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Articles 1 - 11 of 11
Full-Text Articles in Physical Sciences and Mathematics
Need For Shift-Invariant Fractional Differentiation Explains The Appearance Of Complex Numbers In Physics, Olga Kosheleva, Vladik Kreinovich
Need For Shift-Invariant Fractional Differentiation Explains The Appearance Of Complex Numbers In Physics, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Complex numbers are ubiquitous in physics, they lead to a natural description of different physical processes and to efficient algorithms for solving the corresponding problems. But why this seemingly counterintuitive mathematical construction is so natural here? In this paper, we provide a possible explanation of this phenomenon: namely, we show that complex numbers appear if take into account that some physical system are described by derivatives of fractional order and that a physically meaningful analysis of such derivatives naturally leads to complex numbers.
So How Were The Tents Of Israel Placed? A Bible-Inspired Geometric Problem, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
So How Were The Tents Of Israel Placed? A Bible-Inspired Geometric Problem, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In one of the Biblical stories, prophet Balaam blesses the tents of Israel for being good. But what can be so good about the tents? A traditional Rabbinical interpretation is that the placement of the tents provided full privacy: from each entrance, one could not see what is happening at any other entrance. This motivates a natural geometric question: how exactly were these tents placed? In this paper, we provide an answer to this question.
Why Ancient Egyptians Preferred Some Sum-Of-Inverses Representations Of Fractions?, Olga Kosheleva, Vladik Kreinovich
Why Ancient Egyptians Preferred Some Sum-Of-Inverses Representations Of Fractions?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Ancient Egyptians represented a fraction as a sum of inverses of natural numbers, with the smallest possible number of terms. In our previous paper, we explained that this representation makes sense since it leads to the optimal way of solving a problem frequently mentioned in the Egyptian papyri: dividing bread between workers. However, this does not explain why ancient Egyptians preferred some representations with the same number of terms but not others. For example, to represent 2/3, they used the sum 1/2 + 1/6 but not the sum 1/3 + 1/3 with the same number of terms. In this paper, …
What If You Are Late On Several (Relatively Small) Tasks?, Olga Kosheleva, Vladik Kreinovich
What If You Are Late On Several (Relatively Small) Tasks?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In practice, we sometimes end up in a situation when we are late on several relatively small tasks. We cannot finish them all, so which ones should we do first? We show that in general, this is an NP-complete problem. In the typical situation when all the tasks are of approximately the same importance and requires approximately the same time to finish, we can have an explicit solution to this problem. In a nutshell, the resulting (somewhat counterintuitive) recommendation is to start with things which are not yet late or only a few days late. Actually, this recommendation makes sense: …
Possibility To Algorithmically Check: Yet Another Reason Why Current Definitions Have Been Selected In Elementary Mathematics, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Possibility To Algorithmically Check: Yet Another Reason Why Current Definitions Have Been Selected In Elementary Mathematics, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
At first glance, many definitions in mathematics -- especially in elementary mathematics -- seem arbitrary. Why is 1 not considered a prime number? Why is a square considered to be a particular case of a parallelogram -- in some old textbooks, a parallelogram was defined in such a way as to exclude the square. In his 2018 article, Art Duval explained many such definitions by a natural requirement to make the corresponding results (theorems) as simple as possible. However, elementary mathematics is not just about theorems and proofs, it is also about computations. In this paper, we show that from …
Why Quantiles Are A Good Description Of Volatility In Economics: A Pedagogical Explanation, Sean R. Aguilar, Vladik Kreinovich, Uyen Pham
Why Quantiles Are A Good Description Of Volatility In Economics: A Pedagogical Explanation, Sean R. Aguilar, Vladik Kreinovich, Uyen Pham
Departmental Technical Reports (CS)
To make investment decisions, we need to know, for each financial instrument, not only its expected return -- but also how the actual return may deviate from its expected value. A numerical measure of such deviations is known as volatility. Originally, volatility was measured by the srabdard deviation from the expected price, but it turned out that this measure does not always adequately describe our perception of volatility. Empirically, it turned out that quantiles are a more adequate description of volatility. In this paper, we provide an explanation of this empirical phenomenon.
Should Fighting Corruption Always Be One Of The Main Pre-Requisites For Economic Help?, Sean R. Aguilar, Vladik Kreinovich
Should Fighting Corruption Always Be One Of The Main Pre-Requisites For Economic Help?, Sean R. Aguilar, Vladik Kreinovich
Departmental Technical Reports (CS)
In general, corruption is bad. In many cases, it makes sense to make fighting corruption one of the main pre-requisites for getting financial help: we do not want this money to line the pockets of corrupted officials, we want to help the people. In this paper, we argue, however, that in some cases -- of over-regulated and/or oppressive regimes -- too much emphasis on fighting corruption may be counter-productive: instead of helping people, it may hurt them.
Being Active In Research Makes A Person A Better Teacher And Even Helps When Working For A Company, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Being Active In Research Makes A Person A Better Teacher And Even Helps When Working For A Company, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
At first glance, it looks like being active in research is not necessarily related to a person's success in being a teacher or being a productive company employee -- moreover, it looks like research distracts from other tasks. Somewhat surprisingly, however, in practice, the best teachers and the best employees are actually the ones who are active in research. In this paper, we provide an explanation for this seemingly counter-intuitive phenomenon.
Yet Another Possible Explanation Of Egyptian Fractions: Motivated By Fairness, Olga Kosheleva, Vladik Kreinovich
Yet Another Possible Explanation Of Egyptian Fractions: Motivated By Fairness, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Ancient Egyptians represented fractions as sums of inverses of natural numbers, and they made sure that all these natural numbers are different. The representation as a sum of inverses makes some sense: it is known to lead to an optimal solution to the problem of dividing bread between workers, a problem often described in the Egyptian papyri. However, this does not explain why the corresponding natural numbers should be all different: some representations with the same natural number repeated several times lead to the same smallest number of cuts as the representations that the ancient Egyptians actually used. In this …
Why Min, Max, Opening, And Closing Stock Prices Are Empirically Most Appropriate For Predictions, And Why Their Linear Combination Provides The Best Estimate For Beta, Somsak Chanaim, Olga Kosheleva, Vladik Kreinovich
Why Min, Max, Opening, And Closing Stock Prices Are Empirically Most Appropriate For Predictions, And Why Their Linear Combination Provides The Best Estimate For Beta, Somsak Chanaim, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
While we have moment-by-moment prices of each stock, we cannot use all this information to predict the future stock prices, we need to combine them into a few characteristics of the daily stock price. Empirically, it turns out that the best characteristics are the lowest daily price, the highest daily price, the opening price, and the closing price. In the paper, we provide a theoretical explanation for this empirical phenomenon. We also explain why empirically, it turns out that the best way to find the stock's beta coefficient is to consider a convex combination of the about four characteristics.
A Natural Formalization Of Changing-One's-Mind Leads To Square Root Of "Not" And To Complex-Valued Fuzzy Logic, Olga Kosheleva, Vladik Kreinovich
A Natural Formalization Of Changing-One's-Mind Leads To Square Root Of "Not" And To Complex-Valued Fuzzy Logic, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
We show that a natural formalization of the process of changing one's mind leads to such seemingly non-intuitive ideas as square root of "not" and complex-valued fuzzy degrees.