Search results for “powers of x”

Reference table of indefinite integrals of products of powers of x with sine and cosine.

Reference table of indefinite integrals of the exponential function and its products with powers of x.

Reference table of indefinite integrals of sine, cosine, tangent and their powers and products.

Addition, scalar multiplication, transposition and multiplication of matrices, along with subtraction, powers, and trace.

Reference table of the basic indefinite integrals of the elementary functions: power, exponential, logarithmic and trigonometric.

Reference table of the derivatives of the elementary functions: power, exponential, logarithmic, trigonometric and their inverses.

The article examines the issue of representing municipal government in the media space, followed by the proposed solution for automatically identifying signs of destructive and constructive positioning of communicative types of municipal employees in the public information space. The definition of the concept of the communicative type “municipal employee” with verification features is introduced. The results of the analysis of the organization of local self-government on the example of the Moscow region allowed us to conclude that the communicative type “municipal employee” reflects a diversified system of territorial communicative position within the regional government. The information obtained during the analysis of public information space attitudes regarding the activities of municipal employees can be automated with the method of identifying linguistic markers of emotivity to determine the communicative position of territorial authorities. The suggested methodology for effective automation of the studied subject area in the humanities has been verified as possessing a high scientific potential for further research. It is concluded that the development of technology for monitoring and forecasting public threats based on “soft power” methods through automatic and expert work to identify markers of evaluative presentation of communicative types of municipal employees is designed to help regional authorities achieve the desired results in ensuring territorial identity.

LLM-based representation learning is widely used to build effective information retrieval systems, including scientific domains. For making science more open and affordable, it is important that these systems support multilingual (and cross-lingual) search and do not require significant computational power. To address this we propose SciRus-tiny, light multilingual encoder trained from scratch on 44 M abstracts (15B tokens) of research papers and then tuned in a contrastive manner using citation data. SciRus-tiny outperforms SciNCL, English-only SOTA-model for scientific texts, on 13/24 tasks, achieving SOTA on 7, from SciRepEval benchmark. Furthermore, SciRus-tiny is much more effective than SciNCL: it is almost 5x smaller (23 M parameters vs. 110 M), having approximately 2x smaller embeddings (312 vs. 768) and 2x bigger context length (1024 vs. 512). In addition to the tiny model, we also propose the SciRus-small (61 M parameters and 768 embeddings size), which is more powerful and can be used for complicated downstream tasks. We further study different ways of contrastive pre-training and demonstrate that almost SOTA results can be achieved without citation information, operating with only title-abstract pairs.