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An analytical solution for the optical efficiency of a luminescent solar concentrator is presented. Due to a large number of input parameters and their complex effect on the device efficiency numerical simulations have been previously used…
Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and associated with the transition to a new time level on the basis of the…
The paper describes different approaches to generalize the trapezoidal method to fractional differential equations. We analyze the main theoretical properties and we discuss computational aspects to implement efficient algorithms. Numerical…
Recent theoretical work on automatic differentiation (autodiff) has focused on characteristics such as correctness and efficiency while assuming that all derivatives are automatically generated by autodiff using program transformation, with…
The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail…
Context. Modern radio astronomical arrays have (or will have) more than one order of magnitude more receivers than classical synthesis arrays, such as the VLA and the WSRT. This makes gain calibration a computationally demanding task.…
Delta lenses are functors equipped with a suitable choice of lifts, and are used to model bidirectional transformations between systems. In this paper, we construct an algebraic weak factorisation system whose R-algebras are delta lenses.…
We present a simplification of the recursive algorithm for the evaluation of intersection numbers for differential $n$-forms, by combining the advantages emerging from the choice of delta-forms as generators of relative twisted cohomology…
A general conversion strategy by involving a shifted parameter $\theta$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such…
Deep Active Learning (DAL) reduces annotation costs by selecting the most informative unlabeled samples during training. As real-world applications become more complex, challenges stemming from distribution shifts (e.g., open-set…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
A transformation optics approach was used to derive a general method for designing electromagnetic devices able to manipulate the wave vectors in the specific manner required by the functionality of the device. While the wave paths inside…
Tensor algebra is a crucial component for data-intensive workloads such as machine learning and scientific computing. As the complexity of data grows, scientists often encounter a dilemma between the highly specialized dense tensor algebra…
Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions.…
In this paper we propose a dynamic programming solution to the template-based recognition task in OCR case. We formulate a problem of optimal position search for complex objects consisting of parts forming a sequence. We limit the distance…
Scientific computing is an essential tool for scientific discovery and engineering design, and its computational cost is always a main concern in practice. To accelerate scientific computing, it is a promising approach to use machine…
Following the definitions of the algebras of differential operators, $\beta$-differential operators, and the quantum differential operators on a noncommutative (graded) algebra given in \cite{LR}, we describe these operators on the free…
Let $\K$ be an algebraic number field of degree $d$ and discriminant $\Delta$ over $\Q$. Let $\A$ be an associative algebra over $\K$ given by structure constants such that $\A\cong M_n(\K)$ holds for some positive integer $n$. Suppose that…
In this paper, by way of three examples - a fourth order low pass active RC filter, a rudimentary BJT amplifier, and an LC ladder - we show, how the algebraic capabilities of modern computer algebra systems can, or in the last example,…
Many computer algebra systems have more than 1000 built-in functions, making expertise difficult. Using mock dialog boxes, this article describes a proposed interactive general-purpose wizard for organizing optional transformations and…