Vol. 58 No. 1 (263) (2024)

DOI: https://doi.org/10.46991/PYSUA.2024.58.1
Published: 2024-04-24

Mathematics

  • Mathematics

    TWO CROFTON FORMULAS IN THE THREE-DIMENSIONAL SPACE

    Rafik H. Aramyan, Elen R. Aramyan
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    Abstract

    In this article, two Crofton-type integral formulas in the three-dimensional Euclidean space are obtained using integral geometry methods.

    References

    Santalo L. Integral Geometry and Geometric Probability. Cambridge Mathematical Library (2004).

    Ambartzumian R.V. Factorization Calculus and Geometrical Probability. Cambridge, Cambridge University Press (1990).

    Ambartzumian R.V. Combinatorial Integral Geometry, Metric and Zonoids. Acta Appl. Math. 9 (1987), 3-27. http://dx.doi.org/10.1007/BF00580819

    Aramyan R., Mnatsakanyan V. Conditional Moments for a d-Dimensional Convex Body. J. of Contemp. Math. Analysis (Armenian Acad. Sci.) 56 (2021), 3-9. https://doi.org/10.3103/S106836232103002X

  • Mathematics

    ALMOST IDENTITIES IN GROUPS

    Grigor G. Gevorkyan, Vachagan G. Dilanyan
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    Abstract

    In this work we construct a group G, which generates the variety of all groups. At the same time, in each ball of the Cayley graph of this group G,  the ratio of the number of elements that satisfy a fixed equation of the form $x^n=1$ to the number of all elements of this ball tends to one when the radius of the ball tends to $\infty$ .

    References

    Atabekyan V.S. Uniform Nonamenability of Subgroups of Free Burnside Groups of Odd Period. Math. Notes 85 (2009), 496-502. https://doi.org/10.1134/S0001434609030213

    Tointon M.C.H. Commuting Probabilities of Infinite Groups. Journal of the London Mathematical Society 101 (2020), 1280-1297. https://doi.org/10.1112/jlms.12305

    Amir G., Blachar G., et al. Probabilistic Laws on Infinite Groups (2023). https://doi.org/10.48550/arXiv.2304.09144

    Goffer G., Greenfeld B. Probabilistic Burnside Groups (2023). https://doi.org/10.48550/arXiv.2306.11204

    Adian S.I. Periodic Products of Groups. Proc. Steklov Inst. Math. 142 (1976), 3-21.

    Adian S.I., Atabekyan V.S. Periodic Product of Groups. Journal of Contemporary Mathematical Analysis 52 (2017), 111-117. https://doi.org/10.3103/S1068362317030013

    Adian S.I., Atabekyan V.S. n-Torsion Groups. Journal of Contemporary Mathematical Analysis 54 (2019), 319-327. https://doi.org/10.3103/S1068362319060013

    Boatman N.S. Partial-Burnside Groups. PhD Thesis (2012). https://etd.library.vanderbilt.edu/etd-11302012-113318

    Atabekyan V.S., Bayramyan A.A. Probabilistic Identities in n-Torsion Groups. Journal of Contemporary Mathematical Analysis 59 (2024).

    Adian S.I. The Burnside Problem and Identities in Groups. Moscow, Nauka (1975).

Mechanics

  • Mechanics

    ON OPTIMAL CONTROL OF THERMOELASTIC VIBRATIONS OF A PLATE-STRIP

    Samvel H. Jilavyan, Edmon R. Grigoryan
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    Abstract

    The problem of optimal control of elastic vibrations of an isotropic plate-strip under the influence of temperature and force fields is studied. The function of changing the external load on the plane of the plate is represented as a control function. Optimal control is also carried out by the distribution function of the temperature of the external field over the plate. The well-known classical hypotheses of thermo-elastic bending of the plate are accepted. The equations of transverse vibrations of the plate and heat conduction in the plate are solved under the boundary conditions of heat transfer and the stress state on the planes of the plate. The method of Fourier series, the method of representing moment relations, the well-known method of minimizing the functional are used.

    References

    Butkovski A.G. Methods of Control of Systems with Distributed Parameters. Moscow, Nauka (1972), 332 (in Russian).

    Jilavyan S.H., Grigoryan E.R., Khurshudyan As.Zh. Heating Control of Finite Rod with a Mobile Source. Archive of Control Sciences. Polish Academy of Sciences 31 (2021), 417-430. https://doi.org/10.24425/acs.2021.137425

    Jilavyan S.H., Khurshudyan As.Zh. Optimal Control of Anisotropic Layer-Plate Vibrations in View of Transverse Shear. Problems of Control, Information Processing and Transmission 2 (2013), 219-228.

    Ignaczak J. A Review: Thermoelasticity by Witold Nowackiy (2nd ed.). Oxford, Pergamon Press (1986). https://doi.org/10.1080/01495738808961927

    Adams R.J. Analysis and Control of Thermoelastic Vibrations in Plate Structures. University of Oklahoma (2001).

    Xu B., Lu X., Bai Y. A Spatiotemporal Fuzzy Control Approach for Complex Distributed Parameter System with Application to Thermal Processes. J. Process Control 127 (2023). https://doi.org/10.1016/j.jprocont.2023.102993

Informatics

  • Informatics

    ADAPTIVE NOISE CANCELLATION FOR ROBUST SPEECH RECOGNITION IN NOISY ENVIRONMENTS

    Davit S. Karamyan
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    Abstract

    In this paper, we address the challenges faced when combining noise cancellation and automatic speech recognition models. When these models are combined directly, the performance of word recognition often suffers because the distribution of input data changes. To overcome this limitation, we propose a novel method for combining these models, which enhances the ability of the speech recognition model to perform well in noisy environments. The key feature of the proposed method is the introduction of a mechanism to control the aggressiveness of noise reduction. This mechanism enables us to customize the noise reduction process according to the specific requirements of the ASR model, without necessitating any retraining. This advantage makes our method applicable to any ASR model, facilitating its implementation in practical scenarios.

    References

    Radford A., Kim J., et al. Robust Speech Recognition Via Large-scale Weak Supervision. International Conference on Machine Learning(2023), 28492-28518. https://doi.org/10.48550/arXiv.2212.04356

    Gulati A., Qin J., et al. Conformer: Convolution-augmented Transformer for Speech Recognition. INTERSPEECH (2020), 5036-5040. https://doi.org/10.48550/arXiv.2005.08100

    Li J., Lavrukhin V., et al. Jasper: An End-to-End Convolutional Neural Acoustic Model (2019). https://doi.org/10.48550/arXiv.1904.03288

    Boll S. Suppression of Acoustic Noise in Speech Using Spectral Subtraction. IEEE Transactions on Acoustics, Speech, and Signal Processing 27 (1979), 113-120. https://doi.org/10.1109/TASSP.1979.1163209

    Acero A. Acoustical and Environmental Robustness in Automatic Speech Recognition. Springer Science and Business Media (1992). https://doi.org/10.1007/978-1-4615-3122-7

    Cui X., Iseli M., et al. Evaluation of Noise Robust Features on the Aurora Databases. Proc. 7th International Conference on Spoken Language Processing (ICSLP 2002). INTERSPEECH (2002), 481-484. https://doi.org/10.21437/ICSLP.2002-24

    Hermansky H., Morgan N. RASTA Processing of Speech. IEEE Transactions on Speech and Audio Processing 2 (1994), 578-589. https://doi.org/10.1109/89.326616

    Mošner L., Wu M., et al. Improving Noise Robustness of Automatic Speech Recognition Via Parallel Data and Teacher-Student Learning. ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2019), 6475-6479. https://doi.org/10.48550/arXiv.1901.02348

    Gales M., Young S. Robust Continuous Speech Recognition Using Parallel Model Combination. IEEE Transactions on Speech and Audio Processing 4 (1996), 352-359. https://doi.org/10.1109/89.536929

    Gong Y. Speech Recognition in Noisy Environments: A Survey. Speech Communication 19 (1995), 261-291. https://doi.org/10.1016/0167-6393(94)00059-J

    Lippmann R., Martin E., Paul D. Multi-style Training for Robust Isolated-word Speech Recognition. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 12 (1987), 705-708. https://doi.org/10.1109/ICASSP.1987.1169544

    Wang Z., Wang X., et al. Oracle Performance Investigation of the Ideal Masks. IEEE International Workshop on Acoustic Signal Enhancement (IWAENC) (2016), 1-5. https://doi.org/10.1109/IWAENC.2016.7602888

    Xia S., Li H., Zhang X. Using Optimal Ratio Mask as Training Target for Supervised Speech Separation. Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC). Malaysia, Kuala Lumpur, IEEE (2017). https://doi.org/10.48550/arXiv.1709.00917

    Cho K., Merriënboer B., et al. On the Properties of Neural Machine Translation: Encoder–Decoder Approaches. Proceedings of SSST-8, Eighth Workshop on Syntax, Semantics and Structure in Statistical Translation 10 (2014), 103-111. https://doi.org/10.3115/v1/W14-4012

    Panayotov V., Chen G., et al. Librispeech: An ASR Corpus Based on Public Domain Audio Books. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2015), 5206-5210. https://doi.org/10.1109/ICASSP.2015.7178964

    Snyder D., Chen G., Povey D. Musan: A Music, Speech, and Noise Corpus (2015). https://doi.org/10.48550/arXiv.1510.08484

Physics