Статті в журналах: "M-degree"

1

Downey, R. G. "Recursively enumerable m- and tt-degrees. I: The quantity of m-degrees." Journal of Symbolic Logic 54, no. 2 (June 1989): 553–67. http://dx.doi.org/10.2307/2274869.

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In [1], Degtëv constructed a nonzero r.e. tt-degree containing a single r.e. m-degree. It is not difficult to construct an r.e. tt-degree containing infinitely many r.e. m-degrees (Fischer [6]); indeed, in [3], the author constructed an r.e. tt-degree with no greatest r.e. m-degree. Odifreddi [12, Problem 10] asked if every r.e. tt-degree contains either one or infinitely many r.e. m-degrees. The goal of this paper is to solve Odifreddi's question by showing:Theorem. There exists a nonzero r.e. tt-degree containing exactly 3 r.e. m-degrees.This theorem can be extended to show that there exist r.e. tt-degrees with arbitrarily large finite numbers of r.e. m-degrees.We remark that save for the aforementioned results, very little is known about the structures that can be realized as the collection of r.e. m-degrees within an r.e. tt-degree. It seems conceivable that the methods of the present paper may be useful in, for example, embedding distributive (semi) lattices into such structures.In part II of this paper [4], we continue our analysis of r.e. m- and tt-degrees. We define an r.e. tt-degree to be singular if it contains a single r.e. m-degree, and an r.e. T-degree a to be singular if a contains a singular r.e. tt-degree.In [4] we study the distribution (in the r.e. T-degrees) of singular tt-degrees. We show that 0′T is singular (solving a question of Odifreddi [11]), and that the singular T-degrees are dense, but also we construct a nonsingular T-degree. The techniques used for the first results extend those of §2 of the present paper.

2

Cintioli, Patrizio. "Degrees of sets having no subsets of higher m- and t t-degree." Computability 10, no. 3 (July 14, 2021): 235–55. http://dx.doi.org/10.3233/com-200296.

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We consider sets without subsets of higher m- and t t-degree, that we call m-introimmune and t t-introimmune sets respectively. We study how they are distributed in partially ordered degree structures. We show that: each computably enumerable weak truth-table degree contains m-introimmune Π 1 0 -sets; each hyperimmune degree contains bi-m-introimmune sets. Finally, from known results we establish that each degree a with a ′ ⩾ 0 ″ covers a degree containing t t-introimmune sets.

3

Shustin, E. I. "A new M-curve of degree 8." Mathematical Notes of the Academy of Sciences of the USSR 42, no. 2 (August 1987): 606–10. http://dx.doi.org/10.1007/bf01240445.

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4

Korchagin, A. B. "M-curves of degree 9: New prohibitions." Mathematical Notes of the Academy of Sciences of the USSR 39, no. 2 (February 1986): 150–54. http://dx.doi.org/10.1007/bf01159900.

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5

Fiedler-Le Touzé, Séverine. "M -curves of degree 9 with deep nests." Journal of the London Mathematical Society 79, no. 3 (March 27, 2009): 649–62. http://dx.doi.org/10.1112/jlms/jdp010.

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6

Faudree, Ralph J., Ronald J. Gould, Michael S. Jacobson, and Linda Lesniak. "Minimal Degree and (k, m)-Pancyclic Ordered Graphs." Graphs and Combinatorics 21, no. 2 (June 2005): 197–211. http://dx.doi.org/10.1007/s00373-005-0604-5.

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7

Monikandan, S., and S. Sundar Raj. "Adversary degree associated reconstruction number of graphs." Discrete Mathematics, Algorithms and Applications 07, no. 01 (February 2, 2015): 1450069. http://dx.doi.org/10.1142/s1793830914500694.

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A vertex-deleted subgraph of a graph G is called a card of G. A card of G with which the degree of the deleted vertex is also given is called a degree associated card or dacard of G. The adversary degree associated reconstruction number of a graph G, adrn (G), is the minimum number k such that every collection of k dacards of G uniquely determines G. We prove that adrn (G) = 1 + min {t+1, m-t} or 1 + min {t, m - t + 2} for a graph G obtained by subdividing t edges of K1, m. We also prove that if G is a nonempty disconnected graph whose components are cycles or complete graphs, then adrn (G) is 3 or 4, while, if G is a double star whose central vertices have degrees m + 1 and n + 1(m > n ≥ 2), then adrn (G) can be as large as n + 3.

8

SHIMOMURA, KATSUNORI. "On transformations which preserve poly-temperatures of degree m." Mathematical journal of Ibaraki University 33 (2001): 23–34. http://dx.doi.org/10.5036/mjiu.33.23.

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9

Afzal, Farkhanda, Sabir Hussain, Deeba Afzal, and Sidra Razaq. "Some new degree based topological indices via M-polynomial." Journal of Information and Optimization Sciences 41, no. 4 (May 18, 2020): 1061–76. http://dx.doi.org/10.1080/02522667.2020.1744307.

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10

Boden, Hans U. "Nontriviality of the $M$-degree of the $A$-polynomial." Proceedings of the American Mathematical Society 142, no. 6 (March 4, 2014): 2173–77. http://dx.doi.org/10.1090/s0002-9939-2014-11936-8.

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11

Miranda, Eva, and Arnau Planas. "Classification of b m -Nambu structures of top degree." Comptes Rendus Mathematique 356, no. 1 (January 2018): 92–96. http://dx.doi.org/10.1016/j.crma.2017.12.009.

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12

Ali, Akbar, Ivan Gutman, Hicham Saber, and Abdulaziz Alanazi. "On bond incident degree indices of (n,m) -graphs." match Communications in Mathematical and in Computer Chemistry 87, no. 01 (2021): 89–96. http://dx.doi.org/10.46793/match.87-1.089a.

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13

Al-Omeri, Wadei F., O. H. Khalil, and A. Ghareeb. "Degree of (L, M)-Fuzzy Semi-Precontinuous and (L, M)-Fuzzy Semi-Preirresolute Functions." Demonstratio Mathematica 51, no. 1 (September 1, 2018): 182–97. http://dx.doi.org/10.1515/dema-2018-0014.

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AbstractThe aim of this paper is to present the degree of semi-preopenness, semi-precontinuity, and semi-preirresoluteness for functions in (L, M)-fuzzy pretopology with the help of implication operation and (L, M)-fuzzy semi-preopen operator introduced by [Ghareeb A., L-fuzzy semi-preopen operator in L-fuzzy topological spaces, Neural Comput. & Appl., 2012, 21, 87-92]. Further, we generalize the properties of semi-preopenness, semi-precontinuity and semi-preirresoluteness to (L, M)-fuzzy pretopological setting relying on graded concepts. Also, we discuss their relationships with the corresponding degrees of semiprecompactness, semi-preconnectedness and semi-preseparation axioms.

14

Hu, Gang, Cuicui Bo, and Xinqiang Qin. "Continuity conditions for tensor product Q-Bézier surfaces of degree ($$m,\, n$$m,n)." Computational and Applied Mathematics 37, no. 4 (January 8, 2018): 4237–58. http://dx.doi.org/10.1007/s40314-017-0568-0.

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15

Antonov, S. Yu. "The least degree of identities in the subspace M 1 (m,k) (F) of the matrix superalgebra M (m,k)(F)." Russian Mathematics 56, no. 11 (November 2012): 1–16. http://dx.doi.org/10.3103/s1066369x12110011.

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16

Ephremidze, Lasha, and Edem Lagvilava. "On Compact Wavelet Matrices of Rank $$m$$ m and of Order and Degree $$N$$ N." Journal of Fourier Analysis and Applications 20, no. 2 (February 19, 2014): 401–20. http://dx.doi.org/10.1007/s00041-013-9317-y.

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17

Herrmann, E. "1-reducibility inside an m-degree with a maximal set." Journal of Symbolic Logic 57, no. 3 (September 1992): 1046–56. http://dx.doi.org/10.2307/2275448.

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AbstractThe structure of the 1-degrees included in an m-degree with a maximal set together with the 1-reducibility relation is characterized. For this a special sublattice of the lattice of recursively enumerable sets under the set-inclusion is used.

18

WEINGARTNER, ANDREAS. "On the degrees of polynomial divisors over finite fields." Mathematical Proceedings of the Cambridge Philosophical Society 161, no. 3 (May 19, 2016): 469–87. http://dx.doi.org/10.1017/s030500411600044x.

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AbstractWe show that the proportion of polynomials of degree n over the finite field with q elements, which have a divisor of every degree below n, is given by cqn−1 + O(n−2). More generally, we give an asymptotic formula for the proportion of polynomials, whose set of degrees of divisors has no gaps of size greater than m. To that end, we first derive an improved estimate for the proportion of polynomials of degree n, all of whose non-constant divisors have degree greater than m. In the limit as q → ∞, these results coincide with corresponding estimates related to the cycle structure of permutations.

19

Raza, Zahid, and Mark Essa K. Sukaiti. "M-Polynomial and Degree Based Topological Indices of Some Nanostructures." Symmetry 12, no. 5 (May 19, 2020): 831. http://dx.doi.org/10.3390/sym12050831.

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The association of M-polynomial to chemical compounds and chemical networks is a relatively new idea, and it gives good results about the topological indices. These results are then used to correlate the chemical compounds and chemical networks with their chemical properties and bioactivities. In this paper, an effort is made to compute the general form of the M-polynomials for two classes of dendrimer nanostars and four types of nanotubes. These nanotubes have very nice symmetries in their structural representations, which have been used to determine the corresponding M-polynomials. Furthermore, by using the general form of M-polynomial of these nanostructures, some degree-based topological indices have been computed. In the end, the graphical representation of the M-polynomials is shown, and a detailed comparison between the obtained topological indices for aforementioned chemical structures is discussed.

20

Thayamathy, P., P. Elango, and M. Koneswaran. "M-Polynomial and Degree Based Topological Indices for Silicon Oxide." International Research Journal of Pure and Applied Chemistry 16, no. 4 (July 7, 2018): 1–9. http://dx.doi.org/10.9734/irjpac/2018/42645.

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21

Munir, Mobeen, Waqas Nazeer, Shazia Rafique, and Shin Kang. "M-Polynomial and Degree-Based Topological Indices of Polyhex Nanotubes." Symmetry 8, no. 12 (December 6, 2016): 149. http://dx.doi.org/10.3390/sym8120149.

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22

Alsulami, Samirah, Sabir Hussain, Farkhanda Afzal, Mohammad Reza Farahani, and Deeba Afzal. "Topological Properties of Degree-Based Invariants via M-Polynomial Approach." Journal of Mathematics 2022 (March 16, 2022): 1–8. http://dx.doi.org/10.1155/2022/7120094.

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Chemical graph theory provides a link between molecular properties and a molecular graph. The M-polynomial is emerging as an efficient tool to recover the degree-based topological indices in chemical graph theory. In this work, we give the closed formulas of redefined first and second Zagreb indices, modified first Zagreb index, nano-Zagreb index, second hyper-Zagreb index, Randić index, reciprocal Randić index, first Gourava index, and product connectivity Gourava index via M-polynomial. We also present the M-polynomial of silicate network and then closed formulas of topological indices are applied on the silicate network.

23

Chaudhry, Faryal, Mohamad Nazri Husin, Farkhanda Afzal, Deeba Afzal, Muhammad Ehsan, Murat Cancan, and Mohammad Reza Farahani. "M-polynomials and degree-based topological indices of tadpole graph." Journal of Discrete Mathematical Sciences and Cryptography 24, no. 7 (October 3, 2021): 2059–72. http://dx.doi.org/10.1080/09720529.2021.1984561.

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24

Antonov, S. Yu. "Some estimations for the least degree of identities of subspaces M 1 (m,k) (F) of the matrix superalgebra M (m,k)(F)." Russian Mathematics 56, no. 5 (April 17, 2012): 9–22. http://dx.doi.org/10.3103/s1066369x12050027.

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25

FERRARA, MICHAEL, MICHAEL JACOBSON, and FLORIAN PFENDER. "Degree Conditions for H-Linked Digraphs." Combinatorics, Probability and Computing 22, no. 5 (August 8, 2013): 684–99. http://dx.doi.org/10.1017/s0963548313000278.

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Given a (multi)digraph H, a digraph D is H-linked if every injective function ι:V(H) → V(D) can be extended to an H-subdivision. In this paper, we give sharp degree conditions that ensure a sufficiently large digraph D is H-linked for arbitrary H. The notion of an H-linked digraph extends the classes of m-linked, m-ordered and strongly m-connected digraphs.First, we give sharp minimum semi-degree conditions for H-linkedness, extending results of Kühn and Osthus on m-linked and m-ordered digraphs. It is known that the minimum degree threshold for an undirected graph to be H-linked depends on a partition of the (undirected) graph H into three parts. Here, we show that the corresponding semi-degree threshold for H-linked digraphs depends on a partition of H into as many as nine parts.We also determine sharp Ore–Woodall-type degree-sum conditions ensuring that a digraph D is H-linked for general H. As a corollary, we obtain (previously undetermined) sharp degree-sum conditions for m-linked and m-ordered digraphs.

26

NIKSERESHT, A., and A. AZIZI. "ON RADICAL FORMULA IN MODULES." Glasgow Mathematical Journal 53, no. 3 (August 1, 2011): 657–68. http://dx.doi.org/10.1017/s0017089511000243.

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AbstractWe will state some conditions under which if a quotient of a module M satisfies the radical formula of degree k (s.t.r.f of degree k), so does M. Especially, we will introduce some particular modules M′ such that M′ ⊕ M″ s.t.r.f of degree k, when M″ s.t.r.f of degree k. Furthermore, we will show that, under certain conditions, if the completion of a module M s.t.r.f of degree k, then there is a non-negative integer k′ such that M s.t.r.f. of degree k′. Moreover, we state a corrected version of Leung and Man's theorem (K. H. Leung and S. H. Man, On commutative Noetherian rings which satisfy the radical formula, Glasgow Math. J. 39 (1997), 285–293) on Noetherian rings that satisfies the radical formula.

27

Sati, Hisham. "Ninebrane structures." International Journal of Geometric Methods in Modern Physics 12, no. 04 (April 2015): 1550041. http://dx.doi.org/10.1142/s0219887815500413.

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String structures in degree 4 are associated with cancelation of anomalies of string theory in 10 dimensions. Fivebrane structures in degree 8 have recently been shown to be associated with cancelation of anomalies associated to fivebranes in string theory and M-theory. We introduce and describe Ninebrane structures in degree 12 and demonstrate how they capture some anomaly cancelation phenomena in M-theory. Along the way we also define certain variants, considered as intermediate cases in degrees 9 and 10, which we call 2-Orientation and 2-Spin structures, respectively. As in the lower degree cases, we also discuss the natural twists of these structures and characterize the corresponding topological groups associated to each of the structures, which likewise admit refinements to differential cohomology.

28

Yang, Hong, and Muhammad Naeem. "Topological Descriptors of M-Carbon M r , s , t." Journal of Chemistry 2021 (October 18, 2021): 1–14. http://dx.doi.org/10.1155/2021/8792585.

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We have studied topological indices of the one the hardest crystal structures in a given chemical system, namely, M-carbon. These structures are based and obtained by the famous algorithm USPEX. The computations and applications of topological indices in the study of chemical structures is growing exponentially. Our aim in this article is to compare and compute some well-known topological indices based on degree and sum of degrees, namely, general Randić indices, Zagreb indices, atom bond connectivity index, geometric arithmetic index, new Zagreb indices, fourth atom bond connectivity index, fifth geometric arithmetic index, and Sanskruti index of the M-carbon M r , s , t . Moreover, we have also computed closed formulas for these indices.

29

Liang, Cheng-Yu, and Fu-Gui Shi. "Degree of continuity for mappings of (L, M)-fuzzy topological spaces." Journal of Intelligent & Fuzzy Systems 27, no. 5 (2014): 2665–77. http://dx.doi.org/10.3233/ifs-141238.

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30

Adelberg, Arnold, and Michael Filaseta. "On mth order Bernoulli polynomials of degree m that are Eisenstein." Colloquium Mathematicum 93, no. 1 (2002): 21–26. http://dx.doi.org/10.4064/cm93-1-3.

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31

Rapple, Brendan A. "The M. L. S. Degree: Time for a Two-Year Program?" Journal of Education for Library and Information Science 37, no. 1 (1996): 72. http://dx.doi.org/10.2307/40324286.

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32

ZHOU, SIZHONG, QIUXIANG BIAN, and LAN XU. "BINDING NUMBER AND MINIMUM DEGREE FOR FRACTIONAL (k,m)-DELETED GRAPHS." Bulletin of the Australian Mathematical Society 85, no. 1 (October 14, 2011): 60–67. http://dx.doi.org/10.1017/s0004972711002784.

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AbstractLet G be a graph of order n, and let k≥1 be an integer. Let h:E(G)→[0,1] be a function. If ∑ e∋xh(e)=k holds for any x∈V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh ={e∈E(G):h(e)>0}. A graph G is called a fractional (k,m) -deleted graph if for every e∈E(H) , there exists a fractional k-factor G[Fh ] of G with indicator function h such that h(e)=0 , where H is any subgraph of G with m edges. The minimum degree of a vertex in G is denoted by δ(G) . For X⊆V (G), NG(X)=⋃ x∈XNG(x) . The binding number of G is defined by In this paper, it is proved that if then G is a fractional (k,m) -deleted graph. Furthermore, it is shown that this result is best possible in some sense.

33

Kryszewski, W., and M. Maciejewski. "Degree for weakly upper semicontinuous perturbations of quasi- m -accretive operators." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2191 (January 4, 2021): 20190377. http://dx.doi.org/10.1098/rsta.2019.0377.

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In the paper, we provide the construction of a coincidence degree being a homotopy invariant detecting the existence of solutions of equations or inclusions of the form Ax ∈ F ( x ), x ∈ U , where A : D ( A ) ⊸ E is an m -accretive operator in a Banach space E , F : K ⊸ E is a weakly upper semicontinuous set-valued map constrained to an open subset U of a closed set K ⊂ E . Two different approaches are presented. The theory is applied to show the existence of non-trivial positive solutions of some nonlinear second-order partial differential equations with discontinuities. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

34

Benko, David, and Tamás Erdélyi. "Markov inequality for polynomials of degree n with m distinct zeros." Journal of Approximation Theory 122, no. 2 (June 2003): 241–48. http://dx.doi.org/10.1016/s0021-9045(03)00074-1.

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35

Xiu, Zhen-Yu, and Bin Pang. "A degree approach to special mappings between M-fuzzifying convex spaces." Journal of Intelligent & Fuzzy Systems 35, no. 1 (July 27, 2018): 705–16. http://dx.doi.org/10.3233/jifs-171046.

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36

Liang, Chengyu, and Fanghui Li. "A degree approach to separation axioms in M-fuzzifying convex spaces." Journal of Intelligent & Fuzzy Systems 36, no. 3 (March 26, 2019): 2885–93. http://dx.doi.org/10.3233/jifs-171361.

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37

Orevkov, S. Yu. "Classification of flexible M -curves of degree 8 up to isotopy." Geometric And Functional Analysis 12, no. 4 (October 1, 2002): 723–55. http://dx.doi.org/10.1007/s00039-002-8264-6.

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38

Vollala, Satyanarayana, and Indrajeet Saravanan. "Vertex degree-based topological indices of penta-chains using M-polynomial." International Journal of Advances in Engineering Sciences and Applied Mathematics 11, no. 1 (February 27, 2019): 53–67. http://dx.doi.org/10.1007/s12572-019-00245-6.

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39

Elia, Michele. "Are fifth-degree equations over GF(5 m ) solvable by radicals?" Applicable Algebra in Engineering, Communication and Computing 7, no. 1 (January 1996): 27–40. http://dx.doi.org/10.1007/bf01613614.

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40

Li, Fang, and Chunmei Ding. "Adsorption of Reactive Black M-2R on Different Deacetylation Degree Chitosan." Journal of Engineered Fibers and Fabrics 6, no. 3 (September 2011): 155892501100600. http://dx.doi.org/10.1177/155892501100600303.

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Different degree of deacetylation (DD) chitosan was prepared and used for the removal of a Reactive black M-2R (RBM) from aqueous solution. The effects of temperature (298 K~323 K), chitosan dosage, degree of deacetylation on RBM removal were investigated. The adsorption equilibrium was reached within one hour. In order to determine the adsorption capacity, the sorption data were analyzed by using linear form of Langmuir, Freundlich and Tempkin isotherm equation. Langmuir equation shows higher conformity than the other two equations. From the kinetic experiment data, it was found that the sorption process follows the pseudo-second-order kinetic model. Activation energy value for sorption process was found to be 58.28 kJ mol-1. Chitosan with 66% deacetylation degree (DD) exhibited good adsorption performance for RBM. In order to determine the interactions between RBM and chitosan, FTIR analysis was also conducted.

41

Baishya, Tapan Kumar, Bijit Bora, Pawan Chetri, and Upashana Gogoi. "On Degree Based Topological Indices of TiO2 Crystal via M-Polynomial." Trends in Sciences 19, no. 2 (January 15, 2022): 2022. http://dx.doi.org/10.48048/tis.2022.2022.

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Topological indices (TI) (descriptors) of a molecular graph are very much useful to study various physiochemical properties. It is also used to develop the quantitative structure-activity relationship (QSAR), quantitative structure-property relationship (QSPR) of the corresponding chemical compound. Various techniques have been developed to calculate the TI of a graph. Recently a technique of calculating degree-based TI from M-polynomial has been introduced. We have evaluated various topological descriptors for 3-dimensional TiO2 crystals using M-polynomial. These descriptors are constructed such that it contains 3 variables (m, n and t) each corresponding to a particular direction. These 3 variables facilitate us to deeply understand the growth of TiO2 in 1 dimension (1D), 2 dimensions (2D), and 3 dimensions (3D) respectively. HIGHLIGHTS Calculated degree based Topological indices of a 3D crystal from M-polynomial A relation among various Topological indices is established geometrically Variations of Topological Indices along three dimensions (directions) are shown geometrically Harmonic index approximates the degree variation of oxygen atom

42

Liu, Xin, Guiyun Chen, and Yanxiong Yan. "A new characterization of the automorphism groups of Mathieu groups." Open Mathematics 19, no. 1 (January 1, 2021): 1245–50. http://dx.doi.org/10.1515/math-2021-0112.

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Abstract Let cd ( G ) {\rm{cd}}\left(G) be the set of irreducible complex character degrees of a finite group G G . ρ ( G ) \rho \left(G) denotes the set of primes dividing degrees in cd ( G ) {\rm{cd}}\left(G) . For any prime p, let p e p ( G ) = max { χ ( 1 ) p ∣ χ ∈ Irr ( G ) } {p}^{{e}_{p}\left(G)}=\max \left\{\chi {\left(1)}_{p}\hspace{0.08em}| \hspace{0.08em}\chi \in {\rm{Irr}}\left(G)\right\} and V ( G ) = { p e p ( G ) ∣ p ∈ ρ ( G ) } V\left(G)=\left\{{p}^{{e}_{p}\left(G)}\hspace{0.08em}| \hspace{0.1em}p\in \rho \left(G)\right\} . The degree prime-power graph Γ ( G ) \Gamma \left(G) of G G is a graph whose vertices set is V ( G ) V\left(G) , and two vertices x , y ∈ V ( G ) x,y\in V\left(G) are joined by an edge if and only if there exists m ∈ cd ( G ) m\in {\rm{cd}}\left(G) such that x y ∣ m xy| m . It is an interesting and difficult problem to determine the structure of a finite group by using its degree prime-power graphs. Qin proved that all Mathieu groups can be uniquely determined by their orders and degree prime-power graphs. In this article, we continue this topic and successfully characterize all the automorphism groups of Mathieu groups by using their orders and degree prime-power graphs.

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Delen, Sadik, Musa Demirci, Ahmet Sinan Cevik, and Ismail Naci Cangul. "On Omega Index and Average Degree of Graphs." Journal of Mathematics 2021 (November 12, 2021): 1–5. http://dx.doi.org/10.1155/2021/5565146.

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Average degree of a graph is defined to be a graph invariant equal to the arithmetic mean of all vertex degrees and has many applications, especially in determining the irregularity degrees of networks and social sciences. In this study, some properties of average degree have been studied. Effect of vertex deletion on this degree has been determined and a new proof of the handshaking lemma has been given. Using a recently defined graph index called o m e g a index, average degree of trees, unicyclic, bicyclic, and tricyclic graphs have been given, and these have been generalized to k -cyclic graphs. Also, the effect of edge deletion has been calculated. The average degree of some derived graphs and some graph operations have been determined.

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Jákó, Szabolcs, Alexandru Lupan, Attila-Zsolt Kun, and R. Bruce King. "Isocloso versus closo deltahedra in slightly hypoelectronic supraicosahedral 14-vertex dimetallaboranes with 28 skeletal electrons: relationship to icosahedral dimetallaboranes." New Journal of Chemistry 44, no. 39 (2020): 16977–84. http://dx.doi.org/10.1039/d0nj03572f.

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The lowest energy Cp₂M₂B₁₂H₁₂ (M = Rh, Ir) and Cp₂M′₂C₂B₁₀H₁₂ (M′ = Ru, Os) structures have central M₂B₁₂ and M′₂C₂B₁₀ deltahedra with three degree 6 vertices, one degree 4 vertex, ten degree 5 vertices, and the metal atoms located at non-adjacent non-antipodal degree 6 vertices.

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BAZHENOV, NIKOLAY A., ISKANDER SH KALIMULLIN, and MARS M. YAMALEEV. "DEGREES OF CATEGORICITY AND SPECTRAL DIMENSION." Journal of Symbolic Logic 83, no. 1 (March 2018): 103–16. http://dx.doi.org/10.1017/jsl.2017.70.

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AbstractA Turing degreedis the degree of categoricity of a computable structure${\cal S}$ifdis the least degree capable of computing isomorphisms among arbitrary computable copies of${\cal S}$. A degreedis the strong degree of categoricity of${\cal S}$ifdis the degree of categoricity of${\cal S}$, and there are computable copies${\cal A}$and${\cal B}$of${\cal S}$such that every isomorphism from${\cal A}$onto${\cal B}$computesd. In this paper, we build a c.e. degreedand a computable rigid structure${\cal M}$such thatdis the degree of categoricity of${\cal M}$, butdis not the strong degree of categoricity of${\cal M}$. This solves the open problem of Fokina, Kalimullin, and Miller [13].For a computable structure${\cal S}$, we introduce the notion of the spectral dimension of${\cal S}$, which gives a quantitative characteristic of the degree of categoricity of${\cal S}$. We prove that for a nonzero natural numberN, there is a computable rigid structure${\cal M}$such that$0\prime$is the degree of categoricity of${\cal M}$, and the spectral dimension of${\cal M}$is equal toN.

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Hirschfeldt, Denis R. "Degree spectra of intrinsically c.e. relations." Journal of Symbolic Logic 66, no. 2 (June 2001): 441–69. http://dx.doi.org/10.2307/2695024.

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AbstractWe show that for every c.e. degree a > 0 there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is {0, a}. This result can be extended in two directions. First we show that for every uniformly c.e. collection of sets S there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is the set of degrees of elements of S. Then we show that if α ∈ ω ∪ {ω} then for any α-c.e. degree a > 0 there exists an intrinsically α-c.e. relation on the domain of a computable structure whose degree spectrum {0, a}. All of these results also hold for m-degree spectra of relations.

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Alshammari, Ibtesam, Azza M. Alghamdi, and A. Ghareeb. "A New Approach to Concavity Fuzzification." Journal of Mathematics 2021 (January 18, 2021): 1–11. http://dx.doi.org/10.1155/2021/6699295.

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In this paper, we introduce a more general approach to the fuzzification of fuzzy concavity. More specifically, the degree of L , M -fuzzy concavity is introduced and characterized as a generalization of L -concave structure and L , M -fuzzy concave structure. Based on that, the degree of L , M -fuzzy concavity preserving and L , M -fuzzy concave-to-concave of a function are defined. Some properties and relationships between the degree of L , M -fuzzy concavity preserving and L , M -fuzzy concave-to-concave functions are discussed.

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Xiu, Zhen-Yu, and Qing-Guo Li. "Relations among (L, M)-fuzzy convex structures, (L, M)-fuzzy closure systems and (L, M)-fuzzy Alexandrov topologies in a degree sense." Journal of Intelligent & Fuzzy Systems 36, no. 1 (February 16, 2019): 385–96. http://dx.doi.org/10.3233/jifs-181504.

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Kirmani, Syed Ajaz K., Parvez Ali, Faizul Azam, and Parvez Ahmad Alvi. "On Ve-Degree and Ev-Degree Topological Properties of Hyaluronic Acid‐Anticancer Drug Conjugates with QSPR." Journal of Chemistry 2021 (July 2, 2021): 1–23. http://dx.doi.org/10.1155/2021/3860856.

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The design of the quantitative structure-property/activity relationships for drug-related compounds using theoretical methods relies on appropriate molecular structure representations. The molecular structure of a compound comprises all the information required to determine its chemical, biological, and physical properties. These properties can be assessed by employing a graph theoretical descriptor tool widely known as topological indices. Generalization of descriptors may reduce not only the number of molecular graph-based descriptors but also improve existing results and provide a better correlation to several molecular properties. Recently introduced ve-degree and ev-degree topological indices have been successfully employed for development of models for the prediction of various biological activities/properties. In this article, we propose the general ve-inverse sum indeg index ISI α , β ve G and general ve-Zagreb index M α ve G of graph G and compute ISI α , β ve G , M α ve G , and M α ev G (general ev-degree index) of hyaluronic acid-curcumin/paclitaxel conjugates, renowned for its potential anti-inflammatory, antioxidant, and anticancer properties, by using molecular structure analysis and edge partitioning technique. Several ve-degree- and ev-degree-based topological indices are obtained as a special case of ISI α , β ve G , M α ve G , and M α ev G . Furthermore, QSPR analysis of ISI α , β ve G , M α ve G , and M α ev G for particular values of α and β is performed, which reveals their predicting power. These results allow researchers to better understand the physicochemical properties and pharmacological characteristics of these conjugates.

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Chengling, Fang, and Wu Guohua. "Nonhemimaximal degrees and the high/low hierarchy." Journal of Symbolic Logic 77, no. 2 (June 2012): 433–46. http://dx.doi.org/10.2178/jsl/1333566631.

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AbstractAfter showing the downwards density of nonhemimaximal degrees, Downey and Stob continued to prove that the existence of a low2, but not low, nonhemimaximal degree, and their proof uses the fact that incomplete m-topped degrees are low2 but not low. As commented in their paper, the construction of such a nonhemimaximal degree is actually a primitive 0‴ argument. In this paper, we give another construction of such degrees, which is a standard 0″-argument, much simpler than Downey and Stob's construction mentioned above.

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