相关论文: Can our number system be improved?

Recent research argues that exact recursive numeral systems optimize communicative efficiency by balancing a tradeoff between the size of the numeral lexicon and the average morphosyntactic complexity (roughly length in morphemes) of…

All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…

Systematic application of software metric techniques can lead to significant improvements of the quality of a final software product. However, there is still the evident lack of wider utilization of software metrics techniques and tools due…

In this paper, we propose new generalizations of amicable numbers. We also give examples and prove properties of these new concepts.

The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…

Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…

We provide numerical procedures for possibly best evaluating the sum of positive series. Our procedures are based on the application of a generalized version of Kummer's test.

This paper presents a mathematical approach for improving the performance of a control system by modifying the time delay at certain operating conditions. This approach converts a continuous time loop into a discrete time loop. The formula…

We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.

The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…

Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…

We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…

We propose that the SI be modified so that the radian is a base unit. Some of the details and consequences of such a modification are examined.

Eugene Wigner's much-discussed notion of the "unreasonable effectiveness of mathematics" as applied to describing the physics of empirical reality is simultaneously both trivial and profound. After all, the relevant mathematics was (in the…

Simple method to improve traditional approaches to name taxa of higher ranks has been proposed. Instead of base name + postfixes (which vary between codes of nomenclature and sometimes not standardized at all), use numerical prefixes, where…

It is argued that zero should be considered as a cardinal number but not an ordinal number. One should make a clear distinction between order types that are labels for well-ordered sets and ordinal numbers that are labels for the elements…

Computers are a very important part of our lives and the major reason why they have been such a success is because of the excellent graphical operating systems that run on these powerful machines. As the computer hardware is becoming more…

Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…

Despite recent successes in language models, their ability to represent numbers is insufficient. Humans conceptualize numbers based on their magnitudes, effectively projecting them on a number line; whereas subword tokenization fails to…

We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.