This paper deals with a new analytic type of vectorand Clifford algebra valued automorphic forms in one and two vector variables. For hypercomplex generalizations of the classical modular group and their arithmetic congruence subgroups Eisensteinand Poincaré type series that are annihilated by Dirac operators, and more generally, by iterated Dirac operators on the upper half-space of Rn are dis...

Based on the concept of neutrosophic linguistic numbers (NLNs) in symbolic neutrosophic theory presented by Smarandache in 2015, the paper firstly proposes basic operational laws of NLNs and the expected value of a NLN to rank NLNs. Then, we propose the NLN weighted arithmetic average (NLNWAA) and NLN weighted geometric average (NLNWGA) operators and discuss their properties. Further, we establ...

Theories with associative and commutative (AC) operators, such as arithmetic, process algebras, boolean algebras, sets, : : : are ubiquitous in software and hardware veriication. These AC operators are diicult to handle by automatic deduction since they generate complex proofs. In this paper, we present new techniques for combining induction and AC reasoning, in a rewrite-based theorem prover. ...

We investigate the distribution functions and the moments of the so-called Choquet integral, also known as the Lovász extension, when regarded as a real function of a random sample drawn from a continuous population. Since the Choquet integral includes weighted arithmetic means, ordered weighted averaging operators, and lattice polynomials as particular cases, our results encompass the correspo...

Theories with associative and commutative (AC) operators, such as arithmetic, process algebras, boolean algebras, sets, : : : are ubiquitous in software and hardware veriication. These AC operators are diicult to handle by automatic deduction since they generate complex proofs. In this paper, we present new techniques for combining induction and AC reasoning, in a rewrite-based theorem prover. ...

Field Programmable Gate Arrays (FPGAs) are frequently used to accelerate signal and image processing algorithms due to their flexibility, relatively low cost, high performance and fast time to market. For those applications where the data has large dynamic range, floating-point arithmetic is desirable due to the inherent limitations of fixed-point arithmetic. Moreover, optimal reconfigurable ha...

A new model for associative memories is proposed in this paper. The mathematical tools used in this new model, include two binary operators designed specifically for the memories developed here. These operators were arbitrarí/y named as the .first two letters from the Greek alphabet: a and fJ. The new associative memories (afJ)are oftwo kinds and are able to operate in two different modes. The ...

We study adding aggregate operators, such as summing up elements of a column of a relation, to logics with counting mechanisms. The primary motivation comes from database applications, where aggregate operators are present in all real life query languages. Unlike other features of query languages, aggregates are not adequately captured by the existing logical formalisms. Consequently, all previ...

C ertain generating functions—encoding properties of objects like prime numbers, periodic orbits, ...—have received the name of zeta functions. They are useful in studying the statistical properties of the objects in question. Zeta functions have generally been associated with problems of arithmetic or algebra and tend to have common features: meromorphy, Euler product formula, functional equat...