On $m$-th roots of nilpotent matrices

A new necessary and sufficient condition for the existence of an $m$-th root of a nilpotent matrix in terms of the multiplicities of Jordan blocks is obtained and expressed as a system of linear equations with nonnegative integer entries which is suitable for computer programming. Thus, computation of the Jordan form of the $m$-th power of a nilpotent matrix is reduced to a single matrix multiplication; conversely, the existence of an $m$-th root of a nilpotent matrix is reduced to the existence of a nonnegative integer solution to the corresponding system of linear equations. Further, an erroneous result in the literature on the total number of Jordan blocks of a nilpotent matrix having an $m$-th root is corrected and generalized. Moreover, for a singular matrix having an $m$-th root with a pair of nilpotent Jordan blocks of sizes $s$ and $l$, a new $m$-th root is constructed by replacing that pair by another one of sizes $s+i$ and $l-i$, for special $s,l,i$. This method applies to solutions of a system of linear equations having a special matrix of coefficients. In addition, for a matrix $A$ over an arbitrary field that is a sum of two commuting matrices, several results for the existence of $m$-th roots of $A^k$ are obtained.

APPLICATION OF BRANCHES IN MICROSOFT FORMS DOCUMENTS AS FORCED REPLACEMENT OF SIMULATION PRACTICAL-ORIENTED TASKS, WHILE STUDYING CLINICAL DISCIPLINES IN THE CONDITIONS OF THE CONTINUING COVID-19 PANDEMIC

Sorry to state that optimistic forecasts for a quick overcoming of the COVID-19 pandemic, unfortunately, did not come true. Accepting modern challenges, the higher education sector, like other areas of human life, continues to adapt and optimize work to the new conditions of a changing difficult, unpredictable environment. While theoretical medical disciplines are likely to experience this re-equipment with greater ease, practice-oriented subjects are in a situation of crisis in the quality of vocational education. Results. In such circumstances, simulation systems, which are designed to create a safe environment, where, without risks to the patient, the future specialist can work out typical clinical situations, can be useful. Creating the comprehensive models requires considerable effort and highly specialized knowledge of working with specific software. However, if your aim is to create short cases that can be directly integrated in the form of multiple learning tasks to Microsoft Teams - you should pay attention to the well-known Forms tool from the Office365 cloud service package, which is available by subscription in many schools of this country. On purpose of such task formation, we will be able to create branches, providing the use of optional choice questions. When using this function, we get the opportunity to redirect the respondent to different fragments of the form, depending on the chosen answer. Wrong options should be left as well among the proposed, but at the end a result of their choice brief comments, should be made, explaining their absurdity, which would be available for review in case of completion of the task with an erroneous result. The result of such work will be a tree of steps, each of which brings the respondent closer to the case designed by the architect. Based on a system of diagnostic and treatment protocols, it is possible to calculate and formulate algorithms of action in certain clinical circumstances and, finally, create a Microsoft Forms document. This form, provided a combination of text and graphic data, allows you to place the respondent in a professional situation easily. Such system gives the opportunity to make typical correct decisions or to make wrong steps, which brings to the circumstances an element of simulation training. Thanks to the built-in assessment system, it is possible to combine learning processes with ongoing and final monitoring of the quality of learning, to stimulate maximizing the result. Upon reaching a positive outcome, form an opinion about the assimilation of the element, or redirect to additional study of certain fragments of topics, in case of formation of the wrong network of steps. To simplify learning, some cases can be prepared with one pass option, which will allow you to practice skills of emergency situations, or tasks limited to a standardized step-by-step solution. Conclusions. The Microsoft Forms cloud application can be used to create short clinical cases. Requires a combination of different types of input data and the ability to create branches to use it as a simulation learning tool. As a result, a decision tree is formed, which can be focused on assessing the acquisition of skills, and used to grade respondents, or to develop standardized solutions in typical clinical situations. The outlined system has its drawbacks, but it is necessary to take into account the general availability and ease of configuration.

QSPR MODELS FOR ZETA-POTENTIAL OF NANO-OXIDES PREDICTION

Nano-QSPR modeling often requires considering variety of factors, if neglected, may lead to erroneous result of the study. Frequently, the data turned out to be inaccurate, incomplete, or fragmentary. Obviously, the quality of experimental data directly depends on many factors: laboratory equipment, organization of internal regulations, skills of researchers, and so on. As a result of violations of algorithms and protocols of initial data streams processing – there are errors and distortions of data, that is why performing a solid multistep data-curation process is crucial for such procedures. Data curation procedure was performed and approximately 60% was rejected (due to various errors, incomplete or absent records for physicochemical parameters or conditions of performed experiment), followed up by using zeta-potential value dataset for 37 various sizes nanoparticles of 14 metal oxides for calculation of 1D SiRMS descriptors as well as «liquid drop» model cross-descriptors. An efficient consensus model was built (R2 = 0.88, R2test = 0.81). Predictive power (R2 = 0.84) of the model was tested using an external set of 5 nano-oxides and the possibility of satisfactory zeta-potential prediction was shown. Prediction of zeta-potential value within domain applicability of obtained QSPR model confirmed using a Williams plot. The interpretation of the final model was carried out and it was found that the contribution of descriptors was distributed between individual descriptors and cross-descriptors by 46% and 54% respectively. The contribution 1D SiRMS descriptors was 59%, the second group – 41% (liquid drop model descriptors – 29%, descriptors characterizing the metal atom – 12%). It was found that the most influential parameters are the characteristics that reflect the nature of the oxides. The parameters of electrostatic interactions have the highest contribution.

Energy Difference Of High Frequency Electromagnetic Waves Amplitude In Detecting Buried Objects At Ho Chi Minh City, Vietnam

Ground penetrating radar method (GPR) is common place in imaging buried objects, such as: supply water and drainage systems, electric and telecom cables. For shallow geology, GPR method has provided high-resolution sections containing subsurface information. In processing data, the velocity of GPR wave is the most important parameter. It helps to exactly specify the structure of a geology sections. Defining a wrong velocity may lead to an erroneous result. In this research, we are going to present two processing steps to define the electromagnetic wave velocity and the position of object from GPR data that was acquired by using a shield antenna machine prototype. The first step is application of Kirchhoff migration and energy difference graphs to calculate the electromagnetic wave velocity. In the second step, the result of migrated sections consisting of hyperbole diffraction was evaluated. If migrated using the right velocity, the diffracted hyperbola will focus on its peak and have the maximum energy. Finally, we used the workflow to define the velocity, the position and the size of the object from real GPR data collected at Go Vap district, Ho Chi Minh City, Vietnam.

An extensive comparison of CB-SEM and PLS-SEM for reliability and validity

Structural Equation Modeling (SEM) includes measurement and structural model for hypothesis testing. The results yielded from structural model is unlikely to be valid if a poor loading of an indicator is selected. The impact of these erroneous result on standardized loading is disregard. Thus, knowing how poor loading can affect the validity of measurement model is a crucial issue. This paper attempts to compare the standardized loadings result between two prominent SEM methods (CBSEM and PLS-SEM) using three varied of simula-tion models (TRA, Loyalty and UTAUT model) to investigate their effects on reliability and validity of measurement model. The data for each model were generated using R software by setting the value of standardized loading and the construct correlations (N=50, 100, 200 and 500). The value of standardized loadings was set to 0.60 for each construct in the model while the construct correlations were set in the range between 0.45 to 0.65. Then, the AMOS 21.0 and ADANCO 2.0 were used to perform the statistical analysis. It shows that good standardized loading can increase the reliability and validity of construct representation. CBSEM is particularly yielded valid and unbiased estimation under confirmatory condition (established theory) compared with PLS-SEM. The results are illustrated with empirical examples. This paper provides updated evidence about CBSEM and PLS-SEM when assessing the measurement model.

Operational State Complexity and Decidability of Jumping Finite Automata

We consider jumping finite automata and their operational state complexity and decidability status. Roughly speaking, a jumping automaton is a finite automaton with a non-continuous input. This device has nice relations to semilinear sets and thus to Parikh images of regular sets, which will be exhaustively used in our proofs. In particular, we prove upper bounds on the intersection and complementation. The latter result on the complementation upper bound answers an open problem from [G. J. Lavado, G. Pighizzini, S. Seki: Operational State Complexity of Parikh Equivalence, 2014]. Moreover, we correct an erroneous result on the inverse homomorphism closure. Finally, we also consider the decidability status of standard problems as regularity, disjointness, universality, inclusion, etc. for jumping finite automata.

The Control Group and Meta-Analysis

Social scientists use a mixture of different methodologies, which creates problems for researchers attempting to review the cumulative results of all studies. Standard practice for review studies using meta-analysis is to adjust the findings of all studies that use control groups and to include studies not having control groups without adjustment for extraneous effects, or to not use studies that lack a control group, which could produce an erroneous result. Our study develops a novel meta-analytic procedure that combines the evidence on control group change with evidence on change from the intervention, making it possible to adjust for the effects of extraneous factors in all studies and bridges the gap between control group studies and other types of studies. DOI:10.2458/azu_jmmss_v5i1_hunter

DISTANCE AND SIMILARITY MEASURES FOR SOFT SETS

In Ref. 7, the authors use matrix representation-based distances of soft sets to introduce matching function and distance-based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corollary of our result. The fundamental assumption of Ref. 7 has been shown to be flawed. This motivates us to introduce set operations-based measures. We present a case (Example 6.7) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed here decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.

Corrigendum: equivalent weights and standard homomorphisms for convolution algebras on ℝ+

There is an error in one of the major results in our original paper ‘Equivalent weights and standard homomorphisms for convolution algebras on ℝ+’. We describe the error and give a counterexample to the result as stated. We then give a substitute result which is in many ways stronger than the erroneous result. We will also indicate what changes need to be made in the original paper to accommodate the replacement of the erroneous result by the substitute.