Melody refers to a succession of musical notes that can be regarded as complete in a musical sense. For example, a line of a song or a raga bandish is a melody as it is complete. The number of notes in a melody is called its length. Unfortunately, the analysis of melody lengths is a neglected area in music research. Given that the significance of a melody in monophonic music (single melody line), such as Indian classical music is quantified by the product of the length of the melody and its frequency (number of occurrences in the musical piece), the novelty of our research lies in analysing the statistical features of lengths of a well-known bandish in raga Bihag. Additionally, the probability distribution of the notes is presented and a count of rising and falling note transitions in the sthayi and antara of the bandish is also taken. The experimental results are encouraging.
旋律是指在音乐意义上可视为完整的音符序列。例如，一首歌曲或一首拉加乐曲中的一行音符就是完整的旋律。旋律中音符的数量称为旋律长度。遗憾的是，对旋律长度的分析在音乐研究中是一个被忽视的领域。鉴于在印度古典音乐等单声部音乐（单旋律线）中，旋律的重要性是由旋律长度与旋律频率（在音乐作品中出现的次数）的乘积来量化的，我们研究的新颖之处在于分析了著名的拉格-比哈格（Bihag）中的一段带子的长度统计特征。此外，我们还介绍了音符的概率分布，并统计了带状音符在 sthayi 和 antara 中的上升和下降转换。实验结果令人鼓舞。
{"title":"Statistical analysis of melody lengths, note probabilities and note transitions of a bandish in raga Bihag","authors":"Soubhik Chakraborty, Prerna Singh","doi":"10.59400/jam.v1i3.303","DOIUrl":"https://doi.org/10.59400/jam.v1i3.303","url":null,"abstract":"Melody refers to a succession of musical notes that can be regarded as complete in a musical sense. For example, a line of a song or a raga bandish is a melody as it is complete. The number of notes in a melody is called its length. Unfortunately, the analysis of melody lengths is a neglected area in music research. Given that the significance of a melody in monophonic music (single melody line), such as Indian classical music is quantified by the product of the length of the melody and its frequency (number of occurrences in the musical piece), the novelty of our research lies in analysing the statistical features of lengths of a well-known bandish in raga Bihag. Additionally, the probability distribution of the notes is presented and a count of rising and falling note transitions in the sthayi and antara of the bandish is also taken. The experimental results are encouraging.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":"1220 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139204124","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. Roy, Abhishek Sarkar, Kulbhushan Agnihotri, K. Das
Parasites can alter the quality and quantity of participants. On the other hand, the spread of diseases between individuals or species is an important research topic. Here we consider a tritrophic food model in which bacteria spread among the animal's environment where other nutrients are present. We analyze the local stability of the model around the efficiency of the equation. We also report significant numbers of offspring in terms of ecology and disease and use these numbers to analyze community structure of the sample. We started from this situation as a model. Our numerical results show that at low infection level the body causes conflict, but at high infection level conflict prioritizes safety. Our findings therefore challenge previous models’ predictions that the parasite has a negative impact. We also looked at the impact of other foods on chaotic dynamics. When other nutrients increase, stress does not change, but when other nutrients decrease, chaos disappears and the disease among animals is eliminated from the body.
{"title":"The study of chaotic dynamics of an eco-epidemiological predator-prey model with alternative food","authors":"P. Roy, Abhishek Sarkar, Kulbhushan Agnihotri, K. Das","doi":"10.59400/jam.v1i3.129","DOIUrl":"https://doi.org/10.59400/jam.v1i3.129","url":null,"abstract":"Parasites can alter the quality and quantity of participants. On the other hand, the spread of diseases between individuals or species is an important research topic. Here we consider a tritrophic food model in which bacteria spread among the animal's environment where other nutrients are present. We analyze the local stability of the model around the efficiency of the equation. We also report significant numbers of offspring in terms of ecology and disease and use these numbers to analyze community structure of the sample. We started from this situation as a model. Our numerical results show that at low infection level the body causes conflict, but at high infection level conflict prioritizes safety. Our findings therefore challenge previous models’ predictions that the parasite has a negative impact. We also looked at the impact of other foods on chaotic dynamics. When other nutrients increase, stress does not change, but when other nutrients decrease, chaos disappears and the disease among animals is eliminated from the body.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":"11 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139241793","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}
Muhammad Safdar Nazeer, Kifayat Ullah, Amir Hussain
Multi-attribute group decision-making (MAGDM) is very significant technique for selecting an alternative from the provided list. But the major problem is to deal with the information fusion during the information. Aczel-Alsina t-norm (AATN) and Aczel-Alsina t-conorm (AATCN) are the most generalized and flexible t-norm (TN) and t-conorm (TCN) which is used for information processing. Moreover, the interval-valued T-spherical fuzzy set (IVTSFS) is the latest framework to cover the maximum information from the real-life scenarios. Hence, the major contribution of this paper is to deal the information while the MAGDM process by introducing new aggregation operators (AOs). Consequently, the interval-valued T-spherical fuzzy (IVTSF), Aczel-Alsina weighted averaging (IVTSFAAWA), IVTSF Aczel-Alsina (IVTSFAA) ordered weighted averaging (IVTSFAAOWA), IVTSFAA weighted geometric (IVTSFAAWG), IVTSFAA ordered weighted geometric (IVTSFAAOWG), and IVTSFAA hybrid weighted geometric (IVTSFAAHWG) operators are developed. It is shown that the proposed operators are the valid and the results obtained are reliable by discussing some basic properties. To justify the developed AOs, an example of the MAGDM is discussed. The sensitivity of these AOs is observed keeping in view of the variable parameter. To show the importance of the newly developed theory, a comparison of the proposed AOs is established with already existing operators.
多属性群体决策（MAGDM）是一种非常重要的技术，用于从提供的列表中选择一个备选方案。但主要问题是如何处理信息融合。Aczel-Alsina t-norm (AATN) 和 Aczel-Alsina t-conorm (AATCN) 是用于信息处理的最通用、最灵活的 t-norm (TN) 和 t-conorm (TCN)。此外，区间值 T 球形模糊集（IVTSFS）是一种最新的框架，可最大限度地涵盖现实生活场景中的信息。因此，本文的主要贡献在于通过引入新的聚合算子（AO），在 MAGDM 流程中处理信息。因此，本文开发了区间值 T 球形模糊（IVTSF）、Aczel-Alsina 加权平均（IVTSFAAWA）、IVTSF Aczel-Alsina 有序加权平均（IVTSFAA）、IVTSFAA 加权几何（IVTSFAAWG）、IVTSFAA 有序加权几何（IVTSFAAOWG）和 IVTSFAA 混合加权几何（IVTSFAAHWG）算子。通过讨论一些基本特性，证明了所提出的算子是有效的，所获得的结果是可靠的。为了证明所开发的算子的正确性，讨论了 MAGDM 的一个例子。在考虑到可变参数的情况下，观察了这些算子的灵敏度。为了说明新开发理论的重要性，还将建议的 AO 与现有算子进行了比较。
{"title":"A novel decision-making appraoch based on interval-valued T-spherical fuzzy information with applications","authors":"Muhammad Safdar Nazeer, Kifayat Ullah, Amir Hussain","doi":"10.59400/jam.v1i2.79","DOIUrl":"https://doi.org/10.59400/jam.v1i2.79","url":null,"abstract":"Multi-attribute group decision-making (MAGDM) is very significant technique for selecting an alternative from the provided list. But the major problem is to deal with the information fusion during the information. Aczel-Alsina t-norm (AATN) and Aczel-Alsina t-conorm (AATCN) are the most generalized and flexible t-norm (TN) and t-conorm (TCN) which is used for information processing. Moreover, the interval-valued T-spherical fuzzy set (IVTSFS) is the latest framework to cover the maximum information from the real-life scenarios. Hence, the major contribution of this paper is to deal the information while the MAGDM process by introducing new aggregation operators (AOs). Consequently, the interval-valued T-spherical fuzzy (IVTSF), Aczel-Alsina weighted averaging (IVTSFAAWA), IVTSF Aczel-Alsina (IVTSFAA) ordered weighted averaging (IVTSFAAOWA), IVTSFAA weighted geometric (IVTSFAAWG), IVTSFAA ordered weighted geometric (IVTSFAAOWG), and IVTSFAA hybrid weighted geometric (IVTSFAAHWG) operators are developed. It is shown that the proposed operators are the valid and the results obtained are reliable by discussing some basic properties. To justify the developed AOs, an example of the MAGDM is discussed. The sensitivity of these AOs is observed keeping in view of the variable parameter. To show the importance of the newly developed theory, a comparison of the proposed AOs is established with already existing operators.","PeriodicalId":504292,"journal":{"name":"Journal of AppliedMath","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139357363","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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