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We also study those Riemann soliton submanifolds isometrically immersed into a Riemannian manifold endowed with a torse-forming vector field, having as potential vector field its tangential component. We consider the minimal and the totally geodesic cases, too, as well as when the ambient manifold is of constant sectional curvature. In particular, we prove that a totally geodesic submanifold isometrically immersed into a Riemannian manifold endowed with a concircular vector field is a Riemann soliton if and only if it is of constant curvature. Furthermore, we show that, if the potential vector field of a minimal hypersurface Riemann soliton isometrically immersed into a Riemannian manifold of constant curvature and endowed with a concircular vector field is of constant length, then it is a metallic shaped hypersurface.\n",{"EN":132},"On Submanifolds as Riemann Solitons",{"VOID":134},"[\"25543262617370240\"]",{"EN":136},"",{"VOID":138},"Biswas, G.G., Chen, X., De, U.C.: Riemann solitons on almost co-Kähler manifolds. Filomat 36, 1403–1413 (2022). https:\u002F\u002Fdoi.org\u002F10.2298\u002FFIL2204403B\nBlaga, A.M.: Remarks on almost Riemann solitons with gradient or torse-forming vector field. Bull. Malaysian Math. Sci. Soc. 44, 3215–3227 (2021). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs40840-021-01108-9\nBlaga, A.M., Laţcu, D.R.: Remarks on Riemann and Ricci solitons in \\((\\alpha,\\beta )\\)-contact metric manifolds. J. Geom. Symm. Phys. 58, 1–12 (2020). https:\u002F\u002Fdoi.org\u002F10.7546\u002Fjgsp-58-2020-1-12\nBlaga, A.M., Özgür, C.: Almost \\(\\eta \\)-Ricci and almost \\(\\eta \\)-Yamabe solitons with torse-forming potential vector field. Quaestiones Mathematicae 45, 143–163 (2022). https:\u002F\u002Fdoi.org\u002F10.2989\u002F16073606.2020.1850538\nBlaga, A.M., Özgür, C. Remarks on submanifolds as almost \\(\\eta \\)-Ricci-Bourguignon solitons, Facta Universitatis. Series: Mathematics and Informatics, 37, 397–407 (2020). https:\u002F\u002Fdoi.org\u002F10.22190\u002FFUMI220318027B\nChen, B.-Y.: A survey on Ricci solitons on Riemannian submanifolds, Recent advances in the geometry of submanifolds – dedicated to the memory of Franki Dillen (1963–2013), 27–39, Contemp. Math. 674, Amer. Math. Soc., Providence, RI, 2016\nChen, B.-Y., Deshmukh, S.: Ricci solitons and concurrent vector fields. Balkan J. Geom. Appl. 20, 14–25 (2015)\nChen, B.-Y., Yano, K.: Hypersurfaces of a conformally flat space. Tensor NS 26, 318–322 (1972)\nDe, K., De, U.C.: A note on almost Riemann solitons and gradient almost Riemann solitons. Afr. Mat. 33(74), 10 (2022). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs13370-022-01010-y\nDe, K., De, U.C.: Riemann solitons on para-Sasakian geometry. Carpathian Math. Publ. 14, 395–405 (2022)\nDevaraja, M.N., Kumara, H.A., Venkatesha, V.: Riemann soliton within the framework of contact geometry. Quaestiones Mathematicae 44, 637–651 (2021). https:\u002F\u002Fdoi.org\u002F10.2989\u002F16073606.2020.1732495\nGowda, P.D., Naik, D.M., Ravindranatha, A.M., Venkatesha, V.: Riemann solitons on \\((\\kappa, \\mu )\\)-almost cosymplectic manifolds. Commun. Korean Math. Soc. 38, 881–892 (2023). https:\u002F\u002Fdoi.org\u002F10.4134\u002FCKMS.c220243\nManev, M.: Almost Riemann solitons with vertical potential on conformal cosymplectic contact complex Riemannian manifolds. Symmetry 15, 104 (2023). https:\u002F\u002Fdoi.org\u002F10.3390\u002Fsym15010104\nÖzgür, C., Özgür, N.Y.: Classification of metallic shaped hypersurfaces in real space forms. Turk. J. Math. 39, 784–794 (2015). https:\u002F\u002Fdoi.org\u002F10.3906\u002Fmat-1408-17\nHamilton, R.S.: Three-manifolds with positive Ricci curvature. J. Differential Geom. 17, 255–306 (1982). https:\u002F\u002Fdoi.org\u002F10.4310\u002Fjdg\u002F1214436922\nHirică, I.E., Udrişte, C.: Ricci and Riemann solitons. Balkan J. Geom. Appl. 21, 35–44 (2016)\nPigola, S., Rigoli, M., Rimoldi, M., Setti, A.G.: Ricci almost solitons. Ann. Sc. Norm. Super. Pisa Cl. Sci. 5(10), 757–799 (2011)\nRachunek, L., Mikes, J.: On tensor fields semiconjugated with torse-forming vector fields. Acta Univ. Palacki. Olomuc. Fac. Rerum Nat. Math. 44, 151–160 (2005)\nTokura, W., Barboza, M., Batista, E., Menezes, I.: Rigidity results for Riemann and Schouten solitons. Mediterr. J. Math. 20, 112 (2023). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs00009-023-02319-z\nVenkatesha, V., Kumara, H.A., Naik, D.M.: Riemann solitons and almost Riemann solitons on almost Kenmotsu manifolds. Int. J. Geom. Methods Modern Phys. 17(2050105), 22 (2020). https:\u002F\u002Fdoi.org\u002F10.1142\u002FS0219887820501054\nYano, K.: On the torse-forming directions in Riemannian spaces. Proc. Imp. Acad. Tokyo 20, 340–345 (1944). https:\u002F\u002Fdoi.org\u002F10.3792\u002Fpia\u002F1195572958",{"VOID":140},"10.1007\u002Fs40840-024-01661-z","PUBLICATION","VERIFIED","2024-05-13T07:14:42.287+00:00","Auto Verify","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs40840-024-01661-z",[147,165],{"id":148,"sortIndex":23,"researcher":22,"roles":149,"affiliations":151,"properties":160,"displayName":162,"givenName":22,"familyName":22},"f000daff-5382-44c1-95b8-bbbc2fd61825",[150],"AUTHOR",[152],{"id":153,"sortIndex":23,"affiliation":154,"properties":22},"2899f240-c424-4033-9b4a-2faa4389458b",{"id":153,"createTime":22,"updateTime":22,"relativeEntities":155,"slug":22,"properties":156,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":159,"statistic":22},[],{"title":157},{"VI":158},"Department of Mathematics, West University of Timişoara, Timişoara, Romania",[],{"title":161,"gsAuthor":163},{"VI":162},"Adara M. 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By using constraint variational method and quantitative deformation lemma, we derive two results. If \n                \n                  \n                \n                $$\\mu $$\n                \n               is large enough, the system has a least-energy sign-changing solution \n                \n                  \n                \n                $$u_{\\mu }$$\n                \n              . Moreover, the energy of the solution is twice as large as that of the ground state solution.",{"EN":250},"Existence of Least-Energy Sign-Changing Solutions for the Schrödinger–Bopp–Podolsky System with Critical Growth",{"VOID":252},"[\"17362093673122916075\"]",{"VOID":254},"d’Avenia, P., Siciliano, G.: Nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics: Solutions in the electrostatic case. J. Differ. Equ. 267, 1025–1065 (2019)\nBonheure, D., Casteras, J.-B., dos Santos, E.M., Nascimento, R.: Orbitally stable standing waves of a mixed dispersion nonlinear Schrödinger equation. SIAM J. Math. Anal. 50, 5027–5071 (2018)\nFibich, G., Ilan, B., Papanicolaou, G.: Self-focusing with fourth-order dispersion. SIAM J. Appl. Math. 62, 1437–1462 (2002)\nMie, G.: Grundlagen einer Theorie der Materie. Ann. Phys. 345, 1–66 (1913)\nFrenkel, J.: 4\u002F3 Problem in classical electrodynamics. Phys. Rev. E 54, 5859–5862 (1996)\nBorn, M., Infeld, L.: Foundations of the new field theory. Nature 132, 1004 (1933)\nBorn, M., Infeld, L.: Foundations of the new field theory. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 144, 425–451 (1934)\nBorn, M.: Modified field equations with a finite radius of the electron. Nature 132, 282 (1933)\nBorn, M.: On the quantum theory of the electromagnetic field. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 143, 410–437 (1934)\nBertin, M.C., Pimentel, B.M., Valcarcel, C.E., Zambrano, G.E.R.: Hamilton-Jacobi formalism for Podolsky’s electromagnetic theory on the null-plane. J. Math. Phys. 58, 082902 (2017)\nBufalo, R., Pimentel, B.M., Soto, D.E.: Causal approach for the electron-positron scattering in generalized quantum electrodynamics. Phys. Rev. D 90, 085012 (2014)\nBufalo, R., Pimentel, B.M., Soto, D.E.: Normalizability analysis of the generalized quantum electrodynamics from the causal point of view. Internat. J. Modern Phys. A 32, 1750165 (2017)\nCuzinatto, R.R., de Melo, C.A.M., Medeiros, L.G., Pimentel, B.M., Pompeia, P.J.: Bopp-podolsky black holes and the no-hair theorem. Eur. Phys. J. C 78, 43 (2018)\nCuzinatto, R.R., de Melo, E.M., Medeiros, L.G., Souza, C.N.D., Pimentel, B.M.: De Broglie-proca and Bopp-podolsky massive photon gases in cosmology. Europhys. Lett. 118, 19001 (2017)\nChen, S.T., Tang, X.H.: On the critical Schrödinger-Bopp-Podolsky system with general nonlinearities. Nonlinear Analysis. 195, 111734 (2020)\nLin Li, Patrizia Pucci, X. H. Tang, Ground state solutions for the nonlinear Schrödinger-Bopp-Podolsky system with critical sobolev exponent. Adv. Nonlinear Stud. 20(3), 511-538 (2020)\nYang, J., Chen, H., Liu, S.: The existence of nontrivial solution of a class of Schrödinger-Bopp-Podolsky system with critical growth. Bound Value Probl. 2020, 144 (2020)\nAberqi, A., Bennouna, J., Bensliman, O., Ragusa, M.A.: Existence results for double phase problem in Sobolev-Orlicz spaces with variable exponents in complete manifold. Mediterr. J. Math. 19, 158 (2022)\nBenslimane, O., Aberqi, A., Bennouna, J.: Existence and uniqueness of weak solution of p(x)-Laplacian in Sobolev spaces with variable exponents in complete manifolds. Filomat 35(5), 1453–1463 (2021)\nBoulaaras, S.M., Choucha, A., Abderrahmane, Z., Mohamed, A., Cheri, B.B.: Global existence and decay estimates of energy of solutions for a new class of p-Laplacian heat equations with logarithmic nonlinearity. J. Funct. Spaces 2021, 58818–58818 (2021)\nWang, Da-Bin., Zhang, Hua-Bo., Guan, Wen: Existence of least-energy sign-changing solutions for Schrödinger-Poisson system with critical growth. J. Math. Anal. Appl. 479, 2284–2301 (2019)\nBartsch, T., Wang, Z.-Q.: Existence and multiplicity results for some superlinear elliptic problems on \\({R}^{N}\\). Comm. Partial Differential Equations 20, 1725–1741 (1995)\nWillem, M.: Minimax Theorems. Birkhäuser, Boston (1996)",{"VOID":256},"10.1007\u002Fs40840-022-01441-7","2024-08-30T22:40:59.243+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs40840-022-01441-7",[260,275,288],{"id":261,"sortIndex":23,"researcher":22,"roles":262,"affiliations":263,"properties":272,"displayName":274,"givenName":22,"familyName":22},"6e144b9e-6e2a-48a8-98ff-f63efddd7c98",[150],[264],{"id":265,"sortIndex":23,"affiliation":266,"properties":22},"53f877e7-ae61-4fe3-9899-ea20865672a8",{"id":265,"createTime":22,"updateTime":22,"relativeEntities":267,"slug":22,"properties":268,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":271,"statistic":22},[],{"title":269},{"VI":270},"School of Mathematics and Statistics, Southwest University, Chongqing, People’s Republic of China",[],{"title":273},{"VI":274},"Yi-Xin 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Appropriate duality theorems for Wolfe and Mond–Weir-type duals are presented in order to relate the LU optimal solution of primal and dual programs. 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(eds.): Optimality Conditions in Vector Optimization. Bentham Science Publishers Ltd., Bussum (2010)",{},{"id":503,"text":504,"url":505,"identifiers":506},"306074df-670c-48fa-8ead-c5cf5e40b21d","Bhurjee, A.K., Panda, G.: Efficient solution of interval optimization problem. Math. Methods Oper. Res. 76, 273–288 (2012)","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00186-012-0399-0",{"doi":507},"10.1007\u002Fs00186-012-0399-0",{"id":22,"text":509,"url":22,"identifiers":510},"Clarke, F.H.: Nonsmooth Optimization. Wiley Interscience, New York (1983)",{},{"id":512,"text":513,"url":514,"identifiers":515},"4c68646b-0035-4279-8000-0006b275d4fa","Craven, B.D.: Nondifferentiable optimization by smooth approximations. Optimization 17, 3–17 (1986)","https:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs10440-022-00541-7",{"doi":516},"10.1007\u002Fs10440-022-00541-7",{"id":512,"text":518,"url":514,"identifiers":519},"Hanson, M.A.: On sufficiency of the Kuhn-Tuker conditions. J. Math. Anal. Appl. 80, 545–550 (1981)",{"doi":516},{"id":512,"text":521,"url":514,"identifiers":522},"Jayswal, A., Stancu-Minasian, I.M., Ahmad, I.: On sufficiency and duality for a class of interval-valued programming problems. Appl. Math. Comput. 218, 4119–4127 (2011)",{"doi":516},{"id":512,"text":524,"url":514,"identifiers":525},"Jiao, H., Liu, S.: On a nonsmooth vector optimization problem with generalized cone invexity. Abstr. Appl. Anal. 2012, 458983 (2012)",{"doi":516},{"id":512,"text":527,"url":514,"identifiers":528},"Kim, D.S., Lee, H.J.: Optimality conditions and duality in nonsmooth multiobjective programs. J. Ineq. Appl. 2010, 939537 (2010)",{"doi":516},{"id":512,"text":530,"url":514,"identifiers":531},"Sun, Y., Wang, L.: Optimality conditions and duality in nondifferentiable interval-valued programming. J. Ind. Manag. Optim. 9, 131–142 (2013)",{"doi":516},{"id":533,"text":534,"url":535,"identifiers":536},"61e7a84b-c61e-4985-a58b-eccbe333fb74","Sun, Y., Xu, X., Wang, L.: Duality and saddle-point type optimality for interval-valued programming. Optim. Lett. 8, 1077–1091 (2014)","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11590-013-0640-7",{"doi":537},"10.1007\u002Fs11590-013-0640-7",{"id":512,"text":539,"url":514,"identifiers":540},"Urli, B., Nadeau, R.: An interactive method to multiobjective linear programming problems with interval coefficients. INFOR 30, 127–137 (1992)",{"doi":516},{"id":542,"text":543,"url":544,"identifiers":545},"99eb7fb6-0248-4251-9e08-8b741950d343","Wu, H.-C.: The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function. Eur. J. Oper. Res. 176, 46–59 (2007)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0377221705007022",{"doi":546},"10.1016\u002Fj.ejor.2005.09.007",{"id":512,"text":548,"url":514,"identifiers":549},"Wu, H.-C.: Wolfe duality for interval-valued optimization. J. Optim. Theory Appl. 138, 497–509 (2008)",{"doi":516},{"id":512,"text":551,"url":514,"identifiers":552},"Wu, H.-C.: Duality theory for optimization problems with interval-valued objective functions. J. Optim. Theory Appl. 144, 615–628 (2010)",{"doi":516},{"id":512,"text":554,"url":514,"identifiers":555},"Yang, X.M., Yang, X.Q., Teo, K.L.: Duality and saddle-point type optimality for generalized nonlinear fractional programming. J. Math. Anal. Appl. 289, 100–109 (2004)",{"doi":516},{"id":512,"text":557,"url":514,"identifiers":558},"Zalmai, G.J.: Saddle-point-type optimality conditions and lagrangian-type duality for a class of constrained generalized fractional optimal control. Optimization 44, 351–372 (1998)",{"doi":516},{"id":560,"text":561,"url":562,"identifiers":563},"9f4377e6-924e-40b0-8edd-6aa77e3b499a","Zhang, J., Liu, S., Li, L., Feng, Q.: The KKT optimality conditions in a class of generalized convex optimization problems with an interval-valued objective function. Optim. Lett. 8, 607–631 (2014)","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs11590-012-0601-6",{"doi":564},"10.1007\u002Fs11590-012-0601-6",{"id":512,"text":566,"url":514,"identifiers":567},"Zhou, H.-C., Wang, Y.-J.: Optimality condition and mixed duality for interval-valued optimization. In: Fuzzy Information and Engineering, Vol. 2, Advances in Intelligent and Soft Computing”, Vol. 62, Proceedings of the Third International Conference on Fuzzy Information and Engineering (ICFIE 2009), Springer, pp. 1315–1323 (2009)",{"doi":516},{"id":569,"createTime":570,"updateTime":571,"relativeEntities":572,"slug":573,"properties":574,"entityType":141,"verifyStatus":142,"verifyTime":585,"verifyNote":144,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":586,"fullTextUrl":22,"authors":587,"publicationType":182,"publisherRelationship":616,"citationCount":492,"citationInfo":671,"publishDate":674,"publishYear":672,"citationAnalyzeStatus":21,"lastCitationAnalyze":675,"indexDatabases":676,"openAccess":22,"references":22,"isForceReanalyzing":239},"60e92b6d-f2aa-4fd1-80f0-2fe90b74c16b","2024-01-05T19:51:20.969+00:00","2026-07-20T20:13:22.383+00:00",[],"Cellularity-of-Some-Semigroup-Algebras",{"abstract":575,"title":577,"gsPaper":579,"references":581,"doi":583},{"EN":576},"In this paper, we study the cellularity of some semigroup algebras. We show that the semigroup algebra of a U-semiabundant semigroup with Rees matrix semigroups over monoids as its principal \n                  \n                    \n                  \n                  $$\\sim _U$$\n                  \n                    \n                  \n                -factors is a cellular algebra if and only if all of the monoid algebras are cellular. We also study the cellularity of the semigroup algebra of a semilattice of Rees matrix semigroups. As consequences, we get the cellularity of super abundant semigroup algebras and complete regular semigroup algebras.",{"EN":578},"Cellularity of Some Semigroup Algebras",{"VOID":580},"[\"174012558437985611\"]",{"VOID":582},"Clifford, A.H., Preston, G.B.: The Algebraic Theory of Semigroup. American Mathematical Society, Providence (1961)\nEast, J.: Cellular algebras and inverse semigroups. J. Algebra 296(2), 505–519 (2006)\nFountain, J.: Abundant semigroup. Proc. Lond. Math. Soc. 44(3), 103–129 (1982)\nGong, C.M., Guo, Y.Q., Shum, K.P.: Ortho-u-monoids. Acta Math. Sin. (Engl. Ser.) 27(5), 831–844 (2011)\nGraham, J.J., Lehrer, G.I.: Cellular algebras. Invent. Math. 123, 1–34 (1996)\nGuo, X.J., Xi, C.C.: Cellularity of twisted semigroup algebras. J. Pure Appl. Algebra 213, 71–86 (2009)\nGuo, Y.Q., Shum, K.P., Gong, C.M.: On \\((*,\\sim )\\)-Green’s relations and ortho-lc-monoids. Commun. Algebra 39, 5–31 (2011)\nHowie, J.M.: Fundamentals of Semigroup Theory. Clarendon Press\u002FOxford University Press, New York (1995)\nKönig, S., Xi, C.C.: On the structure of cellular algebras. In: Algebras and Modules II (Geiranger 1996), CMS Conference Proceedings, vol. 24, pp 365–386 (1998)\nKönig, S., Xi, C.C.: When is a cellular algebra quasi-hereditary? Math. Ann. 315, 281–293 (1999)\nLawson, M.V.: Rees matrix semigroup. Proc. Edinb. Math. Soc. 33, 23–37 (1990)\nOkninski, J.: Semigroup Algebras. Marcel Dekker, New York (1991)\nPastijn, F.: A representation of a semigroup by a semigroup of matrices over a group with zero. Semigroup Forum 10, 238–249 (1975)\nRees, D.: On semi-groups. Proc. Camb. Philos. Soc. 36, 387–400 (1940)\nRen, X.M., Shum, K.P.: The structure of superabundant semigroups. Sci. China Ser. A 47(5), 756–771 (2004)\nRen, X.M., Shum, K.P., Guo, Y.Q.: A generalized Clifford theorem of semigroups. Sci. China Ser. A 53(4), 1097–1101 (2010)\nWilcox, S.: Cellularity of diagram algebras as twisted semigroup algebras. J. Algebra 309, 10–31 (2007)\nXi, C.C.: Standardly stratified algebra and cellular algebras. Math. Proc. Camb. Philos. 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study the relation between certain non-degenerate lower Hessenberg infinite matrices \n                \n                  \n                \n                $${\\mathcal {G}}$$\n                \n               and the existence of sequences of orthogonal polynomials with respect to Sobolev inner products. In other words, we extend the well-known Favard theorem for Sobolev orthogonality. We characterize the structure of the matrix \n                \n                  \n                \n                $${\\mathcal {G}}$$\n                \n               and the associated matrix of formal moments \n                \n                  \n                \n                $${\\mathcal {M}}_{{\\mathcal {G}}}$$\n                \n               in terms of certain matrix operators.",{"EN":687},"Hessenberg–Sobolev Matrices and Favard Type Theorem",{"VOID":689},"[\"18396226189586566715\"]",{"VOID":691},"Álvarez-Nordase, R., Marcellán, F.: On the Favard theorem and its extensions. J. Comput. Appl. Math. 127, 231–254 (2001)\nAkhiezer, N.I.: The Classical Moment Problem and Some Related Questions in Analysis. Oliver and Boyd, Edinburgh (1965)\nBarrios-Rolanía, D., López-Lagomasino, G., Pijeira-cabrera, H.: The moment problem for a Sobolev inner product. J. Approx. Theory 100, 364–380 (1999)\nCantero, M.J., Marcellán, F., Moral, L., Velázquez, L.: Darboux transformations for CMV matrices. Adv. Math. 298, 122–206 (2016)\nCooke, R.G.: Infinite Matrices and Sequence Spaces. Macmillan and Co., London (1950)\nDíaz-Millán, R.: Characterization of linear functionals associated with bilinear forms of Sobolev type. Rev. Colomb. Mat. 42, 85–98 (2008). ((in Spanish))\nDurán, A.J.: A generalization of Favard’s Theorem for polynomials satisfying a recurrence relation. J. Approx. Theory 74, 83–09 (1993)\nGolub, G.H., Meurant, G.: Matrices, Moments and Quadrature with Applications. Princeton Univ. Press, Princeton, NJ (2010)\nHorn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge Univ. Press, Cambridge (2013)\nKjeldsen, T.H.: The early history of the moment problem. Historia Math. 20, 19–44 (1993)\nLandau , H.J.: (Ed.) Moments in Mathematics, Proc. Symp. Appl. Math., Vol. 37, Amer. Math. Soc., Providence, RI, (1987)\nMarcellán, F., Xu, Y.: On Sobolev orthogonal polynomials. Expo. Math. 33, 308–352 (2015)\nMarcellán, F., Szafraniec, F.H.: The Sobolev-type moment problem. Proc. Amer. Math. Soc. 128, 2309–2317 (2000)\nMarcellán, F., Szafraniec, F.H.: A matrix algorithm towards solving the moment problem of Sobolev type. Linear Algebra Appl. 331, 155–164 (2001)\nPeller, V.: Hankel Operators and Their Applications. Springer-Verlag, New York (2003)\nPijeira-Cabrera, H.: Theory of moments and asymptotic properties of Sobolev orthogonal polynomials, Doctoral Dissertation, Universidad Carlos III de Madrid, (1998) (in Spanish), https:\u002F\u002Fdoi.org\u002F10.13140\u002FRG.2.1.4382.9920\nPijeira-Cabrera, H., Quintana-Mato, Y., Rodríguez-García, J.M.: Sobolev formal orthogonality on algebraic curves and extensions of Favard theorem. Jaen J. Approx. 3, 193–207 (2011)\nQuaintance, J., Gould, H.W.: Combinatorial Identities for Stirling Numbers. The unpublished notes of H. W. Gould, World Scientific. Singapore, (2016)\nRobert, L., Santiago, L.: On a class of Sobolev scalar products in the polynomials. J. Approx. Theory 125, 169–189 (2003)\nSchmüdgen, K.: The Moment Problem, Graduate Texts in Mathematics, vol. 27. Springer, Cham (2017)\nShohat, J.A., Tamarkin, J.D.: The Problem of Moments, Mathematical Surveys, vol. I. Amer. Math. Soc, Providence, RI (1963)\nZagorodnyuk, S.M.: On the moment problem of discrete Sobolev type. Ukr. Math. 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graph G is called a fractional \n                  \n                    \n                  \n                  $$(g,f,n',m)$$\n                  \n                    \n                  \n                -critical deleted graph if after deleting any \n                  \n                    \n                  \n                  $$n'$$\n                  \n                    \n                  \n                 vertices of G the remaining graph is a fractional (g, f, m)-deleted graph. A graph G is called a fractional ID-(g, f, m)-deleted graph if after deleting any independent set I of G the remaining graph is a fractional (g, f, m)-deleted graph. In this paper, we give some sharp degree conditions for a graph to be a fractional \n                  \n                    \n                  \n                  $$(g,f,n',m)$$\n                  \n                    \n                  \n                -critical deleted graph and a fractional ID-(g, f, m)-deleted graph. 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CXIIIA, 49–64 (2014)\nYu, J., Liu, G., Ma, M., Cao, B.: A degree condition for graphs to have fractional factors. Adv. Math. (in Chinese) 35(5), 621–628 (2006)\nZhou, S.: A minimum degree condition of fractional \\((k, m)\\)-deleted graphs. C. R. Math. 347, 1223–1226 (2009)\nZhou, S., Liu, H.: On fractional \\((k, m)\\)-deleted graphs with constrains conditions. World Acad. Sci. Eng. Technol. 79, 983–985 (2011)\nZhou, S., Sun, Z., Liu, H.: A minimum degree condition for fractional ID-[\\(a, b\\)]-factor-critical graphs. Bull. Aust. Math. 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Our special attention will be focused on the reduction of remainder terms in the Gallagherian-type theorem for a family of compact, even-dimensional spaces. The main tool to enable the process will be newly derived explicit formulas for counting functions of appropriate degree.",{"EN":1113},"Gallagherian PGT on Some Compact Riemannian Manifolds of Negative Curvature",{"VOID":1115},"[\"16443767442124842129\"]",{"VOID":1117},"Avdispahić, M.: Gallagherian PGT on \\(PSL{2,\\mathbb{Z}}\\). Funct. Approx. Comment. Math. 58, 207–213 (2018)\nAvdispahić, M.: On Koyama’s refinement of the prime geodesic theorem. Proc. Japan Acad. Ser. A 94, 21–24 (2018)\nAvdispahić, M.: Errata and addendum to On the prime geodesic theorem for hyperbolic 3-manifolds. Math. Nachr. 291(14–15), 2160–2167 (2018)\nAvdispahić, M.: Errata and addendum to On the prime geodesic theorem for hyperbolic 3-manifolds. Math. Nachr. 292, 691–693 (2019)\nAvdispahić, M.: A prime geodesic theorem of Gallagher type for Riemann surfaces. Analysis Math. 46, 26–38 (2020)\nAvdispahić, M., Gušić, D.ž: On the error term in the prime geodesic theorem. Bull. Korean Math. Soc. 49, 367–372 (2012)\nAvdispahić, M., Gušić, D.ž: Order of Selberg’s and Ruelle’s zeta functions for compact even-dimensional locally symmetric spaces. J. Math. Anal. Appl. 413, 525–531 (2014)\nAvdispahić, M., Gušić, D.ž: On the logarithmic derivative of zeta functions for compact even-dimensional locally symmetric spaces of real rank one. Math. Slovaca 69, 311–320 (2019)\nAvdispahić, M., Šabanac, Z.: Gallagherian prime geodesic theorem in higher dimensions. Bull. Malays. Math. Sci. Soc. 43, 3019–3026 (2020)\nBalkanova, O., Frolenkov, D.: Prime geodesic theorem for the Picard manifold. Adv. Math. 375, 107377 (2020)\nBunke, U., Olbrich, M.: Selberg Zeta and Theta Functions. A Differential Operator Approach. Akademie-Verlag, Berlin (1995)\nCai, Y.: Prime geodesic theorem. J. Théor. Nombres Bordeaux 14, 59–72 (2002)\nDeitmar, A.: Higher torsion zeta functions. Adv. Math. 110, 109–128 (1995)\nDeitmar, A.: Class numbers of orders in cubic fields. J. Number Theory 95, 150–166 (2002)\nDeitmar, A., Pavey, M.: A prime geodesic theorem for \\(SL_{4}\\). Ann. Glob. Anal. Geom. 33, 161–205 (2008)\nDuistermaat, J.J., Kolk, J.A.C., Varadarajan, V.S.: Spectra of compact locally symmetric manifolds of negative curvature. Invent. Math. 52, 27–93 (1979)\nFried, D.: Analytic torsion and closed geodesics on hyperbolic manifolds. Invent. Math. 84, 523–540 (1986)\nFried, D.: The zeta functions of Ruelle and Selberg. I. Ann. Sci. Ec. Norm. Sup. 19, 491–517 (1986)\nFried, D.: Torsion and closed geodesics on complex hyperbolic manifolds. Invent. Math. 91, 31–51 (1988)\nGallagher, P.X.: Some consequences of the Riemann hypothesis. Acta Arith. 37, 339–343 (1980)\nGangolli, R.: The length spectrum of some compact manifolds of negative curvature. J. Diff. Geom. 12, 403–426 (1977)\nGangolli, R.: Zeta functions of Selberg’s type for compact space forms of symmetric spaces of rank one. Ill. J. Math. 21, 1–42 (1977)\nGangolli, R., Warner, G.: Zeta functions of Selberg’s type for some noncompact quotients of symmetric spaces of rank one. Nagoya Math. J. 78, 1–44 (1980)\nGon, Y., Park, J.: The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps. Math. Ann. 346, 719–767 (2010)\nGušić, D.ž: Prime geodesic theorems for compact locally symmetric spaces of real rank one. Mathematics 8, 1762 (2020)\nHejhal, D.: The Selberg trace formula for \\(PSL({2,\\mathbb{R}})\\), vol. 1. Springer, Berlin (1976)\nHejhal, D.: The Selberg trace formula for \\(PSL({2,\\mathbb{R}})\\), vol. 2. Springer, Berlin (1983)\nHuber, H.: Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II. Math. Ann. 142, 385–398 (1961)\nHuber, H.: Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II. Math. Ann. 143, 463–464 (1961)\nIwaniec, H.: Prime geodesic theorem. J. Reine Angew. Math. 349, 136–158 (1984)\nKoyama, S.: Prime geodesic theorem for arithmetic compact surfaces. Internat. Math. Res. Notices 8, 383–388 (1998)\nKoyama, S.: Refinement of prime geodesic theorem. Proc. Japan Acad. 92, 77–81 (2016)\nLuo, W., Rudnick, Z., Sarnak, P.: On Selberg’s eigenvalue conjecture. Geom. Funct. Anal. 5, 387–401 (1995)\nLuo, W., Sarnak, P.: Quantum ergodicity of eigenfunctions on \\(PSL_{2}({\\mathbb{Z}})\\backslash {\\mathbb{H}}^{2}\\). Hautes Etudes Sci. Publ. Math. 81, 207–237 (1995)\nMoscovici, H., Stanton, R.: R-torsion and zeta functions for locally symmetric manifolds. Invent. Math. 105, 185–216 (1991)\nPark, J.: Analytic torsion and Ruelle zeta functions for hyperbolic manifolds with cusps. J. Funct. Anal. 257, 1713–1758 (2009)\nPark, J.: Ruelle zeta function and prime geodesic theorem for hyperbolic manifolds with cusps, In: van Dijk, G., Wakayama, M. (eds.) Casimir Force, Casimir Operators and the Riemann Hypothesis, 9–13, 2009, Kyushu University, Fukuoka, Japan, pp. 89–104, Walter de Gruyter (2010)\nParnovskij, L.B.: The trace formula and the Selberg zeta function for co-compact discrete subgroups of \\(SO_{0}({1, n})\\). Funct. Anal. Pril. 26, 55–64 (1992)\nRandol, B.: On the asymptotic distributon of closed geodesics on compact Riemann surfaces. Trans. Am. Math. Soc. 233, 241–247 (1977)\nRuelle, D.: The zeta functions for expanding maps and Anosov flows. Invent. Math. 34, 231–242 (1976)\nRuelle, D.: Thermodynamic Formalism. Addison-Wesley, Reading (1978)\nSchuster, R.: Spectral estimates for compact hyperbolic space forms and the Selberg zeta function for \\(p\\)-spectra. Zeitschr. Anal. Anw. 13, 261–305 (1994)\nScott, D.: Selberg-type zeta functions for the group of complex two by two matrices of determinant one. Math. Ann. 253, 177–194 (1980)\nSelberg, A.: Harmonic analysis and discontinuous groups in weakly symmteric Riemannian spaces with applications to Dirichlet series. J. Indian Math. Soc. 20, 47–87 (1956)\nSoundararajan, K., Young, M.P.: The prime geodesic theorem. J. Reine Angew. Math. 676, 105–120 (2013)\nWakayama, M.: Zeta function of Selberg’s type for compact quotient of \\(SU({n,1})\\)\\(({n\\ge 2})\\). Hiroshima Math. J. 14, 597–618 (1984)\nWakayama, M.: Zeta functions of Selberg’s type associated with homogeneous vector bundles. Hiroshima Math. 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\n                  \n                    \n                  \n                  $$\\mathfrak a, \\mathfrak b$$\n                  \n                    \n                  \n                 be ideals of a commutative Noetherian ring \n                  \n                    \n                  \n                  $$R$$\n                  \n                    \n                  \n                 and let \n                  \n                    \n                  \n                  $$M, N$$\n                  \n                    \n                  \n                 be finite \n                  \n                    \n                  \n                  $$R$$\n                  \n                    \n                  \n                -modules. The concept of an \n                  \n                    \n                  \n                  $$\\mathfrak a$$\n                  \n                    \n                  \n                -filter grade of \n                  \n                    \n                  \n                  $$\\mathfrak b$$\n                  \n                    \n                  \n                 on \n                  \n                    \n                  \n                  $$M$$\n                  \n                    \n                  \n                 is introduced and several characterizations and properties of this notion are given. Then, using the above characterizations, we obtain some results on generalized local cohomology modules \n                  \n                    \n                  \n                  $$\\mathrm{H }^{i}_{\\mathfrak a}(M,N)$$\n                  \n                    \n                  \n                . In particular, first we determine the least integer \n                  \n                    \n                  \n                  $$i$$\n                  \n                    \n                  \n                 for which \n                  \n                    \n                  \n                  $$\\mathrm{H }^{i}_{\\mathfrak a}(M,N)$$\n                  \n                    \n                  \n                 is not Artinian. Then we prove that \n                  \n                    \n                  \n                  $$\\mathrm{H }^{i}_{\\mathfrak a}(M,N)$$\n                  \n                    \n                  \n                 is Artinian for all \n                  \n                    \n                  \n                  $$i\\in \\mathbb N_0$$\n                  \n                    \n                  \n                 if and only if \n                  \n                    \n                  \n                  $$\\dim {R}\u002F({\\mathfrak a+\\mathrm{Ann\\, }\\, M+\\mathrm{Ann\\, }\\, N})=0$$\n                  \n                    \n                  \n                . Also, we establish the Nagel–Schenzel formula for generalized local cohomology modules. Finally, in a certain case, the set of attached primes of \n                  \n                    \n                  \n                  $$\\mathrm{H }^{i}_{\\mathfrak a}(M,N)$$\n                  \n                    \n                  \n                 is determined and a comparison between this set and the set of attached primes of \n                  \n                    \n                  \n                  $$\\mathrm{H }^{i}_{\\mathfrak a}(N)$$\n                  \n                    \n                  \n                 is given.",{"EN":1207},"Filter Regular Sequences and Generalized Local Cohomology Modules",{"VOID":1209},"[\"7460309290871698251\"]",{"VOID":1211},"Amjadi, J., Naghipour, R.: Cohomological dimension of generalized local cohomology modules. Algebra Colloq. 15(2), 303–308 (2008)\nBagheri, A.: A non-vanishing Theorem for local cohomology modules, Bull. Malay. Math Sci. Soc. (2), accepted\nBelshoff, R.G., Enochs, E.E., García Rozas, J.R.: Generalized Matlis duality. Proc. Amer. Math. Soc. 128(5), 1307–1312 (2000)\nBijan-Zadeh, M.H.: A common generalization of local cohomology theories. Glasg. Math. J. 21(2), 173–181 (1980)\nBourbaki, N.: Commutative Algebra, Chapter 1–7, Elements of Mathematics. Springer-Verlag, Berlin (1998)\nBrodmann, M.P., Sharp, R.Y.: Local Cohomology: an Algebraic introduction with geometric applications, Cambridge Studies in Advanced Mathematics, 60. Cambridge University Press, Cambridge (1998)\nBruns, W., Herzog, J.: Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, 39. Cambridge University Press, Cambridge (1993)\nChu, L., Tang, Z.: On the Artinianness of generalized local cohomology. Comm. Algebra 35(12), 3821–3827 (2007)\nDibaei, M.T., Yassemi, S.: Attached primes of the top local cohomology modules with respect to an ideal. Arch. Math. (Basel) 84(4), 292–297 (2005)\nGu, Y., Chu, L.: Attached primes of the top generalized local cohomology modules. Bull. Aust. Math. Soc. 79(1), 59–67 (2009)\nHerzog, J.: Komplexe. Habilitationsschrift, Universität Regensburg, Auflösungen und Dualität in der lokalen Algebra (1970)\nHuneke, C.: Problems on local cohomology, In: Eisenbud, D., Huneke, C. (eds.) Free resolutions in commutative algebra and algebraic geometry, Sundance 90, pp. 93–108. Jones and Bartlett, Boston (1992)\nKhashyarmanesh, K., Salarian, Sh: Filter regular sequences and the finiteness of local cohomology modules. Comm. Algebra 26(8), 2483–2490 (1998)\nKhashyarmanesh, K., Yassi, M., Abbasi, A.: Filter regular sequences and generalized local cohomology modules. Comm. Algebra 32(1), 253–259 (2004)\nLü, R., Tang, Z.: The \\(f\\)-depth of an ideal on a module. Proc. Am. Math. Soc. 130(7), 1905–1912 (2002)\nMacDonald, I.G.: Secondary representation of modules over a commutative ring, Symposia Mathematica, Vol. XI (Convegno di Algebra Commutativa, INDAM, Rome, 1971), pp. 23–43. Academic Press, London (1973)\nMacdonald, I.G., Sharp, R.Y.: An elementary proof of the non-vanishing of certain local cohomology modules. Quart. J. Math. Oxf. Ser. (2) 23, 197–204 (1972)\nMafi, A.: On the associated primes of generalized local cohomology modules. Comm. Algebra 34(7), 2489–2494 (2006)\nMafi, A.: Top generalized local cohomology modules. Turkish J. Math. 35(4), 611–615 (2011)\nMatsumura, H.: Commutative ring theory, Cambridge Studies in Advanced Mathematics, 8. Cambridge University Press, Cambridge (1986)\nMelkersson, L.: Some applications of a criterion for Artinianness of a module. J. Pure Appl. Algebra 101(3), 291–303 (1995)\nNagel, U., Schenzel, P.: Cohomological annihilators and Castelnuovo-Mumford regularity, Commutative algebra: syzygies, multiplicities, and birational algebra (South Hadley, MA, 1992), 307–328, Contemp. Math., 159, Amer. Math. Soc., Providence, RI, (1994)\nPayrovi, Sh, Lotfi Parsa, M.: Artinianness of local cohomology modules defined by a pair of ideals. Bull. Malay. Math. Sci. Soc. (2) 35(4), 877–883 (2012)\nRotman, J.J.: An introduction to homological algebra, Pure and Applied Mathematics 85. Academic Press Inc, New York (1979)\nSharp, R.Y.: Steps in commutative algebra, London Mathematical Society Student Texts, 19. Cambridge University Press, Cambridge (1990)\nStückrad, J., Vogel, W.: Buchsbaum rings and applications. An interaction between algebra, geometry and topology. Springer-Verlag, Berlin (1986)\nSuzuki, N.: On the generalized local cohomology and its duality. J. Math. Kyoto Univ. 18(1), 71–85 (1978)\nTang, Z.: Local-global principle for the Artinianness of local cohomology modules. Comm. Algebra 40(1), 58–63 (2012)\nTrung, N.V.: Absolutely superficial sequences. Math. Proc. Camb. Philos. Soc. 93(1), 35–47 (1983)\nYassemi, S., Khatami, L., Sharif, T.: Associated primes of generalized local cohomology modules. Comm. Algebra 30(1), 327–330 (2002)\nZamani, N.: On graded generalized local cohomology. Arch. Math. 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