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The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
Using quantum maps we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy, in some systems, is demonstrated quantitatively. However, our study of the standard map cautions that this…
The regular separability problem asks, for two given languages, if there exists a regular language including one of them but disjoint from the other. Our main result is decidability, and PSpace-completeness, of the regular separability…
Forecast combinations have been widely applied in the last few decades to improve forecasting. Estimating optimal weights that can outperform simple averages is not always an easy task. In recent years, the idea of using time series…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
Establishing the chronology of the Vedas has interested scholars for the last two centuries. The oldest among them is Rig-Veda which has ten Mandalas, each composed separately. In this paper, we look at deciphering plausible pointers to the…
The connection between the commutativity of a family of $n\times n$ matrices and the generalized joint numerical ranges is studied. For instance, it is shown that ${\cal F}$ is a family of mutually commuting normal matrices if and only if…
Personnel scheduling problems have received considerable academic attention due to their relevance in various real-world applications. These problems involve preparing feasible schedules for an organization's employees and often account for…
An $(a,b)$-difference necklace of length $n$ is a circular arrangement of the integers $0, 1, 2, \ldots , n-1$ such that any two neighbours have absolute difference $a$ or $b$. We prove that, subject to certain conditions on $a$ and $b$,…
A major focus of the archaeoastronomical research conducted around the world focuses on understanding how ancient cultures observed sunrise and sunset points along the horizon, particularly at the solstices and equinoxes. Scholars argue…
Innovating mathematics by research approaches in Indonesia from middle schools to undergraduates are explained here where geometry is typical example to be innovated. Topics in plane geometry to be platonic solids and non platonic solids…
The dominant part in the mental calculation of the day of the week for any given date is to determine the year share, that is, the contribution of the two-digit year part of the date. This paper describes a number of year share computation…
We introduce the Statistical Asynchronous Regression (SAR) method: a technique for determining a relationship between two time varying quantities without simultaneous measurements of both quantities. We require that there is a time…
In this paper, we study congruences on sums of products of binomial coefficients that can be proved by using properties of the Jacobi polynomials. We give special attention to polynomial congruences containing Catalan numbers, second-order…
We develop a formal perspective on how regular expression matching works in Java, a popular representative of the category of regex-directed matching engines. In particular, we define an automata model which captures all the aspects needed…
Fundamental mathematical constants appear in nearly every field of science, from physics to biology. Formulas that connect different constants often bring great insight by hinting at connections between previously disparate fields.…
Consider the many shared resource scheduling problem where jobs have to be scheduled on identical parallel machines with the goal of minimizing the makespan. However, each job needs exactly one additional shared resource in order to be…
The paper presents a comparative analysis of iterative numerical methods of Jacobi and Gauss-Seidel for solving systems of linear algebraic equations (SLAEs) with complex and real matrices. The ranges of convergence for both methods for…
The science of versification and analysis of verse in Sanskrit is governed by rules of metre or chandas. Such metre-wise classification of verses has numerous uses for scholars and researchers alike, such as in the study of poets and their…
We propose an extension of the asynchronous pi-calculus with a notion of random choice. We define an operational semantics which distinguishes between probabilistic choice, made internally by the process, and nondeterministic choice, made…