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Super Congruences Involving Alternating Harmonic Sums
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作者 zhongyan shen Tianxin Cai 《Advances in Pure Mathematics》 2020年第10期611-622,共12页
Let <em>p</em> be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizatio... Let <em>p</em> be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, <img alt="" src="Edit_e97d0c64-3683-4a75-9d26-4b371c2be41e.bmp" /> where P<em><sub>P </sub></em>denotes the set of positive integers which are prime to <em>p</em>. And we establish the combinational congruences involving alternating harmonic sums for positive integer <em>n</em>=3,4,5. 展开更多
关键词 Bernoulli Numbers Alternating Harmonic Sums CONGRUENCES Modulo Prime Powers
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Glacial bedforms in the Northwind Abyssal Plain,Chukchi Borderland 被引量:1
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作者 zhongyan shen Tao Zhang +2 位作者 Jinyao Gao Chunguo Yang Qingsheng Guan 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2021年第5期114-119,共6页
A series of sub-parallel linear glacial scours are identified on the crest of the Baoshi Seamount in the Northwind Abyssal Plain by compiling new multibeam data acquired during the 9 th Chinese Arctic Research Expedit... A series of sub-parallel linear glacial scours are identified on the crest of the Baoshi Seamount in the Northwind Abyssal Plain by compiling new multibeam data acquired during the 9 th Chinese Arctic Research Expedition(CHINARE-Arc9)in 2018 and previously published data.The new data reveal scours that developed at water depths of 850–1030 m with an orientation of about 75°/255°.The maximum water depth occurs in the southernmost scour and is deeper than that from previous investigations,which showed a maximum scouring depth of about 900 m on the seamount.The topographic and geomorphological characteristics suggest that these scours resulted from erosion by the ice shelf extending from the Chukchi margin and/or Laurentide Ice Sheet that grounded on the crest of the seamount and moved in a NE–SW direction.Other possibilities of their genesis include armadas of large icebergs/multi-keel icebergs calved from the Chukchi Shelf or the Laurentide Ice Sheet.The new data provide new constraints for assessing the extent and volume of the ice sheet in the Chukchi area during glacial maxima. 展开更多
关键词 Chukchi Borderland Northwind Abyssal Plain glacial bedforms mega-scale glacial lineations ice shelf
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Neogene faulting and volcanism in the Victoria Land Basin of the Ross Sea, Antarctica 被引量:1
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作者 Mei Yue JinYao Gao +7 位作者 ChunFeng Li Chao Zhu XinZhi Fan Guochao Wu zhongyan shen Han Shi XiaoXian Cai YiDong Guo 《Earth and Planetary Physics》 EI CSCD 2022年第3期248-258,共11页
The Neogene Terror Rift in the Antarctic Victoria Land Basin(VLB)of the Ross Sea,Antarctica,is composed of the Discovery Graben and the Lee Arch.Many Neogene volcanoes are aligned in the north-south direction in the s... The Neogene Terror Rift in the Antarctic Victoria Land Basin(VLB)of the Ross Sea,Antarctica,is composed of the Discovery Graben and the Lee Arch.Many Neogene volcanoes are aligned in the north-south direction in the southern VLB,belonging to the McMurdo Volcanic Group.However,due to multiple glaciations and limited seismic data,the volcanic processes are still unclear in the northern VLB,especially in the Terror Rift.Multichannel seismic profiles were collected at the VLB from the 32nd Chinese National Antarctic Research Expedition(CHINARE).We utilized four seismic profiles from the CHINARE and additional historical profiles,along with gravity and magnetic anomalies,to analyze faults and stratigraphic characteristics in the northern Terror Rift and volcanism in the VLB.Negative flower structures found in the northern Terror Rift suggest that the Terror Rift was affected by dextral strike-slip faults extending from the northern Victoria Land(NVL).After the initial orthogonal tension,the rift transited into an oblique extension,forming a set of downward concaving normal faults and accommodation zones in the Terror Rift.On the Lee Arch,several imbricated normal faults formed and converged into a detachment fault.Under gravitational forces,the strata bent upward and formed a rollover anticline.Many deep faults and thin strata subjected to erosion facilitated volcanic activity.A brittle volcanic region in the VLB was affected by dextral strike-slip movements and east-west extension,resulting in two Neogene volcanic chains that connect three igneous provinces in the VLB:the Hallett,Melbourne,and Erebus Provinces.These two chains contain mud volcanoes with magnetic nuclei,volcanic intrusions,and late-stage volcanic eruptions.Volcanisms have brought about opposite polarities of magnetic anomalies in Antarctica,indicating the occurrence of multiple volcanic activities. 展开更多
关键词 Victoria Land Basin Terror Rift seismic stratigraphy gravity and magnetic modeling FAULTING Neogene volcanic intrusion
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The Odd Solutions of Equations Involving Euler-Like Function
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作者 Jiaxin Wu zhongyan shen 《Advances in Pure Mathematics》 2021年第5期440-446,共7页
<span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><spa... <span style="white-space:nowrap;"><em><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">φ</span></span></span></span></span></span><sub>e</sub></em>(<em>n</em>) </span>is a function similar to Euler function <em><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;"><span style="white-space:nowrap;">φ</span></span></span></span></span></em>(<em>n</em>). We discussed and obtained all the odd solutions of the equations <em style="white-space:normal;"><span style="white-space:nowrap;">φ<sub>e</sub></span></em><span style="white-space:nowrap;">(<em>xy</em>) </span><span style="white-space:nowrap;">= <em style="white-space:normal;"><span style="white-space:nowrap;">φ<sub>e</sub></span></em><span style="white-space:nowrap;"><sub></sub>(<em>x</em>)</span></span><span style="white-space:nowrap;"> + </span><span style="white-space:nowrap;">2</span><em style="white-space:normal;"><span style="white-space:nowrap;"><em style="white-space:normal;"><span style="white-space:nowrap;">φ<sub>e</sub></span></em></span></em><span style="white-space:nowrap;"><span style="white-space:nowrap;"><sub></sub>(</span></span><em style="white-space:normal;"><span style="white-space:nowrap;"><em style="white-space:normal;"><span style="white-space:nowrap;">y)</span></em></span></em>, <em style="white-space:normal;"><span style="white-space:nowrap;">φ<sub>e</sub></span></em>(<em>xy</em>) = 2<em style="white-space:normal;"><span style="white-space:nowrap;">φ<sub>e</sub></span></em><sub></sub>(<em>x</em>) + 3<em style="white-space:normal;"><span style="white-space:nowrap;"><em style="white-space:normal;"><span style="white-space:nowrap;">φ<sub>e</sub></span></em></span></em><sub></sub>(<em style="white-space:normal;"><span style="white-space:nowrap;">y) </span></em>and <em style="white-space:normal;"><span style="white-space:nowrap;">φ<sub>e</sub></span></em><span style="white-space:normal;">(</span><em style="white-space:normal;">xyz</em><span style="white-space:normal;">) = </span><em style="white-space:normal;"><span style="white-space:nowrap;">φ<sub>e</sub></span></em><sub style="white-space:normal;"></sub><span style="white-space:normal;">(</span><em style="white-space:normal;">x</em><span style="white-space:normal;">) + </span><em style="white-space:normal;"><span style="white-space:nowrap;"><em style="white-space:normal;"><span style="white-space:nowrap;">φ<sub>e</sub></span></em></span></em><sub style="white-space:normal;"></sub><span style="white-space:normal;">(</span><em style="white-space:normal;"><span style="white-space:nowrap;">y)</span></em> <span style="white-space:normal;">+ </span><em style="white-space:normal;"><span style="white-space:nowrap;"><em style="white-space:normal;"><span style="white-space:nowrap;">φ<sub>e</sub></span></em></span></em><sub style="white-space:normal;"></sub><span style="white-space:normal;">(</span><em style="white-space:normal;"><span style="white-space:nowrap;">z)</span></em><span style="white-space:normal;"> </span>by using the methods and techniques of elementary number theory. 展开更多
关键词 Euler-Like Function Diophantine Equation Odd Solutions
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