the concept of “infinite essence” that is both philosophically and theologically important, has passed many different evolutions in western history of thought. presocratics has evaluated it in two different ways. anaximender and melissus agree that the principle substance is infinite and divine, but neither absolutly transcendent nor anthropomorphic. the infinite is the fusis in its substantial...

Convex relaxations have been instrumental in solvability of constraint satisfaction problems (CSPs), as well the three different generalisations CSPs: valued CSPs, infinite-domain and most recently promise CSPs. In this work, we extend an existing tractability result to CSPs combined: We give a sufficient condition for combined basic linear programming affine integer relaxation exact over infin...

We consider the existence, uniqueness and effectiveness of solutions to infinite systems of equations in certain inverse limits of algebras. The notion of a guarded infinite system of equations is defined and used to establish existence and uniqueness results about the solutions. A domain structure associated with the inverse limit is used to prove the theorems. The use of infinite systems of e...

In this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon–Nikod´ym property, Clarke's generalized Jacobian will be extended to this setting. Characterization and fundamental properties of the extended generalized Jacobian are established including the nonemptiness, the β-compactness, the β-...

We consider localization of gravity in domain wall solutions of Einstein’s gravity coupled to a scalar field with a generic potential. We discuss conditions on the scalar potential such that domain wall solutions are non-singular. Such solutions even exist for appropriate potentials which have no minima at all and are unbounded below. Domain walls of this type have infinite tension, while usual...

In this paper, we show decidabil i ty of a rather expressive fragment of the situation calculus. We allow second order quantif ication over finite and inf inite sets of situations. We do not impose a domain closure assumption on actions; therefore, infinite and even uncountable domains are allowed. The decision procedure is based on automata accepting infinite trees.

The study of fixpoints has long been at the heart of logic programming. However, whereas least fixpoint semantics works well for SLD-refutations (i.e. is sound and complete), there is no satisfactory (i.e. complete) fixpoint semantics for infinite derivations. In this paper, we focus on this problem. Standard approaches in this area consist in concentrating on infinite derivations that can be s...

We describe the class of polynomial functions which are barycentrically associative over an infinite commutative integral domain.

in this paper we consider the group algebra $r(c_2times‎ ‎d_infty)$‎. ‎it is shown that $r(c_2times d_infty)$ can be‎ ‎represented by a $4times 4$ block circulant matrix‎. ‎it is also‎ ‎shown that $mathcal{u}(mathbb{z}_2(c_2times d_infty))$ is‎ ‎infinitely generated‎.

A standard result from unification theory says that if a finite set E of equations between finite terms is unifiable, then there exists a most general unifier for E. In this paper, the theorem is generalized to the case where E may be infinite. In order to obtain this result, substitutions are allowed to have an infinite domain.