Related papers: Non-negative Rational Semantic Numeration Systems
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
For a computational system to be intelligent, it should be able to perform, at least, basic deductions. Nonetheless, since deductions are, in some sense, equivalent to tautologies, it seems that they do not provide new information. The…
A representation of complex rational numbers in quantum mechanics is described that is not based on logical or physical qubits. It stems from noting that the zeros in a product qubit state do not contribute to the number. They serve only as…
Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual and…
We continue previous work to count non-equivalent dynamical systems over finite fields generated by polynomials or rational functions.
Neurotechnology has made great strides in the last 20 years. However, we still have a long way to go to commercialize many of these technologies as we lack a unified framework to study cyber-neural systems (CNS) that bring the hardware,…
Complete residue systems play an integral role in abstract algebra and number theory, and a description is typically found in any number theory textbook. This note provides a concise overview of complete residue systems, including a robust…
Semantic properties are domain-specific specification constructs used to augment an existing language with richer semantics. These properties are taken advantage of in system analysis, design, implementation, testing, and maintenance…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
In a recent article, we introduced and studied a precise class of dynamical systems called solvable systems. These systems present a dynamic ruled by discontinuous ordinary differential equations with solvable right-hand terms and unique…
It is well-known that when a positively expansive dynamical system is invertible then its underlying space is finite. C.Morales has introduced a decade ago a natural way to generalize positive expansiveness, by introducing other properties…
Noncommutative rational functions appeared in many contexts in system theory and control, from the theory of finite automata and formal languages to robust control and LMIs. We survey the construction of noncommutative rational functions,…
Sumterms are introduced as syntactic entities, and sumtuples are introduced as semantic entities. Equipped with these concepts a new description is obtained of the notion of a sum as (the name for) a role which can be played by a number.…
Recently, ranking-based semantics is proposed to rank-order arguments from the most acceptable to the weakest one(s), which provides a graded assessment to arguments. In general, the ranking on arguments is derived from the strength values…
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…
We consider the set of power functions defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative…
The role of the descriptor system representation as basis for reliable numerical computations for system analysis and synthesis, and in particular, for the manipulation of rational matrices, is discussed and available robust numerical…
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we…