Summary In this paper, some qualitative behaviors of solutions for certain second-order nonlinear differential equation with damping and resonance effects are considered. By employing Lyapunov’s direct method, a complete Lyapunov function was used to investigate the stability of the system. Krasnoselskii’s fixed point theorem was used to establish sufficient conditions that guaranteed the existence and boundedness of a unique solution. The results show that the equilibrium point was asymptotically stable. Furthermore, a test for periodicity was conducted using the Bendixson criterion, and the results showed that the solution of the second-order nonlinear differential equation is aperiodic, which extends some results from the literature.
{"title":"Existence, uniqueness, boundedness and stability of periodic solutions of a certain second-order nonlinear differential equation with damping and resonance effects","authors":"Everestus Obinwanne Eze, Uchenna Emmanuel Obasi, Godwin Ezugorie, Enyiduru Ekwomchi Hannah","doi":"10.2478/bile-2023-0008","DOIUrl":"https://doi.org/10.2478/bile-2023-0008","url":null,"abstract":"Summary In this paper, some qualitative behaviors of solutions for certain second-order nonlinear differential equation with damping and resonance effects are considered. By employing Lyapunov’s direct method, a complete Lyapunov function was used to investigate the stability of the system. Krasnoselskii’s fixed point theorem was used to establish sufficient conditions that guaranteed the existence and boundedness of a unique solution. The results show that the equilibrium point was asymptotically stable. Furthermore, a test for periodicity was conducted using the Bendixson criterion, and the results showed that the solution of the second-order nonlinear differential equation is aperiodic, which extends some results from the literature.","PeriodicalId":8933,"journal":{"name":"Biometrical Letters","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134956889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary Oat is a grain in high demand, due to its physiological and nutritional attributes as a functional food. Oat is rich in β− glucans, and high in tocopherol and other dietary fibre components. It is also used for forage, fodder, chaff and as a major component of infant foods. In the present study, oat yields from six experimental stations in south-western Poland, obtained in 2019–2022, were analysed using three different linear mixed models that can be associated with three different stabilities. It is shown that the geno-type Perun had the highest mean yield among the tested genotypes, while the genotype Armani was the most stable. Armani and Pablo had the lowest values of the GSI index, making them the most favourable genotypes for cultivation in that region.
{"title":"Stability analysis of spring oat genotypes in south-west Poland","authors":"Konrad Banaś, Marcin Przystalski, Agnieszka Łacka","doi":"10.2478/bile-2023-0007","DOIUrl":"https://doi.org/10.2478/bile-2023-0007","url":null,"abstract":"Summary Oat is a grain in high demand, due to its physiological and nutritional attributes as a functional food. Oat is rich in β− glucans, and high in tocopherol and other dietary fibre components. It is also used for forage, fodder, chaff and as a major component of infant foods. In the present study, oat yields from six experimental stations in south-western Poland, obtained in 2019–2022, were analysed using three different linear mixed models that can be associated with three different stabilities. It is shown that the geno-type Perun had the highest mean yield among the tested genotypes, while the genotype Armani was the most stable. Armani and Pablo had the lowest values of the GSI index, making them the most favourable genotypes for cultivation in that region.","PeriodicalId":8933,"journal":{"name":"Biometrical Letters","volume":"119 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134957728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary Regression analysis methods, such as linear regression for continuous outcomes and logistic regression for binary outcomes, have been widely used in medical research data analysis for many years. However, there have been instances of misconceptions and misinterpretations of regression results within the medical community. Univariate and multiple regression analyses are commonly used by medical publications to identify factors that are significantly correlated with the outcome. In this manuscript, we critically evaluate the validity of this approach. Our findings indicate that this method is invalid and should be completely disregarded by medical researchers.
{"title":"Univariate and Multiple Regression Analyses in Medical Research","authors":"Ethan Poon, Changyong Feng","doi":"10.2478/bile-2023-0005","DOIUrl":"https://doi.org/10.2478/bile-2023-0005","url":null,"abstract":"Summary Regression analysis methods, such as linear regression for continuous outcomes and logistic regression for binary outcomes, have been widely used in medical research data analysis for many years. However, there have been instances of misconceptions and misinterpretations of regression results within the medical community. Univariate and multiple regression analyses are commonly used by medical publications to identify factors that are significantly correlated with the outcome. In this manuscript, we critically evaluate the validity of this approach. Our findings indicate that this method is invalid and should be completely disregarded by medical researchers.","PeriodicalId":8933,"journal":{"name":"Biometrical Letters","volume":"51 1","pages":"65 - 76"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84660852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary In this paper, the problem of indicating chemical balance weighing designs satisfying the criterion of D-optimality is considered. Moreover, we study such designs under the assumption that the measurements are equally positively correlated and they have the same variances. We formulate a method to add at most four runs to a regular D-optimal chemical balance weighing design to obtain a highly D-efficient chemical balance weighing deign.
{"title":"D-optimal chemical balance weighing designs with positively correlated errors: part I","authors":"M. Graczyk, B. Ceranka","doi":"10.2478/bile-2023-0004","DOIUrl":"https://doi.org/10.2478/bile-2023-0004","url":null,"abstract":"Summary In this paper, the problem of indicating chemical balance weighing designs satisfying the criterion of D-optimality is considered. Moreover, we study such designs under the assumption that the measurements are equally positively correlated and they have the same variances. We formulate a method to add at most four runs to a regular D-optimal chemical balance weighing design to obtain a highly D-efficient chemical balance weighing deign.","PeriodicalId":8933,"journal":{"name":"Biometrical Letters","volume":"22 1","pages":"53 - 63"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77325441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary In this research, an intrinsically nonlinear split-plot design model (INSPDM) is formulated and studied. It was formulated by fitting a Johnson–Schumacher (JS) function to the split-plot model mean function. The fitted model parameters are estimated using the estimated generalized least squares (EGLS) technique based on a Gauss–Newton procedure with Taylor series expansion, by minimizing the objective function of the model. The variance components for the whole plot and subplot random effects are estimated using restricted maximum likelihood estimation (REML) techniques. The adequacy of the fitted INSPDM was tested using four median adequacy measures: resistant coefficient of determination, resistant prediction coefficient of determination, the resistant modeling efficiency statistic, and the median square error prediction statistic based on the residuals of the fitted model. Akaike’s Information Criterion (AIC), Corrected Akaike’s Information Criterion (AICC) and Bayesian Information Criterion (BIC) statistics are used to select the best parameter estimation technique. The results obtained are compared with the techniques of ordinary least squares (OLS) and EGLS via maximum likelihood estimation (MLE). The results showed the model to be adequate, reliable, stable, and a good fit based on EGLS-REML when compared with OLS and EGLS-MLE fitted model parameter estimates.
{"title":"Johnson–Schumacher Split-Plot Design Modelling of Rice Yield","authors":"I. David, O. Asiribo, H. G. Dikko, P. O. Ikwuoche","doi":"10.2478/bile-2023-0003","DOIUrl":"https://doi.org/10.2478/bile-2023-0003","url":null,"abstract":"Summary In this research, an intrinsically nonlinear split-plot design model (INSPDM) is formulated and studied. It was formulated by fitting a Johnson–Schumacher (JS) function to the split-plot model mean function. The fitted model parameters are estimated using the estimated generalized least squares (EGLS) technique based on a Gauss–Newton procedure with Taylor series expansion, by minimizing the objective function of the model. The variance components for the whole plot and subplot random effects are estimated using restricted maximum likelihood estimation (REML) techniques. The adequacy of the fitted INSPDM was tested using four median adequacy measures: resistant coefficient of determination, resistant prediction coefficient of determination, the resistant modeling efficiency statistic, and the median square error prediction statistic based on the residuals of the fitted model. Akaike’s Information Criterion (AIC), Corrected Akaike’s Information Criterion (AICC) and Bayesian Information Criterion (BIC) statistics are used to select the best parameter estimation technique. The results obtained are compared with the techniques of ordinary least squares (OLS) and EGLS via maximum likelihood estimation (MLE). The results showed the model to be adequate, reliable, stable, and a good fit based on EGLS-REML when compared with OLS and EGLS-MLE fitted model parameter estimates.","PeriodicalId":8933,"journal":{"name":"Biometrical Letters","volume":"66 1","pages":"37 - 52"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76859025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary Mumps is a viral contagious disease associated with puffy cheeks and tender and swollen jaw. It spreads through direct contact with saliva or respiratory droplets from the mouth, nose or throat of infected persons. In this work, we present a mathematical model which describes the dynamics of the disease in a human population. The model incorporates isolation and treatment of infected individuals as a control measure. It is shown that the disease-free equilibrium (DFE) is locally and globally asymptotically stable when the control reproduction number Rc is less than one. It is also shown that the model has a unique endemic equilibrium which exists when Rc > 1. The existence of a unique endemic equilibrium confirms the global stability of the DFE, and the absence of backward bifurcation in the model. Optimal control analysis is performed on the model to obtain the proportion of infected humans to be isolated for optimal control of the disease. Plots are presented to show the dynamics of the disease in the presence of the control measures.
{"title":"Mathematical model for the transmission of mumps and its optimal control","authors":"Emmanuel Chidiebere Duru, M. Anyanwu","doi":"10.2478/bile-2023-0006","DOIUrl":"https://doi.org/10.2478/bile-2023-0006","url":null,"abstract":"Summary Mumps is a viral contagious disease associated with puffy cheeks and tender and swollen jaw. It spreads through direct contact with saliva or respiratory droplets from the mouth, nose or throat of infected persons. In this work, we present a mathematical model which describes the dynamics of the disease in a human population. The model incorporates isolation and treatment of infected individuals as a control measure. It is shown that the disease-free equilibrium (DFE) is locally and globally asymptotically stable when the control reproduction number Rc is less than one. It is also shown that the model has a unique endemic equilibrium which exists when Rc > 1. The existence of a unique endemic equilibrium confirms the global stability of the DFE, and the absence of backward bifurcation in the model. Optimal control analysis is performed on the model to obtain the proportion of infected humans to be isolated for optimal control of the disease. Plots are presented to show the dynamics of the disease in the presence of the control measures.","PeriodicalId":8933,"journal":{"name":"Biometrical Letters","volume":"32 1","pages":"77 - 95"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72775409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary Sclerotinia sclerotiorum is a pathogen which causes a disease of oilseed rape. Severe plant infection contributes to a decrease in the quality of the crop. It is therefore important to pay attention to whether hybrids are highly tolerant to this fungal disease at the early stages of breeding. In this study, the question of interest is whether there has been progress in increasing the tolerance of new hybrids to this pathogen. Three years of breeding experiments (2014, 2015, 2017) are included in the analysis. Each year, three to five experiments were carried out, with several dozen varieties and three standards. Each series of experiments was repeated in several locations. Because the degree of infection was assessed on a scale (from 1 – the highest infection – to 9 – the least infection), the analysis is carried out using an ordinal logistic model. It is noted that in earlier years the standard varieties’ probability of infection with this disease had a smaller range (empirical probability 0.5–0.83) than in the last analyzed year (empirical probability 0.33–1.00). The results of the analysis show that in 2014 and 2015 several hybrids exhibited a significantly higher tolerance to Sclerotinia, but in 2017 none of the hybrids were significantly better than the standard. Perhaps breeding selection of hybrids has eliminated the less tolerant varieties. However, to be able to draw more general conclusions, it would be necessary to repeat the study in controlled conditions (a greenhouse), where the level of fungal spores and their effect on plants could be controlled. Obtaining tolerant hybrids will enable a reduction in production costs, since there will be no need to monitor whether disease infestation occurs and no need to use corresponding plant protection products.
{"title":"Progress in plant tolerance to the fungal disease Sclerotinia in breeding experiments on winter oilseed rape","authors":"B. Zawieja, Laura Slebioda, T. Mikulski","doi":"10.2478/bile-2023-0002","DOIUrl":"https://doi.org/10.2478/bile-2023-0002","url":null,"abstract":"Summary Sclerotinia sclerotiorum is a pathogen which causes a disease of oilseed rape. Severe plant infection contributes to a decrease in the quality of the crop. It is therefore important to pay attention to whether hybrids are highly tolerant to this fungal disease at the early stages of breeding. In this study, the question of interest is whether there has been progress in increasing the tolerance of new hybrids to this pathogen. Three years of breeding experiments (2014, 2015, 2017) are included in the analysis. Each year, three to five experiments were carried out, with several dozen varieties and three standards. Each series of experiments was repeated in several locations. Because the degree of infection was assessed on a scale (from 1 – the highest infection – to 9 – the least infection), the analysis is carried out using an ordinal logistic model. It is noted that in earlier years the standard varieties’ probability of infection with this disease had a smaller range (empirical probability 0.5–0.83) than in the last analyzed year (empirical probability 0.33–1.00). The results of the analysis show that in 2014 and 2015 several hybrids exhibited a significantly higher tolerance to Sclerotinia, but in 2017 none of the hybrids were significantly better than the standard. Perhaps breeding selection of hybrids has eliminated the less tolerant varieties. However, to be able to draw more general conclusions, it would be necessary to repeat the study in controlled conditions (a greenhouse), where the level of fungal spores and their effect on plants could be controlled. Obtaining tolerant hybrids will enable a reduction in production costs, since there will be no need to monitor whether disease infestation occurs and no need to use corresponding plant protection products.","PeriodicalId":8933,"journal":{"name":"Biometrical Letters","volume":"17 1","pages":"23 - 35"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82005421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary Linearly structured covariance matrices are widely used in multivariate analysis. The covariance structure can be chosen from a class of linear structures. Therefore, the optimal structure is identified in terms of minimizing the discrepancy function. In this research, the entropy loss function is used as the discrepancy function. We give a methodology and algorithm for determining the optimal structure from the class of structures under consideration. The accuracy of the proposed method is checked using a simulation study.
{"title":"Structure identification for a linearly structured covariance matrix","authors":"Adam Mieldzioc","doi":"10.2478/bile-2022-0011","DOIUrl":"https://doi.org/10.2478/bile-2022-0011","url":null,"abstract":"Summary Linearly structured covariance matrices are widely used in multivariate analysis. The covariance structure can be chosen from a class of linear structures. Therefore, the optimal structure is identified in terms of minimizing the discrepancy function. In this research, the entropy loss function is used as the discrepancy function. We give a methodology and algorithm for determining the optimal structure from the class of structures under consideration. The accuracy of the proposed method is checked using a simulation study.","PeriodicalId":8933,"journal":{"name":"Biometrical Letters","volume":"69 1","pages":"159 - 169"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77868532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Szulc, K. Ambroży-Deręgowska, J. Kobus‐Cisowska, P. Kardasz, Rafał Nowaczyk
Summary The Faculty of Agronomy at the University of Life Sciences in Poznań conducted laboratory tests on the content of B vitamins in the grain of three varieties of yellow-colored fodder maize. The grains of the variety ES Metronom had the statistically significantly highest content of vitamins B1 and B9. In the case of vitamin B3, the significantly highest concentration was recorded in the grain of the variety ES Abakus, while the lowest concentration was found for the variety ES Metronom. In contrast, the grain of the variety ES Bombastic had significantly higher vitamin B6 content than that of the varieties ES Abakus and ES Metronom. The grain of the variety ES Metronom had significantly higher vitamin B9 content than the other two varieties tested. In general, it should be concluded that the content of B vitamins in maize grain is not determined by the type of maize hybrid.
{"title":"The role of maize variety (Zea mays L.) in shaping the grain vitamin content","authors":"P. Szulc, K. Ambroży-Deręgowska, J. Kobus‐Cisowska, P. Kardasz, Rafał Nowaczyk","doi":"10.2478/bile-2022-0012","DOIUrl":"https://doi.org/10.2478/bile-2022-0012","url":null,"abstract":"Summary The Faculty of Agronomy at the University of Life Sciences in Poznań conducted laboratory tests on the content of B vitamins in the grain of three varieties of yellow-colored fodder maize. The grains of the variety ES Metronom had the statistically significantly highest content of vitamins B1 and B9. In the case of vitamin B3, the significantly highest concentration was recorded in the grain of the variety ES Abakus, while the lowest concentration was found for the variety ES Metronom. In contrast, the grain of the variety ES Bombastic had significantly higher vitamin B6 content than that of the varieties ES Abakus and ES Metronom. The grain of the variety ES Metronom had significantly higher vitamin B9 content than the other two varieties tested. In general, it should be concluded that the content of B vitamins in maize grain is not determined by the type of maize hybrid.","PeriodicalId":8933,"journal":{"name":"Biometrical Letters","volume":"6 1","pages":"171 - 177"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79936800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary Prostate cancer is a severe threat to human lives. Approximately 1 in 7 men will be diagnosed with prostate cancer throughout their lifetimes, and 1 in 39 men will die from prostate cancer. There are many factors which increase or decrease the survival time of prostate cancer patients. Data is used here from a randomised clinical trial for the choice of treatment for prostate cancer patients in stages 3 and 4. This study is done to identify probable variables that influence the survival time of patients only for these two stages. The AFT and the Cox-PH models determine how variables affect prostate cancer patients' survival time.
{"title":"Evaluation of the Effect of Prognostic Variables on the Survival Analysis of Prostate Cancer","authors":"Shafiq Hossain Sourav, Rownak Jahan Tamanna","doi":"10.2478/bile-2022-0007","DOIUrl":"https://doi.org/10.2478/bile-2022-0007","url":null,"abstract":"Summary Prostate cancer is a severe threat to human lives. Approximately 1 in 7 men will be diagnosed with prostate cancer throughout their lifetimes, and 1 in 39 men will die from prostate cancer. There are many factors which increase or decrease the survival time of prostate cancer patients. Data is used here from a randomised clinical trial for the choice of treatment for prostate cancer patients in stages 3 and 4. This study is done to identify probable variables that influence the survival time of patients only for these two stages. The AFT and the Cox-PH models determine how variables affect prostate cancer patients' survival time.","PeriodicalId":8933,"journal":{"name":"Biometrical Letters","volume":"315 1","pages":"77 - 98"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76354874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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