An estimation is given for the free vibration eigenfrequencies (normal modes) of a homogeneous solid sphere with a large radius, with application to Earth's free vibrations. The free vibration eigenfrequencies of a fluid sphere are also derived as a particular case. Various corrections arising from static and dynamic gravitation, rotation, and inhomegeneities are estimated, and a tentative notion of an earthquake temperature is introduced.
{"title":"Vibration eigenfrequencies of an elastic sphere with a large radius","authors":"Apostol Bogdan Felix","doi":"10.17352/amp.000116","DOIUrl":"https://doi.org/10.17352/amp.000116","url":null,"abstract":"An estimation is given for the free vibration eigenfrequencies (normal modes) of a homogeneous solid sphere with a large radius, with application to Earth's free vibrations. The free vibration eigenfrequencies of a fluid sphere are also derived as a particular case. Various corrections arising from static and dynamic gravitation, rotation, and inhomegeneities are estimated, and a tentative notion of an earthquake temperature is introduced.","PeriodicalId":502339,"journal":{"name":"Annals of Mathematics and Physics","volume":"31 36","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141005574","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}
An analysis of known experiments was carried out to determine the dependence of the mass of electrons on their speed. Errors were discovered in determining the sign of the electron mass. It is shown that at electron velocities above the critical ω = 235696.8871 km/s their masses are negative. The results obtained are explained on the basis of the Principle of Nonequivalence of inertial and gravitational masses since inertial mass can only be positive, and gravitational mass can only be positive or negative The purpose of this work is to show that since radioactive substances can emit electrons with negative mass at velocities above ω, they can be a source of their production.
{"title":"Generation of a substance with negative mass","authors":"Golovkin Bg","doi":"10.17352/amp.000108","DOIUrl":"https://doi.org/10.17352/amp.000108","url":null,"abstract":"An analysis of known experiments was carried out to determine the dependence of the mass of electrons on their speed. Errors were discovered in determining the sign of the electron mass. It is shown that at electron velocities above the critical ω = 235696.8871 km/s their masses are negative. The results obtained are explained on the basis of the Principle of Nonequivalence of inertial and gravitational masses since inertial mass can only be positive, and gravitational mass can only be positive or negative The purpose of this work is to show that since radioactive substances can emit electrons with negative mass at velocities above ω, they can be a source of their production.","PeriodicalId":502339,"journal":{"name":"Annals of Mathematics and Physics","volume":"59 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140248388","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 practice, under the conditions of perfection and constructive development of modern equipment and machines, nonlinear mechanical systems with distributed parameters are often encountered, which, depending on the principles of operation, are affected by vibration shock. Therefore, the study of vibration shock processes of the mentioned systems has great theoretical and practical importance and as a result to determine the optimal parameters of vibration protection devices to ensure their safe operation. In our case, the displacement field of two interacting non-linear mechanical systems with distributed parameters is considered, when their interaction is of vibration shock nature. Obviously, the mentioned events are more pronounced when the self-oscillation frequency of one or both systems momentarily approaches the frequency of forced vibration shock processes. In addition, critical moments are fixed during the phase shifts of forced oscillations of oscillatory systems, in this case, the frequencies of forced oscillations approach mutually opposing phase moments. By choosing the optimal parameters of hysteresis losses, it is possible to almost exclude sub-harmonic modes superimposed on the main resonance modes in vibration shock processes. During hysteresis losses of the parabolic type, the value of µ changes automatically in connection with impulsive loads, which will allow us to transfer the vibration shock processes to automatic modes and, accordingly, the practically safe operation of the mentioned systems.
{"title":"Study of vibration shock processes of non-linear mechanical systems with distributed parameters","authors":"Gavasheli Levan, Gavasheli Anri","doi":"10.17352/amp.000109","DOIUrl":"https://doi.org/10.17352/amp.000109","url":null,"abstract":"In practice, under the conditions of perfection and constructive development of modern equipment and machines, nonlinear mechanical systems with distributed parameters are often encountered, which, depending on the principles of operation, are affected by vibration shock. Therefore, the study of vibration shock processes of the mentioned systems has great theoretical and practical importance and as a result to determine the optimal parameters of vibration protection devices to ensure their safe operation. In our case, the displacement field of two interacting non-linear mechanical systems with distributed parameters is considered, when their interaction is of vibration shock nature. Obviously, the mentioned events are more pronounced when the self-oscillation frequency of one or both systems momentarily approaches the frequency of forced vibration shock processes. In addition, critical moments are fixed during the phase shifts of forced oscillations of oscillatory systems, in this case, the frequencies of forced oscillations approach mutually opposing phase moments. By choosing the optimal parameters of hysteresis losses, it is possible to almost exclude sub-harmonic modes superimposed on the main resonance modes in vibration shock processes. During hysteresis losses of the parabolic type, the value of µ changes automatically in connection with impulsive loads, which will allow us to transfer the vibration shock processes to automatic modes and, accordingly, the practically safe operation of the mentioned systems.","PeriodicalId":502339,"journal":{"name":"Annals of Mathematics and Physics","volume":"24 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140248506","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}
We consider two inertial frames S and and suppose that frame moves, for simplicity, in a single direction: the X -direction of frame S with a constant velocity v as measured in frame S. Using homogeneity of space and time we derive a modified Lorentz Transformation (LT) between two inertial reference frames without using the second postulate of Einstein, i.e., we do not assume the invariant speed of light (in vacuum) under LT. Roughly speaking we suppose: (H) Any clock which is at rest in its frame measures a small increment of time by some factor s=s(v). As a corollary of relativity theory (H) holds with Lorentz factor 1/γ. For s=1 we get the Galilean transformation of Newtonian physics, which assumes an absolute space and time. We also consider the relation between absolute space and Special Relativity Theory, thereafter STR. It seems here that we need a physical explanation for (H). We introduce Postulate 3. The two-way speed of light in and -directions are c and outline derivation of (LT) in this setting. Note that Postulate 3 is a weaker assumption than Einstein's second postulate.
我们考虑两个惯性参照系 S 和 S，为了简单起见，假设参照系沿单一方向运动：参照系 S 的 X 方向，在参照系 S 中以恒定速度 v 测量。利用空间和时间的同质性，我们在两个惯性参照系之间推导出修正的洛伦兹变换（LT），而不使用爱因斯坦的第二公设，也就是说，我们不假设在 LT 下光速（真空中）不变。粗略地说，我们假设：（H）在其参照系中处于静止状态的任何时钟都会以某个系数 s=s(v) 来测量时间的微小增量。作为相对论的一个推论，(H) 在洛伦兹系数为 1/γ 时成立。当 s=1 时，我们得到了牛顿物理学的伽利略变换，它假定了绝对空间和时间。我们还要考虑绝对空间与狭义相对论（STR）之间的关系。在这里，我们似乎需要对（H）进行物理解释。我们引入假设 3。和 方向的双向光速均为 c，并概述了（LT）在这种情况下的推导。请注意，公设 3 是比爱因斯坦第二公设更弱的假设。
{"title":"Lorentz Transformation and time dilatation","authors":"Mateljević Miodrag","doi":"10.17352/amp.000104","DOIUrl":"https://doi.org/10.17352/amp.000104","url":null,"abstract":"We consider two inertial frames S and and suppose that frame moves, for simplicity, in a single direction: the X -direction of frame S with a constant velocity v as measured in frame S. Using homogeneity of space and time we derive a modified Lorentz Transformation (LT) between two inertial reference frames without using the second postulate of Einstein, i.e., we do not assume the invariant speed of light (in vacuum) under LT. Roughly speaking we suppose: (H) Any clock which is at rest in its frame measures a small increment of time by some factor s=s(v). As a corollary of relativity theory (H) holds with Lorentz factor 1/γ. For s=1 we get the Galilean transformation of Newtonian physics, which assumes an absolute space and time. We also consider the relation between absolute space and Special Relativity Theory, thereafter STR. It seems here that we need a physical explanation for (H). We introduce Postulate 3. The two-way speed of light in and -directions are c and outline derivation of (LT) in this setting. Note that Postulate 3 is a weaker assumption than Einstein's second postulate.","PeriodicalId":502339,"journal":{"name":"Annals of Mathematics and Physics","volume":" 43","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139627562","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}
Chukwuma Prince O, Harrison Etaga O, Ibeakuzie Precious, Anabike Ifeanyi C, Obulezi Okechukwu J
In this paper, a variant of the T-X(Y) generator was developed by suppressing the scale parameter of the classical Lomax distribution in the quantile function. Uniquely, the reduction of the number of parameters essentially accounts for the parsimony of the attendant model. The study considered the Exponential distribution as the transformer and consequently obtained the New Reduced Quantile Exponential-G (NRQE-G) family. The Type-II Gumbel distribution was deployed as the baseline to obtain a special sub-model known as the New Reduced Quantile Exponential Type-II Gumbel (NRQE-T2G) model. Some functional properties of the distribution namely, moment and its related measures such as the mean, variance, second, third, and fourth moments were obtained. The Mode, skewness, Kurtosis, index of dispersion, coefficient of variation, order statistics, survival, hazard, and quantile function were also derived. The maximum likelihood estimation method was used to estimate its parameters. The model's credibility, applicability, and flexibility were proven using two real-life datasets.
{"title":"A new reduced quantile function for generating families of distributions","authors":"Chukwuma Prince O, Harrison Etaga O, Ibeakuzie Precious, Anabike Ifeanyi C, Obulezi Okechukwu J","doi":"10.17352/amp.000103","DOIUrl":"https://doi.org/10.17352/amp.000103","url":null,"abstract":"In this paper, a variant of the T-X(Y) generator was developed by suppressing the scale parameter of the classical Lomax distribution in the quantile function. Uniquely, the reduction of the number of parameters essentially accounts for the parsimony of the attendant model. The study considered the Exponential distribution as the transformer and consequently obtained the New Reduced Quantile Exponential-G (NRQE-G) family. The Type-II Gumbel distribution was deployed as the baseline to obtain a special sub-model known as the New Reduced Quantile Exponential Type-II Gumbel (NRQE-T2G) model. Some functional properties of the distribution namely, moment and its related measures such as the mean, variance, second, third, and fourth moments were obtained. The Mode, skewness, Kurtosis, index of dispersion, coefficient of variation, order statistics, survival, hazard, and quantile function were also derived. The maximum likelihood estimation method was used to estimate its parameters. The model's credibility, applicability, and flexibility were proven using two real-life datasets.","PeriodicalId":502339,"journal":{"name":"Annals of Mathematics and Physics","volume":" 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139628556","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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