Proceedings of the Institute of Mathematics and Mechanics最新文献

{"title":"Existence of solutions for a resonant problem under Landesman-Lazer type conditions involving more general elliptic operators in divergence form","authors":"Rabil Ayazoglu- Sidika S¸ ule S¸ ener · Tuba Agırman Ayd","doi":"10.29228/proc.63","DOIUrl":"https://doi.org/10.29228/proc.63","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69844605","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}

{"title":"Asymptotics of solution of a boundary value problem for a singularly perturbed quasilinear one-characteristic equation","authors":"Mahir M. Sabzaliev · Mahbuba E. Kerimova","doi":"10.29228/proc.74","DOIUrl":"https://doi.org/10.29228/proc.74","url":null,"abstract":". A complete asymptotics of the solution of a boundary value problem on a rectangle is constructed for one-characteristic nonclassic type differential equation of third order, degenerating into nonlinear hyperbolic equation. The remainder term is estimated.","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69844867","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}

{"title":"Department of Surgical Diseases, Azerbaijan Clinical characteristics, risk factors and outcome of the mild and moderate COVID-19 infection","authors":"N.Bayramov, T.B. Sadigzade, T.Aliyev, A.Rustam, G.Sadigova","doi":"10.29228/proc.93","DOIUrl":"https://doi.org/10.29228/proc.93","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69845137","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}

{"title":"Prospective directions for searching new medicines of plant origin, effective in infections of different etiology","authors":"N. Mehdiyeva","doi":"10.29228/PROC.90","DOIUrl":"https://doi.org/10.29228/PROC.90","url":null,"abstract":"The global community is concerned about the COVID-19 pandemic. Existing capacities are mobilized and new ways to counter the growing threat are actively sought. The scientific development of traditional medicine is a promising way of solving this problem. Information on the use of medicinal plants by different peoples is fragmented and largely unavailable to the world scientific community. The flora of Azerbaijan including almost 1600 species of medicinal plants with antiviral, anti-inflammatory, immunomodulatory, vitamin, general tonic and other properties are distributed in the Flora of Azerbaijan. Modern protocols for the treatment of infection caused by COVID-19, along with other therapeutic agents, will include drugs with the above properties. The article contains information about a computer database of medicinal plants in Azerbaijan, developed by the author in the frame of the doctoral thesis in the 2006 year. These data enable us to distinguish species with a set of biologically active substances that determine their required necessary physiological activity from the total number of medicinal plants. Therefore, the intensification of work on the study of traditional medicine and the creation of a worldwide information platform on medicinal plants can become the basis for the search and development of new antiviral drugs, including those effective and against COVID-19.","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69845057","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}

{"title":"Some inequalities for weighted and integral means of convex functions on linear spaces","authors":"S. Dragomir","doi":"10.29228/proc.29","DOIUrl":"https://doi.org/10.29228/proc.29","url":null,"abstract":"Let f be a convex function on a convex subset C of a linear space and x; y 2 C; with x 6= y: If p : [0; 1] ! R is a Lebesgue integrable and symmetric function, namely p (1 t) = p (t) for all t 2 [0; 1] and such that the condition 0 Z 0 p (s) ds Z 1 0 p (s) ds for all 2 [0; 1] holds, then we have 1 R 1 0 p ( ) d Z 1 0 p ( ) f ((1 )x+ y) d Z 1 0 f ((1 )x+ y) d 1 R 1 0 p ( ) d Z 1 0 Z 0 p (s) ds (1 ) d [r fy (y x) r+fx (y x)] 1 2 [r fy (y x) r+fx (y x)] : Some applications for norms and semi-inner products are also provided. 1. Introduction LetX be a real linear space, x; y 2 X, x 6= y and let [x; y] := f(1 )x+ y; 2 [0; 1]g be the segment generated by x and y. We consider the function f : [x; y]! R and the attached function '(x;y) : [0; 1]! R, '(x;y) (t) := f [(1 t)x+ ty], t 2 [0; 1]. It is well known that f is convex on [x; y] i¤ ' (x; y) is convex on [0; 1], and the following lateral derivatives exist and satisfy (i) '0 (x;y) (s) = r f(1 s)x+sy (y x), s 2 [0; 1); (ii) '+(x;y) (0) = r+fx (y x) ; (iii) '0 (x;y) (1) = r fy (y x) ; where r fx (y) are the Gâteaux lateral derivatives, we recall that r+fx (y) : = lim h!0+ f (x+ hy) f (x) h ; r fx (y) : = lim k!0 f (x+ ky) f (x) k ; x; y 2 X: The following inequality is the well-known Hermite-Hadamard integral inequality for convex functions de\u0085ned on a segment [x; y] X : (HH) f x+ y 2 Z 1 0 f [(1 t)x+ ty] dt f (x) + f (y) 2 ; 1991 Mathematics Subject Classi\u0085cation. 26D15; 46B05. Key words and phrases. Convex functions, LInear spaces, Integral inequalities, HermiteHadamard inequality, Féjer’s inequalities, Norms and semi-inner products. 1 2 S. S. DRAGOMIR which easily follows by the classical Hermite-Hadamard inequality for the convex function ' (x; y) : [0; 1]! R '(x;y) 1 2 Z 1 0 '(x;y) (t) dt '(x;y) (0) + '(x;y) (1) 2 : For other related results see the monograph on line [8]. For some recent results in linear spaces see [1], [2] and [9]-[12]. In the recent paper we established the following re\u0085nements and reverses of Féjer’s inequality for functions de\u0085ned on linear spaces: Theorem 1. Let f be an convex function on C and x; y 2 C with x 6= y: If p : [0; 1] ! [0;1) is Lebesgue integrable and symmetric, namely p (1 t) = p (t) for all t 2 [0; 1] ; then 0 1 2 h r+f x+y 2 (y x) r f x+y 2 (y x) i Z 1 0 t 12 p (t) dt (1.1) Z 1 0 f ((1 t)x+ ty) p (t) dt f x+ y 2 Z 1 0 p (t) dt 1 2 [r fy (y x) r+fx (y x)] Z 1 0 t 1 2 p (t) dt and 0 1 2 h r+f x+y 2 (y x) r f x+y 2 (y x) i Z 1 0 1 2 t 1 2 p (t) dt (1.2) f (x) + f (y) 2 Z 1 0 p (t) dt Z 1 0 f ((1 t)x+ ty) p (t) dt 1 2 [r fy (y x) r+fx (y x)] Z 1 0 1 2 t 12 p (t) dt: If we take p 1 in (1.1), then we get 0 1 8 h r+f x+y 2 (y x) r f x+y 2 (y x) i (1.3) Z 1 0 f [(1 t)x+ ty] dt f x+ y 2 1 8 [r fy (y x) r+fx (y x)] that was \u0085rstly obtained in [4], while from (1.2) we recapture the result obtained in [5] 0 1 8 h r+f x+y 2 (y x) r f x+y 2 (y x) i (1.4) f (x) + f (y) 2 Z 1 0 f [(1 t)x+ ty] dt 1 8 [r fy (y x) r+fx (y x)] : Motivated by the above results, we establish in this","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69844031","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}

{"title":"A new approach for solving nonlinear Volterra integro-differential equations with Mittag--Leffler kernel","authors":"R. Jafari","doi":"10.29228/proc.24","DOIUrl":"https://doi.org/10.29228/proc.24","url":null,"abstract":"In this work, we consider a general class of nonlinear Volterra integro-differential equations with Atangana–Baleanu derivative. We use the operational matrices based on the shifted Legendre polynomials to obtain numerical solution of the considered equations. By approximating the unknown function and its derivative in terms of the shifted Legendre polynomials and substituting these approximations into the original equation and using the collocation points, the original equation is reduced to a system of nonlinear algebraic equations. An error estimate of the numerical solution is proved. Finally, some examples are included to show the accuracy and validity of the proposed method.","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69844463","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}

{"title":"Co-infections in COVID-19 patients and the importance of microbial diagnosis for disease management","authors":"R. Eftekhari, H. Hosainzadegan","doi":"10.29228/PROC.82","DOIUrl":"https://doi.org/10.29228/PROC.82","url":null,"abstract":"1 Department of Biophysics and Biochemistry, Baku State University, 23 academician Z.Khalilov Str., Baku AZ1148, Azerbaijan Joint Ukraine-Azerbaijan International Research and Education Center of Nanobiotechnology and Functional Nanosystems, Drohobych, Ukraine & Baku, Azerbaijan Institute of Radiation Problems, Azerbaijan National Academy of Sciences, 9 B.Vahabzadeh Str., Baku AZ1143, Azerbaijan Pharmacology and Toxicology Department, Maragheh University of Medical Sciences, Maragheh, Iran * For correspondence: hasanhosainy122@yahoo.com","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69844887","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}

{"title":"Co-infections in COVID-19 patients and the importance of microbial diagnosis for disease management","authors":"R. Khalilov, A. Eftekhari H. Hosainzadegan","doi":"10.29228/proc.98","DOIUrl":"https://doi.org/10.29228/proc.98","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69845319","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}

{"title":"Existence of solutions for a resonant problem under Landesman-Lazer type conditions involving more general elliptic operators in divergence form","authors":"Rabil Ayazoglu Sidika S¸ ule S¸ ener · Tuba Agırman Aydın","doi":"10.29228/proc.62","DOIUrl":"https://doi.org/10.29228/proc.62","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69844548","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}

{"title":"On uniform equiconvergence for Dirac type 2m × 2m systems","authors":"Gunel R. Hajiyeva","doi":"10.29228/proc.66","DOIUrl":"https://doi.org/10.29228/proc.66","url":null,"abstract":"","PeriodicalId":54068,"journal":{"name":"Proceedings of the Institute of Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69844654","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}