Defining a feasible notion of space over the Blum-Shub-Smale (BSS) model of algebraic computation is a long standing open problem. In an attempt to define a right notion of space complexity for the BSS model, Naurois [CiE, 2007] introduced the notion of weak-space. We investigate the weak-space bounded computations and their plausible relationship with the classical space bounded computations. ...

The complete first order theories of the exponential differential equations of semiabelian varieties are given. It is shown that these theories also arise from an amalgamation-with-predimension construction in the style of Hrushovski. The theories include necessary and sufficient conditions for a system of equations to have a solution. The necessary conditions generalize Ax’s differential field...

Let k be an algebraically closed field. We will employ the following notation. If I ⊂ k[X1, . . . , Xn] is an ideal, we let Z(I) denote the affine algebraic set in An defined by the vanishing of the polynomials in I . Conversely, if X is an affine algebraic set, I(X) denotes the ideal of polynomials in k[X1, . . . , Xn] vanishing on X . We will give a proof of the following result, called the w...

We define global dimension and weak dimension for the structured ring spectra that arise in algebraic topology. We provide a partial classification of ring spectra of global dimension zero, the semisimple ring spectra of the title. These ring spectra are closely related to classical rings whose projective modules admit the structure of a triangulated category. Applications to two analogues of t...

Lambda-calculus is extended in order to represent a rather large class of recursive equation systems, implicitly characterizing function(al)s or mappings of some algebraic domain into arbitrary sets. Algebraic equality will then be represented by λβδ-convertibility (or even reducibility). It is then proved, under very weak assumptions on the structure of the equations, that there always exist s...

Considered are linear algebraic systems of equations and/or inequalities involving linear dependencies between interval-valued parameters. The goal is to characterize weak and strong solvability of such systems. Since any parametric interval equation is equivalent to a system of parametric interval inequalities, the focus is on the latter. We discuss an algorithmic procedure for characterizing ...

The “weak” BSD conjecture predicts that for an elliptic curve E over a number field K, we have rankE(K) = ords=1 L(E/K, s). The miracle of this formula is that it relates two quantities with very different origins: the left hand side is an algebraic object while the right hand side is an analytic object. Furthermore, the algebraic rank is “global” in nature, while the analytic rank can be defin...

In a previous work we have introduced the (P,Q)-superlattice, a hyperstructure of the form (L, P ∨, Q ∧). Here (L,∨,∧) is a lattice and the hyperoperations P ∨, Q ∧ are defined by a P ∨b . = a∨b∨P , a Q ∧b . = a∧b∧Q; when the sets P,Q ⊆ L satisfy appropriate conditions (L, P ∨, Q ∧) is a superlattice. In this work we continue the investigation of (P,Q)superlattice and consider the structure of ...

Most of the existing simultaneous approaches for heat exchanger network synthesis assume that only one type of hot/cold utility is available to adjust the final temperatures. In this work, we propose a simultaneous mixed-integer nonlinear programming formulation based on a more generalized stagewise superstructure. We allow utilities to adjust the temperature of process streams in each stage. W...