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Hakobyan A. On the absence of a solution to a system of nonlinear infinite algebraic equations with Toeplitz type matrixes
ABSTRACT. The work is devoted to the study of one system of infinite algebraic equations with monotone nonlinearity. The system of such equations has applications in discrete problems of p-adic string theory and mathematical biology. We prove that there is no sign-preserved solution for this system in the class of bounded sequences. At the end, concrete examples of an applied nature are given.
Keywords: nonlinearity, infinite system, convexity, monotonicity, sequence.
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7 |
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Manukyan A., Mikaelyan H. Оn Antimagic Edge Colorings of Simple Cycles and Regular Bipartite Graphs
ABSTRACT. For a given graph G and a proper edge t-coloring α defined on G, denote by ܵSumg (ν, α), the sum of colors of edges neighboring ν ∈ V (G). In that case, α is called an antimagic edge t-coloring of the graph G, «G if for every pair of distinct vertices ν1, v2 ∈ V (G), SumG (ν1, α) ≠ SumG (ν2, α). The set of graphs G, for which there exists some t, such that G admits an antimagic edge t-coloring, is denoted by АМ. For any graph G∈ АМ, let ωam mean the least positive integer t, for which G admits an antimagic edge t-coloring. In this paper, we determine ωam (G) for simple cycles and regular bipartite graphs.
Keywords: Antimagic edge-coloring, edge-coloring.
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16 |
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Aramyan E. Representations for the distributions of the length of the random chord in the direction of convex figures
ABSTRACT. Reconstruction of convex figures using the distributions of the length of the random chord in directions of a convex figure plays an important role in integral geometry and in the theory of reconstruction of convex figures. In this work, a new expression for the distribution of the length of the random chord in the direction of convex polygons is found. The representation can be used to reconstruct convex figures. Also, we're proposing an algorithm for reconstructing an arbitrary convex quadrilateral.
Keywords: convex figures, length of the chord, reconstructing an arbitrary convex figure.
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25 |
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Karamyan D. Text Realignment for Speaker Diarisation
ABSTRACT. Speech applications dealing with conversations require not only recognizing the spoken words but also determining who spoke when. The task of assigning words to speakers is typically addressed by merging the outputs of two separate systems, namely, an automatic speech recognition (ASR) system and a speaker diarisation (SD) system. In practical settings, speaker diarisation systems can experience significant degradation in performance due to a variety of factors, including uniform segmentation with a high temporal resolution, inaccurate word timestamps, incorrect clustering and estimation of speaker numbers, as well as background noise and reverberation. Therefore, it is important to automatically detect these errors and make corrections if possible. In this study, we employ the Word Diarisation Error Rate (WDER) metric to pinpoint diarisation errors at the word level and classify them into three categories. Furthermore, we investigate two realignment strategies, namely an N-gram language model-based realignment and a punctuationbased realignment, to correct mistakes in words placed at the borders of sentences spoken by different speakers. Both methods resulted in an improvement in diarisation performance, with punctuation-based realignment providing the most significant word diarisation error rate reduction.
Keywords: Speaker Diarisation, Error Correction, Text Realignment, Word Diarisation Error Rate.
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34 |
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Kroyan A. On the solvability of one two-dimentional nonlinear infinite algebraic system of the Toeplitz-type
ABSTRACT. Thе paper is devoted to the study and solution of one class of nonlinear infinite systems of algebraic equations with monotone nonlinearity and two-dimensional Toeplitz-type matrices. With specific representations of nonlinearities, the indicated system arises in discrete problems of mathematical physics and mathematical biology. By combining special iterative methods with methods for constructing invariant cone segments for the corresponding nonlinear operator, we prove the existence of a nontrivial positive solution of this system in the space ݈
Keywords: system of nonlinear equations, monotonicity, nonlinearity, Toeplitz-type matrix.
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44 |
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Galoyan H. Design and Analysis of a Novel Tripteron-Inspired Micromanipulator with Flexure Hinges
ABSTRACT. This paper proposes a novel design of a Tripteron-inspired micromanipulator with flexure hinges to address the issue of accuracy, which can arise when traditional joints are replaced with flexure hinges. The classic Tripteron manipulator with flexure hinges has been shown to have accuracy issues, particularly with the replacement of traditional joints, which can cause inaccuracies of end effector motion. The end effector of traditional Tripteron manipulator with flexure hinges is making rotational motions instead of clear translational motions. This is because of stiffness of flexure hinges. To minimize the effects of rotational motion and improve the accuracy, the novel design adds additional legs symmetrically for each leg, resulting in six legs and providing clear translational motions. The proposed design significantlyimproves the issue of unwanted rotational motion of the end effector. To validate the effectiveness of the new design, finite element analysis was performed using ANSYS. The analysis showed that the stress and deformation levels were well within acceptable limits for the material used, and the simulations demonstrated the new design's ability to achieve precise and accurate manipulation tasks.
Keywords: Tripteron, micromanipulator, finite element method, flexure hinge, flexure pivot.
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54 |
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Karapetyan M. On free subgroup of automorphism of free periodic groups
ABSTRACT. In this paper, we construct free semigroup of infinite order automorphisms of free periodic groups B (m, n) of sufficiently large period n with m ≥ 3 generators.
Keywords: free Burnside group, automorphisms group, free semigroup.
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65 |
