Search results for "Linear"
showing 10 items of 7165 documents
Multi-stage Linear Programming Optimization for Pump Scheduling
2014
This study presents a methodology based on Linear Programming for determining the optimal pump schedule on a 24-hour basis, considering as decision variables the continuous pump flow rates which are subsequently transformed into a discrete schedule. The methodology was applied on a case study derived from the benchmark Anytown network. To evaluate the LP reliability, a comparison was made with solutions generated by a Hybrid Discrete Dynamically Dimensioned Search (HD-DDS) algorithm. The cost associated with the result derived from the LP initial solution was shown to be lower than that obtained with repeated HD-DDS runs with differing random seeds. (C) 2013 The Authors. Published by Elsevi…
A note on faithful traces on a von Neumann algebra
2009
In this short note we give some techniques for constructing, starting from a {\it sufficient} family $\mc F$ of semifinite or finite traces on a von Neumann algebra $\M$, a new trace which is faithful.
Analyticity of a restricted formality
2020
International audience; The Kontsevich formality can be viewed as a non-linear map ℱ from the L∞ algebra of poly-vector fields on ℝd to the space of poly-differential operators. The space of the half-homogenous poly-vector fields is a sub-L∞ algebra. We prove here that the restriction of ℱto this subspace is weakly analytic.
Relative cohomology spaces for some osp($n|2$)-modules
2018
International audience; In this work, we describe the H-invariant, so(n)-relative cohomology of a natural class of osp(n|2)-modules M, for n ≠ 2. The Lie superalgebra osp(n|2) can be realized as a superalgebra of vector fields on the superline R1|n. This yields canonical actions on spaces of densities and differential operators on the superline. The above result gives the zero, first, and second cohomology spaces for these modules of densities and differential operators.
The diamond partial order in rings
2013
In this paper we introduce a new partial order on a ring, namely the diamond partial order. This order is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, A further algebraic version of Cochran's theorem and matrix partial orderings, Linear Algebra and its Applications, 127, 157--169, 1990]. We characterize the diamond partial order on rings and study its relationships with other partial orders known in the literature. We also analyze successors, predecessors and maximal elements under the diamond order.
Quantifier Elimination and Rectilinearisation Theorem for Generalised Quasianalytic Algebras
2013
International audience; An algebra of germs of real functions is generalised quasianalytic if to each element of the algebra we can associate, injectively, a power series with nonnegative real exponents. We prove a quantifier elimination and a rectilinearisation result for generalised quasianalytic algebras.
Representation Theorems for Solvable Sesquilinear Forms
2017
New results are added to the paper [4] about q-closed and solvable sesquilinear forms. The structure of the Banach space $\mathcal{D}[||\cdot||_\Omega]$ defined on the domain $\mathcal{D}$ of a q-closed sesquilinear form $\Omega$ is unique up to isomorphism, and the adjoint of a sesquilinear form has the same property of q-closure or of solvability. The operator associated to a solvable sesquilinear form is the greatest which represents the form and it is self-adjoint if, and only if, the form is symmetric. We give more criteria of solvability for q-closed sesquilinear forms. Some of these criteria are related to the numerical range, and we analyse in particular the forms which are solvable…
Linear extension operators on products of compact spaces
2003
Abstract Let X and Y be the Alexandroff compactifications of the locally compact spaces X and Y , respectively. Denote by Σ( X × Y ) the space of all linear extension operators from C(( X × Y )⧹(X×Y)) to C(( X × Y )) . We prove that X and Y are σ -compact spaces if and only if there exists a T∈Σ( X × Y ) with ‖ T ‖ Γ∈Σ( X × Y ) with ‖ Γ ‖=1. Assuming the existence of a T∈Σ( X × Y ) with ‖ T ‖ X and Y is equivalent to the fact that ‖ Γ ‖⩾2 for every Γ∈Σ( X × Y ) .
Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems
2020
We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is $$(p-1)$$-superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation-type result for the set of positive solutions as the parameter $$\lambda >0$$ varies. Also we prove the existence of a minimal positive solution $$u_\lambda ^*$$ and determine the monotonicity and continuity properties of the map $$\lambda \rightarrow u_\lambda ^*$$.
A note on homoclinic solutions of (p,q)-Laplacian difference equations
2019
We prove the existence of at least two positive homoclinic solutions for a discrete boundary value problem of equations driven by the (p,q) -Laplace operator. The properties of the nonlinearity ensure that the energy functional, corresponding to the problem, satisfies a mountain pass geometry and a Palais–Smale compactness condition.