ in the rest of $\Omega$. We study the asymptotic behavior of the eigenvalues $\lambda(\varepsilon)$ and the eige…
Multiplicity results for asymptotically linear equations, using the rotation number approach
2007
By using a topological approach and the relation between rotation numbers and weighted eigenvalues, we give some multiplicity results for the boundary value problem u′′ + f(t, u) = 0, u(0) = u(T) = 0, under suitable assumptions on f(t, x)/x at zero and infinity. Solutions are characterized by their nodal properties.
Analysis of pesticides in fruits by pressurized liquid extraction and liquid chromatography-ion trap-triple stage mass spectrometry.
2005
A multi-residue method using pressurized liquid extraction (PLE) and liquid chromatography-quadrupole ion trap-triple stage mass spectrometry (LC-IT-MS(3)) has been developed for determining trace levels of pesticides in fruits. The selected pesticides can be distinguished in: benzimidazoles and azoles, organophosphorus, carbamates, neonicotinoids, and acaricides. PLE has been optimized to extract these pesticide residues from oranges and peaches by studying the effect of experimental variables on PLE efficiency. Samples were extracted at high temperature and pressure (75 degrees C and 1500psi) using ethyl acetate as extraction solvent and acidic alumina as drying agent. The recoveries obta…
Enzyme and lateral flow monoclonal antibody-based immunoassays to simultaneously determine spirotetramat and spirotetramat-enol in foodstuffs.
2021
Spirotetramat is employed worldwide to fight insect pests due to its high efficiency. This chemical is quickly metabolized by plants into spirotetramat-enol, so current regulations establish that both compounds must be determined in foodstuffs for monitoring purposes. Nowadays, immunochemical methods constitute rapid and cost-effective strategies for chemical contaminant analysis at trace levels. However, high-affinity binders and suitable bioconjugates are required. In this study, haptens with opposite functionalisation sites were synthesized in order to generate high-affinity monoclonal antibodies. A direct competitive enzyme-linked immunosorbent assay with an IC50 value for the sum of sp…
Antibody generation and immunoassay development in diverse formats for pyrimethanil specific and sensitive analysis
2012
Immunochemical techniques are complementary tools to modern analytical requirements. These methods rely on the production of immunoreagents with adequate binding properties. In the present study, a rationally designed and functionalized derivative of pyrimethanil-a modern anilinopyrimidine fungicide-was synthesized in order to generate for the first time high-affinity and selective antibodies to this xenobiotic. A single coupling procedure-based on hapten activation using N,N′-disuccinimidyl carbonate and purification of the active ester-was followed to prepare both immunizing and assay conjugates. Polyclonal antibodies were produced and characterized by enzyme-linked immunosorbent assay (E…