Mathematical Researches
پژوهش های ریاضی
mmr
Basic Sciences
http://mmr.khu.ac.ir
1
admin
2588-2546
2588-2554
10.61186/mmr
fa
jalali
1400
9
1
gregorian
2021
12
1
7
3
online
1
fulltext
fa
مترهای (alpha, beta) تعمیم یافته لندسبرگ ضعیف
جبر
alg
مقاله مستقل
Original Manuscript
<span style="font-size:11pt"><span style="line-height:21.0pt"><span style="direction:rtl"><span style="unicode-bidi:embed"><span style="font-family:Calibri,sans-serif"><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin"">در این مقاله، مترهای </span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1025" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image001.wmz" style="width:29.25pt; height:15pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span style="font-size:10.0pt"><span style="font-family:"B Nazanin""> تعمیمیافته </span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1026" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image002.wmz" style="width:60.75pt; height:18pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> را مورد بررسی قرار میدهیم. این نوع مترها از مترهای ریمانی</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:3.0pt"><img alt="" id="_x0000_i1027" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image003.wmz" style="width:11.25pt; height:9pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin"">و یک 1-فرم</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1028" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image004.wmz" style="width:11.25pt; height:14.25pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin"">تشکیل شدهاند. ما ثابت کردیم که اگر</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1029" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image005.wmz" style="width:59.25pt; height:18pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> یک چندجملهای برحسب</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:3.0pt"><img alt="" id="_x0000_i1030" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image006.wmz" style="width:14.25pt; height:15.75pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> و</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:3.0pt"><img alt="" id="_x0000_i1031" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image007.wmz" style="width:9pt; height:11.25pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> باشد، هر متر</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1032" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image001.wmz" style="width:29.25pt; height:15pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> تعمیم یافته لندسبرگ ضعیف، بروالد است که در آن</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1033" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image008.wmz" style="width:11.25pt; height:14.25pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> یک 1-فرمی بسته و همدیس است. این نشان میدهد که در ردۀ مترهای</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1034" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image001.wmz" style="width:29.25pt; height:15pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin"">تعمیم یافته هیچ متر یونیکورن تعمیم یافتهای وجود ندارد. علاوه بر این نشان میدهیم که برای</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1035" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image009.wmz" style="width:9pt; height:15.75pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> چندجملهای،</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:2.0pt"><img alt="" id="_x0000_i1036" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image010.wmz" style="width:12pt; height:11.25pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> متر</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1037" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image001.wmz" style="width:29.25pt; height:15pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> تعمیم یافته لندسبرگ است اگر و تنها اگر متر</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1038" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image001.wmz" style="width:29.25pt; height:15pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> تعمیم یافته لندسبرگ ضعیف باشد که در آن</span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"><span style="position:relative"><span style="top:5.0pt"><img alt="" id="_x0000_i1039" o:ole="" src="file:///C:UsersUser1AppDataLocalTempmsohtmlclip1 1clip_image008.wmz" style="width:11.25pt; height:14.25pt" > </span></span></span></span><span dir="LTR" style="font-size:10.0pt"><span style="font-family:"Times New Roman",serif"></span></span><span lang="FA" style="font-size:10.0pt"><span style="font-family:"B Nazanin""> یک 1- فرمی بسته و همدیس است.</span></span></span></span></span></span></span><br>
هندسه فینسلر, متر (alpha, beta) تعمیمیافته, متر لندسبرگ ضعیف, مسئله یونیکورن تعمیم یافته
Finsler geometry, General (alpha, beta)-metric, weak Landsberg metric, Generalized Unicorn problem.
617
630
http://mmr.khu.ac.ir/browse.php?a_code=A-10-504-1&slc_lang=fa&sid=1
Ali
Ala
علی
علاء
ali.ala@stu.umz.ac.ir
10031947532846005760
10031947532846005760
No
University of Mazandaran
دانشگاه مازندران
Abolfazl
Behzadi
ابوالفضل
بهزادی
behzadi@umz.ac.ir
10031947532846005761
10031947532846005761
Yes
University of Mazandaran
دانشگاه مازندران
Mehdi
Rafie-rad
مهدی
رفیعی راد
rafie-rad@umz.ac.ir
10031947532846005762
10031947532846005762
No
University of Mazandaran
دانشگاه مازندران