Search results for "Linear function"

Four solutions for fractional p-Laplacian equations with asymmetric reactions

2020

We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, whose reaction combines a sublinear term depending on a positive parameter and an asymmetric perturbation (superlinear at positive infinity, at most linear at negative infinity). By means of critical point theory and Morse theory, we prove that, for small enough values of the parameter, such problem admits at least four nontrivial solutions: two positive, one negative, and one nodal. As a tool, we prove a Brezis-Oswald type comparison result.

Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems

2017

We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\…

Two-way quantum and classical machines with small memory for online minimization problems

2019

We consider online algorithms. Typically the model is investigated with respect to competitive ratio. In this paper, we explore algorithms with small memory. We investigate two-way automata as a model for online algorithms with restricted memory. We focus on quantum and classical online algorithms. We show that there are problems that can be better solved by two-way automata with quantum and classical states than classical two-way automata in the case of sublogarithmic memory (sublinear size).

Estimating the temperature evolution of foodstuffs during freezing with a 3D meshless numerical method

2015

Abstract Freezing processes are characterised by sharp changes in specific heat capacity and thermal conductivity for temperatures close to the freezing point. This leads to strong nonlinearities in the governing PDE that may be difficult to resolve using traditional numerical methods. In this work we present a meshless numerical method, based on a local Hermite radial basis function collocation approach in finite differencing mode, to allow the solution of freezing problems. By introducing a Kirchhoff transformation and solving the governing equations in Kirchhoff space, the strength of nonlinearity is reduced while preserving the structure of the heat equation. In combination with the hig…

Bounds to internal forces for elastic-plastic solids subjected to variable loads

1979

Considering an elastic-plastic workhardening solid with piecewise linear yield surfaces and a piecewise linear workhardening law, we give a method for constructing bounds to the internal forces and to the (hardened) yield stresses produced by the action of variable loads at any point of the body and at any time. The loading history is supposed to be unknown, but the loads range within a given domain.

Determination of molecular weights and Stokes' radii of non-denatured proteins by polyacrylamide gradient gel electrophoresis. 1. An equation relatin…

1982

Untreated and processed gel plates of polyacrylamide (PAA) gradient gels were cut into strips perpendicularly to their length, and the wet and dry matter of the sections was determined. In untreated gels the apparent dry matter, as well as the relative dry matter, are a linear function of the gel length. In processed gels, however, only the apparent gel concentration increases linearly with the gel length, whereas the relative dry matter increases linearly with the square root of the gel length. The %T (content in polyacrylamide) was calculated from the apparent dry matter. The gel gradients used were found to be linear with respect to %T. Six different calibration proteins were run and the…

1986

The variation of the Huggins coefficient KH with the relative molecular mass M of the polymers was measured for solutions of polystyrene and of polyisobutylene and found to be most pronounced in the case of thermodynamically good solvents but vanishing at the theta-temperature, where the individual curves kH (T; M) intersect with each other. The experimental results are interpreted as a consequence of the rheological inequality of inter- and intra-molecular contacts between polymer segments. A model is presented according to which kH should be a linear function of M−(a−0,5), where a is the exponent of the intrinsic viscosity-relative molecular mass relationship (Kuhn-Mark-Houwink). The eval…

Extensions of representable linear functionals to unitized quasi *-algebras

2013

This paper starts from noting that, under certain conditions, *-representability and extensibility to the unitized *-algebra of a positive linear functional, defined on a *-algebra without unit, are equivalent. Here some conditions for the equivalence of the same concepts for a hermitian linear functional defined on a quasi *-algebra $(\A,\Ao)$ without unit are given. The approach is twofold: on the one hand, conditions for the equivalence are exhibited by introducing a condition for the *- representability of the extension of a *-representable functional to the unitized quasi *-algebra, on the other hand a *-representable extension to the unitization of a hermitian linear functional by mea…