We describe data structures and algorithms for performing a path-sensitive program analysis to discover equivalences of expressions involving linear arithmetic or uninterpreted functions. We assume that conditionals are abstracted as boolean variables, which may be repeated to reflect equivalent conditionals. We introduce free conditional expression diagrams (FCEDs), which extend binary decisio...

Recalling the insights of McCulloch and Pitts [4], von Neumann [9] and Minsky [5] we introduce some non monotonic operators implemented by means of new electronic devices (FPGA) for a NeuroSymbolic Processor (NSP). Some nets performing logical and arithmetic functions are also presented.

Paul Gunnells has developed an algorithm for computing actions of Hecke operators on arithmetic cohomology below the cohomological dimension. One version of his algorithm uses a conjecture concerning LLL-reduced matrices. We prove this conjecture for dimensions 2 through 5 and disprove it for all higher dimensions.

We give complexity estimates for the problems of evaluation and interpolation on various polynomial bases. We focus on the particular cases when the sample points form an arithmetic or a geometric sequence, and we discuss applications, respectively to computations with linear differential operators and to polynomial matrix multiplication.

In this paper, we study some complementary inequalities to Jensen's inequality for self-adjoint operators, unital positive linear mappings, and real valued twice differentiable functions. New improved complementary inequalities are presented by using an improvement of the Mond-Pečarić method. These results are applied to obtain some inequalities with quasi-arithmetic means.

In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator...

where Aj = −d/dx + fj(x) are first order differential operators. A Darboux chain is called periodic if Lj+r = Lj for some r and for all j = 1, 2, . . . . Number r is called the period of a Darboux chain. The operator L+ α2 appears to be the harmonic oscillator in the particular case r = 1. Periodic Darboux chains lead to integrable systems of differential equations for functions fj, which are e...

Avinash Lingamneni1 3 ∗, Christian Enz3, Krishna Palem1 2, and Christian Piguet3 1Deptarment of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, USA 2NTU-Rice Institute for Sustainable and Applied Infodynamics (ISAID), Nanyang Technological University, Singapore 3Wireless and Integrated Systems, Centre Suisse d’Electronique et de Microtechnique (CSEM) SA, Neuchatel 20...

Techniques based on Interval and Affine Arithmetic and their modifications are shown to provide reliable function range evaluation for the purposes of surface interrogation. In this paper we present a technique for the reliable interrogation of implicit surfaces using a modification of Affine Arithmetic called Revised Affine Arithmetic. We extend the range of functions presented in Revised Affi...

Fuzzy subgroups and T -vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T -vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T -indistinguishability operators (fuzzy equivalence relations). In this pa...