In this paper, we observe and compare results concerning solvability of systems of fuzzy relation equations with different types of composition. In fact, two types of composition are considered sup−∗ and inf → composition where ∗ is a continuous tnorm and→ is residuation operation with respect to the t-norm ∗.

A family of discontinuous Galerkin finite element methods is formulated and analyzed for Stokes and Navier-Stokes problems. An inf-sup condition is established as well as optimal energy estimates for the velocity and L2 estimates for the pressure. In addition, it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces.

The aim of this paper is to propose a stabilization technique in order to circumvent the two inf{sup conditions needed for stability of the discretization of the Three Fields Formulation for domain decomposition methods BM93, BM94]. Realization of this technique in terms of wavelets is presented. Furthermore, the resulting discrete problem is shown to admit an asymptotically optimal preconditio...

These are the lecture notes from week 2 of Ma1d, the Caltech mathematics course on sequences and series. 1. Limits Superior and Inferior So: most of the definitions and theorems we’ve developed so far for sequences are centered around the concept of convergence – we have lots of ways of talking about when things converge, where they converge to, and under what conditions they will be forced to ...

This lecture—based on the author's book, General Lattice Theory , Birkhäuser Verlag, 1978—briefly introduces the basic concepts of lattice theory, as needed for the lecture " Some combinatorial aspects of congruence lattice representations ". 1.1. Posets. A partially ordered set A; ≤≤ consists of a nonvoid set A and a binary relation ≤ on A such that the relation ≤ satisfies properties (P1)–(P3...

The main aim of this paper is to present the properties of the sup F composition based on the aggregation operator F de ned by Mayor and Torrens and analyze some properties about the pseudocomplement and the inf composition to show that these compositions have analogous properties to the based on t norms

This work deals with the optimization problem sup inf S(x, y), which plays, undoubtedly xeX yeY a crucial part in mathematical programming and game theory. On the basis of probability theory, a solving approach — semistochastic decomposition is proposed. This method is finite with probability 1 without any hypothesis about convexity or differentiability as it is usually required in traditional ...

Finite element methods for problems given in complex domains are often based on tetrahedral meshes. This paper demonstrates that the so–called rational Large Eddy Simulation model and a projection–based Variational Multiscale method can be extended in a straightforward way to tetrahedral meshes. Numerical studies are performed with an inf–sup stable second order pair of finite elements with dis...

This paper presents a mixed variational formulation and its discretization by finite elements of higher-order for the Signorini problem with Tresca friction. To guarantee the unique existence of the solution to the discrete mixed problem, a discrete inf-sup condition is proved. Moreover, a solution scheme based on the dual formulation of the problem is proposed. Numerical results confirm the th...

For r ∈ (0, 1), let Z r = {x ∈ R 2 | dist(x, Z 2) > r/2} and τ r (x, v) = inf{t > 0 | x + tv ∈ ∂Z r }. Let Φ r (t) be the probability that τ r (x, v) ≥ t for x and v uniformly distributed in Z r and S 1 respectively. We prove in this paper that lim sup ǫ→0 +