An existence level for the residual sum of squares of the power-law regression with an unknown location parameter

In a recent paper [JUKIĆ, D.: A necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set, J. Comput. Appl. Math. 375 (2020)], a new existence level was introduced and then was used to obtain a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set. In this paper, we determined that existence level for the residual sum of squares of the power-law regression with an unknown location parameter, and so we obtained a necessary and sufficient condition which guarantee the existence of the least squares estimate.

New Stability Criterion for Fractional-Order Quaternion-Valued Neural Networks Involving Discrete and Leakage Delays

In the current work, we are devoted to the issue of uniform stability of fractional-order quaternion-valued neural networks involving discrete and leakage delays. Making use of the contracting mapping theory, we prove that the equilibrium point of the involved fractional-order quaternion-valued neural networks exists and is unique. Taking advantage of mathematical analysis strategy, a sufficient criterion involving delay to verify the global uniform stability for the considered fractional-order quaternion-valued neural networks is set up. Computer simulation figures are displayed to sustain the rationality of the established conclusions. This study generalizes and supplements the research of Xiu et al. (2020).

Degree of independence of numbers

A new concept of independence of real numbers, called degree independence, which contains those of linear and algebraic independences, is introduced. A sufficient criterion for such independence is established based on a 1988 result of Bundschuh, which in turn makes use of a generalization of Liouville’s estimate due to Feldman in 1968. Applications to numbers represented by Cantor series and product expansions are derived.

New results for the realization of interfered direct-form digital filters with single two's complement nonlinearity

PurposeThis paper deals with the problem of input/output-to-state stability (IOSS) of direct-form digital filters, which simultaneously contain external disturbances and two's complement nonlinearity. The nonlinearity under consideration is confined to the sector [–1, 1], which contains saturation, zeroing, two's complement and triangular.Design/methodology/approachThe proposed condition is based on IOSS approach, which is capable of providing a framework for checking and analysing the stability of nonlinear system based on input as well as output information.FindingsA linear matrix inequality (LMI)-based new sufficient criterion for the IOSS of the suggested system is obtained. The obtained criterion is capable of detecting the output-to-state stability (OSS) and asymptotic stability of direct-form digital filters with zero external disturbances. In addition, state-norm estimator for the filter under consideration is constructed by adopting an exponential-decay IOSS criterion. Several examples are provided to illustrate the usefulness of the proposed criteria.Originality/valueThe result of the paper is introduced for the first time, and it is suitable for stability analysis of interfered direct-form digital filter with two's complement overflow using IOSS approach.

UPAYA MENINGKATKAN KETERAMPILAN GURU DALAM MEMBUAT MEDIA PEMBELAJARAN POWER POINT MELALUI IN HOUSE TRAINING

This research is motivated by the limited learning activities that must be done remotely and online, there are still many teachers who have not been able to make ICT-based learning media, especially power points, and power point making training can be done offline and online so that in-house training is believed to be helpful. teachers in improving skills in making power points. This research is a classroom action research conducted at SDN 021 Pendekar Bahan from August to September 2020. The instruments used were the observation and interview sheets. The results of the study showed an increase in the skills of teachers in making power points with an average cycle I of 60.85 which is a sufficient criterion, in cycle II it reached 75.42 with good criteria. The conclusion based on the research results is that through in-house training can improve the skills of teachers in making power point learning media.

A French corpus annotated for multiword expressions and named entities

We present the enrichment of a French treebank of various genres with a new annotation layer for multiword expressions (MWEs) and named entities (NEs).1 Our contribution with respect to previous work on NE and MWE annotation is the particular care taken to use formal criteria, organized into decision flowcharts, shedding some light on the interactions between NEs and MWEs. Moreover, in order to cope with the well-known difficulty to draw a clear-cut frontier between compositional expressions and MWEs, we chose to use sufficient criteria only. As a result, annotated MWEs satisfy a varying number of sufficient criteria, accounting for the scalar nature of the MWE status. In addition to the span of the elements, annotation includes the subcategory of NEs (e.g., person, location) and one matching sufficient criterion for non-verbal MWEs (e.g., lexical substitution). The 3,099 sentences of the treebank were double-annotated and adjudicated, and we paid attention to cross-type consistency and compatibility with thesyntactic layer. Overall inter-annotator agreement on non-verbal MWEs and NEs reached 71.1%. The released corpus contains 3,112 annotated NEs and 3,440 MWEs, and is distributed under an open license.

Further Study on Dynamics for a Fractional-Order Competitor-Competitor-Mutualist Lotka–Volterra System

On the basis of the previous publications, a new fractional-order prey-predator model is set up. Firstly, we discuss the existence, uniqueness, and nonnegativity for the involved fractional-order prey-predator model. Secondly, by analyzing the characteristic equation of the considered fractional-order Lotka–Volterra model and regarding the delay as bifurcation variable, we set up a new sufficient criterion to guarantee the stability behavior and the appearance of Hopf bifurcation for the addressed fractional-order Lotka–Volterra system. Thirdly, we perform the computer simulations with Matlab software to substantiate the rationalisation of the analysis conclusions. The obtained results play an important role in maintaining the balance of population in natural world.

Periodic wave solutions of non-Newtonian filtration equations with nonlinear sources and singularities

This paper is concerned with a kind of non-Newtonian filtration equation with nonlinear sources and singularities. Based on the mountain pass theorem and variational methods, a sufficient criterion for the new results on the periodic wave solutions has been provided. Here not only the structure is more general and practical than the existing works but the conditions imposed are concise. Consequently, compared with the previous results on the singular equations and non-Newtonian filtration equations, the results we established are more generalized and some previous ones can been complemented and improved. Finally, the effectiveness of the established results are validated via two numerical examples and simulations.