Sanjeev Dhawan, Kulvinder Singh, A. Rabaea, Amit Batra
Abstract Session centered recommender systems has emerged as an interesting and challenging topic amid researchers during the past few years. In order to make a prediction in the sequential data, prevailing approaches utilize either left to right design autoregressive or data augmentation methods. As these approaches are used to utilize the sequential information pertaining to user conduct, the information about the future context of an objective interaction is totally ignored while making prediction. As a matter of fact, we claim that during the course of training, the future data after the objective interaction are present and this supplies indispensable signal on preferences of users and if utilized can increase the quality of recommendation. It is a subtle task to incorporate future contexts into the process of training, as the rules of machine learning are not followed and can result in loss of data. Therefore, in order to solve this problem, we suggest a novel encoder decoder prototype termed as space filling centered Recommender (SRec), which is used to train the encoder and decoder utilizing space filling approach. Particularly, an incomplete sequence is taken into consideration by the encoder as input (few items are absent) and then decoder is used to predict these items which are absent initially based on the encoded interpretation. The general SRec prototype is instantiated by us employing convolutional neural network (CNN) by giving emphasis on both e ciency and accuracy. The empirical studies and investigation on two real world datasets are conducted by us including short, medium and long sequences, which exhibits that SRec performs better than traditional sequential recommendation approaches.
{"title":"Session centered Recommendation Utilizing Future Contexts in Social Media","authors":"Sanjeev Dhawan, Kulvinder Singh, A. Rabaea, Amit Batra","doi":"10.2478/auom-2021-0036","DOIUrl":"https://doi.org/10.2478/auom-2021-0036","url":null,"abstract":"Abstract Session centered recommender systems has emerged as an interesting and challenging topic amid researchers during the past few years. In order to make a prediction in the sequential data, prevailing approaches utilize either left to right design autoregressive or data augmentation methods. As these approaches are used to utilize the sequential information pertaining to user conduct, the information about the future context of an objective interaction is totally ignored while making prediction. As a matter of fact, we claim that during the course of training, the future data after the objective interaction are present and this supplies indispensable signal on preferences of users and if utilized can increase the quality of recommendation. It is a subtle task to incorporate future contexts into the process of training, as the rules of machine learning are not followed and can result in loss of data. Therefore, in order to solve this problem, we suggest a novel encoder decoder prototype termed as space filling centered Recommender (SRec), which is used to train the encoder and decoder utilizing space filling approach. Particularly, an incomplete sequence is taken into consideration by the encoder as input (few items are absent) and then decoder is used to predict these items which are absent initially based on the encoded interpretation. The general SRec prototype is instantiated by us employing convolutional neural network (CNN) by giving emphasis on both e ciency and accuracy. The empirical studies and investigation on two real world datasets are conducted by us including short, medium and long sequences, which exhibits that SRec performs better than traditional sequential recommendation approaches.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78808042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this manuscript, by using weakly Picard operators we investigate the Ulam type stability of fractional q-difference An illustrative example is given in the last section.
摘要本文利用弱Picard算子研究分数阶q差的Ulam型稳定性，最后给出了一个例子。
{"title":"Dynamics and Ulam Stability for Fractional q-Difference Inclusions via Picard Operators Theory","authors":"S. Abbas, M. Benchohra, E. Karapınar","doi":"10.2478/auom-2021-0031","DOIUrl":"https://doi.org/10.2478/auom-2021-0031","url":null,"abstract":"Abstract In this manuscript, by using weakly Picard operators we investigate the Ulam type stability of fractional q-difference An illustrative example is given in the last section.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83640964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polynomials.
{"title":"Bounds for the zeros of unilateral octonionic polynomials","authors":"R. Serôdio, P. Beites, J. Vitória","doi":"10.2478/auom-2021-0043","DOIUrl":"https://doi.org/10.2478/auom-2021-0043","url":null,"abstract":"Abstract In the present work it is proved that the zeros of a unilateral octonionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polynomials.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83895269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we study generalized helicoidal surfaces in Euclidean 5-space. We obtain the necessary and sufficient conditions for generalized helicoidal surfaces in Euclidean 5-space to be minimal, flat or of zero normal curvature tensor, which are ordinary differential equations. We solve those equations and discuss the completeness of the surfaces.
{"title":"Generalized Helicoidal Surfaces in Euclidean 5-space","authors":"A. Uçum, M. Sakaki","doi":"10.2478/auom-2021-0044","DOIUrl":"https://doi.org/10.2478/auom-2021-0044","url":null,"abstract":"Abstract In this paper, we study generalized helicoidal surfaces in Euclidean 5-space. We obtain the necessary and sufficient conditions for generalized helicoidal surfaces in Euclidean 5-space to be minimal, flat or of zero normal curvature tensor, which are ordinary differential equations. We solve those equations and discuss the completeness of the surfaces.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85772541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2.
设m >1为正整数。我们证明了指数丢芬图方程mx + (m + 1)y = (1 + m + m2)z在m≥2时只有正整数解(x, y, z) =(2,1,1)。
{"title":"On the exponential Diophantine equation mx+(m+1)y=(1+m+m2)z","authors":"M. Alan","doi":"10.2478/auom-2021-0032","DOIUrl":"https://doi.org/10.2478/auom-2021-0032","url":null,"abstract":"Abstract Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80475605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We consider the existence of solutions of the following weighted problem: {L:=-div(ρ(x)|∇u|N-2∇u)+ξ(x)|u|N-2u=f(x,u)inBu>0inBu=0on∂B, left{ {matrix{{L: = - divleft( {rho left( x right){{left| {nabla u} right|}^{N - 2}}nabla u} right) + xi left( x right){{left| u right|}^{N - 2}}} hfill & {u = fleft( {x,u} right)} hfill & {in} hfill & B hfill cr {} hfill & {u > 0} hfill & {in} hfill & B hfill cr {} hfill & {u = 0} hfill & {on} hfill & {partial B,} hfill cr } } right. where B is the unit ball of ℝN, N #62; 2, ρ(x)=(loge|x|)N-1 rho left( x right) = {left( {log {e over {left| x right|}}} right)^{N - 1}} the singular logarithm weight with the limiting exponent N − 1 in the Trudinger-Moser embedding, and ξ(x) is a positif continuous potential. The nonlinearities are critical or subcritical growth in view of Trudinger-Moser inequalities of double exponential type. We prove the existence of positive solution by using Mountain Pass theorem. In the critical case, the function of Euler Lagrange does not fulfil the requirements of Palais-Smale conditions at all levels. We dodge this problem by using adapted test functions to identify this level of compactness.
摘要考虑以下加权问题解的存在性:{L:=-div(ρ(x)|∇u|N-2∇u)+ξ(x)|u|N-2u=f(x,u)inBu>0inBu=0on∂B， left{矩阵{{L:= - div 离开({ρ离开(x 右){{左|{微分算符u} 右|}^ {N - 2}} 微分算符u} 右)+ xi 离开(x 右){{左| u 右|}^ {N - 2}}} hfill & {u = f 离开({x, u} 右)} hfill &的{} hfill & B hfill cr {} hfill & u > {0} hfill &的{} hfill & B hfill cr {} hfill & u = {0} hfill &上{} hfill & { B部分} hfill cr}} 。式中B为单位球，N #62;2、ρ(x)=(loge|x|)N-1 rho left(x right) = {left({log {e / {left| x right}}} right)^{N -1}}是Trudinger-Moser嵌入中极限指数为N−1的奇异对数权值，ξ(x)是一个正连续势。对于双指数型Trudinger-Moser不等式，非线性是临界或亚临界增长。利用山口定理证明了正解的存在性。在临界情况下，欧拉-拉格朗日函数在各个层次上都不满足Palais-Smale条件的要求。我们通过使用适应的测试函数来识别这种紧凑程度来避免这个问题。
{"title":"Non-autonomous weighted elliptic equations with double exponential growth","authors":"S. Baraket, Rached Jaidane","doi":"10.2478/auom-2021-0033","DOIUrl":"https://doi.org/10.2478/auom-2021-0033","url":null,"abstract":"Abstract We consider the existence of solutions of the following weighted problem: {L:=-div(ρ(x)|∇u|N-2∇u)+ξ(x)|u|N-2u=f(x,u)inBu>0inBu=0on∂B, left{ {matrix{{L: = - divleft( {rho left( x right){{left| {nabla u} right|}^{N - 2}}nabla u} right) + xi left( x right){{left| u right|}^{N - 2}}} hfill & {u = fleft( {x,u} right)} hfill & {in} hfill & B hfill cr {} hfill & {u > 0} hfill & {in} hfill & B hfill cr {} hfill & {u = 0} hfill & {on} hfill & {partial B,} hfill cr } } right. where B is the unit ball of ℝN, N #62; 2, ρ(x)=(loge|x|)N-1 rho left( x right) = {left( {log {e over {left| x right|}}} right)^{N - 1}} the singular logarithm weight with the limiting exponent N − 1 in the Trudinger-Moser embedding, and ξ(x) is a positif continuous potential. The nonlinearities are critical or subcritical growth in view of Trudinger-Moser inequalities of double exponential type. We prove the existence of positive solution by using Mountain Pass theorem. In the critical case, the function of Euler Lagrange does not fulfil the requirements of Palais-Smale conditions at all levels. We dodge this problem by using adapted test functions to identify this level of compactness.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80902038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This work continues our previous analysis concerning the numerical solution of the multi-component mass transfer equations. The present test problems are two-dimensional, parabolic, non-linear, diffusion- reaction equations. An implicit finite difference method was used to discretize the mathematical model equations. The algorithm used to solve the non-linear system resulted for each time step is the modified Picard iteration. The numerical performances of the preconditioned conjugate gradient algorithms (BICGSTAB and GMRES) in solving the linear systems of the modified Picard iteration were analysed in detail. The numerical results obtained show good numerical performances.
{"title":"On numerical solution of nonlinear parabolic multicomponent diffusion-reaction problems","authors":"G. Juncu, C. Popa, Gheorghe Sarbu","doi":"10.2478/auom-2021-0040","DOIUrl":"https://doi.org/10.2478/auom-2021-0040","url":null,"abstract":"Abstract This work continues our previous analysis concerning the numerical solution of the multi-component mass transfer equations. The present test problems are two-dimensional, parabolic, non-linear, diffusion- reaction equations. An implicit finite difference method was used to discretize the mathematical model equations. The algorithm used to solve the non-linear system resulted for each time step is the modified Picard iteration. The numerical performances of the preconditioned conjugate gradient algorithms (BICGSTAB and GMRES) in solving the linear systems of the modified Picard iteration were analysed in detail. The numerical results obtained show good numerical performances.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75371385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, we set up a new nonlinear dynamical system which is derived by combining logistic map and sine square map in Mann orbit (a two step feedback process) for ameliorating the stability performance of chaotic system and name it Standard Logistic Sine Square Map (SLSSM). The purpose of this paper is to study the whole dynamical behavior of the proposed map (SLSSM) through various introduced aspects consisting fixed point and stability analysis, time series representation, bifurcation diagram and Lyapunov exponent. Moreover, we show that our map is significantly superior than existing other one dimensional maps. We investigate that the chaotic and complex behavior of SLSSM can be controlled by selecting control parameters carefully. Also, the range of convergence and stability can be made to increase drastically. This new system (SLSSM) might be used to achieve better results in cryptography and to study chaos synchronization.
{"title":"On the Complex and Chaotic Dynamics of Standard Logistic Sine Square Map","authors":"S. Kumari, Renu Chugh, Radu Miculescu","doi":"10.2478/auom-2021-0041","DOIUrl":"https://doi.org/10.2478/auom-2021-0041","url":null,"abstract":"Abstract In this article, we set up a new nonlinear dynamical system which is derived by combining logistic map and sine square map in Mann orbit (a two step feedback process) for ameliorating the stability performance of chaotic system and name it Standard Logistic Sine Square Map (SLSSM). The purpose of this paper is to study the whole dynamical behavior of the proposed map (SLSSM) through various introduced aspects consisting fixed point and stability analysis, time series representation, bifurcation diagram and Lyapunov exponent. Moreover, we show that our map is significantly superior than existing other one dimensional maps. We investigate that the chaotic and complex behavior of SLSSM can be controlled by selecting control parameters carefully. Also, the range of convergence and stability can be made to increase drastically. This new system (SLSSM) might be used to achieve better results in cryptography and to study chaos synchronization.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79886087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Raúl M. Falcón, M. Venkatachalam, S. Gowri, G. Nandini
Abstract In this paper, we determine the r-dynamic chromatic number of the fan graph Fm,n and determine sharp bounds of this graph invariant for four related families of graphs: The middle graph M(Fm,n), the total graph T (Fm,n), the central graph C(Fm,n) and the line graph L(Fm,n). In addition, we determine the r-dynamic chromatic number of each one of these four families of graphs in case of being m = 1.
{"title":"On the r-dynamic coloring of some fan graph families","authors":"Raúl M. Falcón, M. Venkatachalam, S. Gowri, G. Nandini","doi":"10.2478/auom-2021-0039","DOIUrl":"https://doi.org/10.2478/auom-2021-0039","url":null,"abstract":"Abstract In this paper, we determine the r-dynamic chromatic number of the fan graph Fm,n and determine sharp bounds of this graph invariant for four related families of graphs: The middle graph M(Fm,n), the total graph T (Fm,n), the central graph C(Fm,n) and the line graph L(Fm,n). In addition, we determine the r-dynamic chromatic number of each one of these four families of graphs in case of being m = 1.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84204317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abdelhaq El Khalfi, N. Mahdou, Ünsal Tekir, Suat Koç
Abstract Let R be a commutative ring with nonzero identity. Let 𝒥(R) be the set of all ideals of R and let δ : 𝒥 (R) → 𝒥 (R) be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J ⊆ I, we have L ⊆ δ (L) and δ (J) ⊆ δ (I). Let δ be an expansion function of ideals of R. In this paper, we introduce and investigate a new class of ideals that is closely related to the class of δ -primary ideals. A proper ideal I of R is said to be a 1-absorbing δ -primary ideal if whenever nonunit elements a, b, c ∈ R and abc ∈ I, then ab ∈ I or c ∈ δ (I). Moreover, we give some basic properties of this class of ideals and we study the 1-absorbing δ-primary ideals of the localization of rings, the direct product of rings and the trivial ring extensions.
{"title":"On 1-absorbing δ-primary ideals","authors":"Abdelhaq El Khalfi, N. Mahdou, Ünsal Tekir, Suat Koç","doi":"10.2478/auom-2021-0038","DOIUrl":"https://doi.org/10.2478/auom-2021-0038","url":null,"abstract":"Abstract Let R be a commutative ring with nonzero identity. Let 𝒥(R) be the set of all ideals of R and let δ : 𝒥 (R) → 𝒥 (R) be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J ⊆ I, we have L ⊆ δ (L) and δ (J) ⊆ δ (I). Let δ be an expansion function of ideals of R. In this paper, we introduce and investigate a new class of ideals that is closely related to the class of δ -primary ideals. A proper ideal I of R is said to be a 1-absorbing δ -primary ideal if whenever nonunit elements a, b, c ∈ R and abc ∈ I, then ab ∈ I or c ∈ δ (I). Moreover, we give some basic properties of this class of ideals and we study the 1-absorbing δ-primary ideals of the localization of rings, the direct product of rings and the trivial ring extensions.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80748100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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