Pub Date : 1900-01-01DOI: 10.12988/imf.2021.912252
Olege. Fanuel
{"title":"Determination of generators of codes of ideals of the polynomial ring F2N[X]/(XN-1)","authors":"Olege. Fanuel","doi":"10.12988/imf.2021.912252","DOIUrl":"https://doi.org/10.12988/imf.2021.912252","url":null,"abstract":"","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115859426","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}
In this paper, we introduce the notion of symmetric bi-generalized derivation of incline algebras and investigated some related properties. Also, we introduce the notion of joinitive symmetric mapping and obtain some interesting results. Mathematics Subject Classification: Primary 16Y30
{"title":"On symmetric bi-generalized derivations of incline algebras","authors":"K. Kim","doi":"10.12988/imf.2019.81163","DOIUrl":"https://doi.org/10.12988/imf.2019.81163","url":null,"abstract":"In this paper, we introduce the notion of symmetric bi-generalized derivation of incline algebras and investigated some related properties. Also, we introduce the notion of joinitive symmetric mapping and obtain some interesting results. Mathematics Subject Classification: Primary 16Y30","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134571398","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}
To compare two different hypothesis testing techniques, researchers use the following heuristic idea: for each technique, they form a curve describing how the probabilities of type I and type II errors are related for this technique, and then compare areas under the resulting curves. In this paper, we provide a justification for this heuristic idea. 1 Formulation of the Problem Type I and type II errors. There are many different techniques for hypothesis testing, i.g., for deciding, based on the observation, whether the original (null) hypothesis is valid or whether this hypothesis has to be rejected (and the alternative hypothesis has to be considered true); see, e.g., [3]. In hypothesis testing, we can have two different types of errors: • a type I error (also known as False Negative) is when the correct null hypothesis is erroneously rejected, while • a type II error (also known as False Positive) is when the false null hypothesis is erroneously accepted. The probability of the type I error is usually denoted by α and the probability of the type II error is usually denoted by β. In different situations, we have different requirements on the allowed probabilities of these two errors. For example, in early cancer diagnostics, when the null hypothesis means no cancer, type I error is not that critical – it simply
{"title":"Why area under the curve in hypothesis testing?","authors":"Griselda Acosta, Eric Smith, V. Kreinovich","doi":"10.12988/imf.2019.9834","DOIUrl":"https://doi.org/10.12988/imf.2019.9834","url":null,"abstract":"To compare two different hypothesis testing techniques, researchers use the following heuristic idea: for each technique, they form a curve describing how the probabilities of type I and type II errors are related for this technique, and then compare areas under the resulting curves. In this paper, we provide a justification for this heuristic idea. 1 Formulation of the Problem Type I and type II errors. There are many different techniques for hypothesis testing, i.g., for deciding, based on the observation, whether the original (null) hypothesis is valid or whether this hypothesis has to be rejected (and the alternative hypothesis has to be considered true); see, e.g., [3]. In hypothesis testing, we can have two different types of errors: • a type I error (also known as False Negative) is when the correct null hypothesis is erroneously rejected, while • a type II error (also known as False Positive) is when the false null hypothesis is erroneously accepted. The probability of the type I error is usually denoted by α and the probability of the type II error is usually denoted by β. In different situations, we have different requirements on the allowed probabilities of these two errors. For example, in early cancer diagnostics, when the null hypothesis means no cancer, type I error is not that critical – it simply","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"05 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130703673","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}
Pub Date : 1900-01-01DOI: 10.12988/imf.2020.912103
Yun Zhao, Yuanlan Zhou, T. Zeng
In this paper, we defined the congruence extension property, biideal extension property for semirings and bi-ideal semirings. Relations among the various extensions are explored. Properties of bi-ideal semirings are studied. Also, we gave some examples that a bi-ideal semiring which has the bi-ideal extension property does not have the congruence extension property, a subsemiring of a bi-ideal semiring may not be a bi-ideal semiring, etc. Finally, a necessary and sufficient condition of a special rectangular ring with congruence extension property was established. Mathematics Subject Classification: 16Y60
{"title":"Congruence extension property for semirings","authors":"Yun Zhao, Yuanlan Zhou, T. Zeng","doi":"10.12988/imf.2020.912103","DOIUrl":"https://doi.org/10.12988/imf.2020.912103","url":null,"abstract":"In this paper, we defined the congruence extension property, biideal extension property for semirings and bi-ideal semirings. Relations among the various extensions are explored. Properties of bi-ideal semirings are studied. Also, we gave some examples that a bi-ideal semiring which has the bi-ideal extension property does not have the congruence extension property, a subsemiring of a bi-ideal semiring may not be a bi-ideal semiring, etc. Finally, a necessary and sufficient condition of a special rectangular ring with congruence extension property was established. Mathematics Subject Classification: 16Y60","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124106737","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}
Pub Date : 1900-01-01DOI: 10.12988/imf.2022.912304
Jr R. L. Lewis
In this article, we prove the limit formula lim x →∞
本文证明了极限公式lim x→∞
{"title":"A formula for Mertens' function and its applications","authors":"Jr R. L. Lewis","doi":"10.12988/imf.2022.912304","DOIUrl":"https://doi.org/10.12988/imf.2022.912304","url":null,"abstract":"In this article, we prove the limit formula lim x →∞","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125758051","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}
Let XH(t) be a fractional Brownian motion with index H (1/2 < H < 1), and let Dn(t0, t1, . . . tn) (0 ≤ t0 < t1 < · · · < tn) denote the correlation matrix of {X(tk)−X(tk−1) : k = 1, . . . , n}. In this paper, we give an evaluation of detDn. Mathematics Subject Classification: 60G15, 60G18
{"title":"A note on the correlation matrix of fractional Brownian motion","authors":"N. Kosugi","doi":"10.12988/IMF.2019.917","DOIUrl":"https://doi.org/10.12988/IMF.2019.917","url":null,"abstract":"Let XH(t) be a fractional Brownian motion with index H (1/2 < H < 1), and let Dn(t0, t1, . . . tn) (0 ≤ t0 < t1 < · · · < tn) denote the correlation matrix of {X(tk)−X(tk−1) : k = 1, . . . , n}. In this paper, we give an evaluation of detDn. Mathematics Subject Classification: 60G15, 60G18","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130201710","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}
R. N. Nyabwanga, Fredrick Onyango, Edgar Ouko Otumba
The Quasi-likelihood information criterion (QIC)which results from utilizing Kullbacks I-divergence as the targeted discrepancy is widely used in the GEE framework to select the best correlation structure and the best subset of predictors. We investigated the inference properties of QIC in variable selection with focus on its consistency, sensitivity and sparsity. We established through numerical simulations that QIC had high sensitivity but low sparsity. Its type I error rate was approximately 30% which implied fairly high chances of selecting over-fit models. On the other side,it had low under-fitting probabilities. The statistical power of QIC was established to be high hence rejecting any given false null hypothesis is essentially guaranteed for sufficiently large N even if the effect size is small. Mathematics Subject Classification: 62J12, 62F07, 62F15
拟似然信息准则(quasylikelihood information criterion, QIC)被广泛应用于GEE框架中，以Kullbacks I-divergence作为目标差异来选择最佳相关结构和最佳预测因子子集。研究了QIC在变量选择中的推理性质，重点研究了它的一致性、灵敏度和稀疏性。通过数值模拟证明了QIC具有高灵敏度和低稀疏性。其I型错误率约为30%，这意味着选择过拟合模型的可能性相当高。另一方面，它的欠拟合概率很低。QIC的统计能力很高，因此即使效应大小很小，也可以保证在足够大的N下拒绝任何给定的错误零假设。数学学科分类:62J12、62F07、62F15
{"title":"Inference properties of QIC in the selection of covariates for generalized estimating equations","authors":"R. N. Nyabwanga, Fredrick Onyango, Edgar Ouko Otumba","doi":"10.12988/imf.2019.9315","DOIUrl":"https://doi.org/10.12988/imf.2019.9315","url":null,"abstract":"The Quasi-likelihood information criterion (QIC)which results from utilizing Kullbacks I-divergence as the targeted discrepancy is widely used in the GEE framework to select the best correlation structure and the best subset of predictors. We investigated the inference properties of QIC in variable selection with focus on its consistency, sensitivity and sparsity. We established through numerical simulations that QIC had high sensitivity but low sparsity. Its type I error rate was approximately 30% which implied fairly high chances of selecting over-fit models. On the other side,it had low under-fitting probabilities. The statistical power of QIC was established to be high hence rejecting any given false null hypothesis is essentially guaranteed for sufficiently large N even if the effect size is small. Mathematics Subject Classification: 62J12, 62F07, 62F15","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131348510","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}
Pub Date : 1900-01-01DOI: 10.12988/imf.2023.912386
D. P. Pombo Jr.
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of bounded group homomorphisms are established.
建立了一类有界群同态序列在代数意义上的精确性的充分必要条件。
{"title":"On exact diagrams and strict bounded group homomorphisms","authors":"D. P. Pombo Jr.","doi":"10.12988/imf.2023.912386","DOIUrl":"https://doi.org/10.12988/imf.2023.912386","url":null,"abstract":"Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of bounded group homomorphisms are established.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125471524","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}
Every coordinate net on a rotating surface is a semi-geodesic coordinate net composed of a family of curves of constant geodesic curvature. In this paper, using semi-geodesic coordinate nets on special rotating surfaces such as a conical surface, a catenoid, and a rotational hyperboloid surface, we give families of curves of constant geodesic curvature on some surfaces through isometric mappings. Also, with the aid of the software Mathematica, we draw images of the semi-geodesic coordinate nets and the family of curves obtained through isometric mappings.
{"title":"Semi-geodetic coordinate nets through isometries","authors":"Yuying Wu, Tuya Bao, Xiaodong Shan, Xinxuan Wang, Yu Zhang, Lixia Xiao","doi":"10.12988/imf.2022.912326","DOIUrl":"https://doi.org/10.12988/imf.2022.912326","url":null,"abstract":"Every coordinate net on a rotating surface is a semi-geodesic coordinate net composed of a family of curves of constant geodesic curvature. In this paper, using semi-geodesic coordinate nets on special rotating surfaces such as a conical surface, a catenoid, and a rotational hyperboloid surface, we give families of curves of constant geodesic curvature on some surfaces through isometric mappings. Also, with the aid of the software Mathematica, we draw images of the semi-geodesic coordinate nets and the family of curves obtained through isometric mappings.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133395986","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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