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Journal articles on the topic '2)*-g-closed set'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Dr., C. Rajan. "ON (1, 2)*- - CLOSED SETS IN BITOPOLOGICAL SPACE." International Journal of Current Research and Modern Education, Special Issue (August 24, 2017): 148–55. https://doi.org/10.5281/zenodo.848255.

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In this paper, we offer a new class of sets called (1, 2)*--closed sets in bitopological spaces and we study some of its basic properties. It turns out that this class lies between the class of t<sub>1,2</sub>-closed sets and the class of (1, 2)*-g-closed sets.

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E., Kungumaraj, and Nirmaladevi K. "Fuzzy Strongly g s Closed sets in Fuzzy Topological spaces." International Journal of Trend in Scientific Research and Development 2, no. 2 (2018): 857–59. https://doi.org/10.31142/ijtsrd9482.

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In this paper, we have introduced and study the concept of strongly g s closed set in Fuzzy topological spaces and discuss some of its properties. E. Kungumaraj | K. Nirmaladevi "Fuzzy Strongly g*s Closed sets in Fuzzy Topological spaces" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018, URL: https://www.ijtsrd.com/papers/ijtsrd9482.pdf

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Ankit, Gupta. "On \(\pi gs-\lambda\) Closed Sets in Generalized Topological Spaces." Journal of Advanced Studies in Topology 13, no. 1-2 (2023): 7–13. https://doi.org/10.5281/zenodo.7905124.

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In this paper, a new class of generalized closed sets called \(\pi gs-\lambda\) closed sets are introduced and some of its properties are studied. Along with this, the notion of \(\pi gs-\lambda\)-continuity and \(\pi gs-\lambda\)-\(T(1/2)\) spaces are introduced.

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4

Adolfo, Niña Jeane, Imelda Aniversario, and Ferdinand Jamil. "Closed Geodetic Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 1618–36. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5241.

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Let G be a simple, undirected and connected graph. A subset S ⊆ V (G) is a geodetic cover of G if IG[S] = V (G), where IG[S] is the set of all vertices of G lying on any geodesic between two vertices in S. A geodetic cover S of G is a closed geodetic cover if the vertices in S are sequentially selected as follows: Select a vertex v1 and let S1 = {v1}. If G is nontrivial, select a vertex v2 ̸= v1 and let S2 = {v1, v2}. Where possible, for i ≥ 3, successively select vertex vi ∈/ IG[Si−1] and let Si = {v1, v2, ..., vi}. Then there exists a positive integer k such that Sk = S. A geodetic cover S o

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P., Padma. "( τi , τj ) * - Q* g closed sets in Bitopological spaces". Journal of Progressive Research in Mathematics 2, № 1 (2015): 69–79. https://doi.org/10.5281/zenodo.3980807.

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The aim of this paper is to introduced the new type of closed sets called ( τ<sub>i</sub> , τ<sub>j</sub> )* - Q* g closed set . We introduce and study a new class of spaces namely (τ<sub>i</sub> , τ<sub>j</sub> )* - Q*g T1/2 space and ( τ<sub>i</sub> , τ<sub>j</sub> )* - Q* g T3/4 space . Also we find some basic properties and applications of ( τ<sub>i</sub> , τ<sub>j</sub> )* - Q* g closed sets .

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6

Selvi, G., and I. Rajasekaran. "ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES." Advances in Mathematics: Scientific Journal 9, no. 11 (2020): 9353–60. http://dx.doi.org/10.37418/amsj.9.11.41.

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This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.

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Hamja, Jamil, Imelda S. Aniversario, and Helen M. Rara. "On Weakly Connected Closed Geodetic Domination in Graphs Under Some Binary Operations." European Journal of Pure and Applied Mathematics 15, no. 2 (2022): 736–52. http://dx.doi.org/10.29020/nybg.ejpam.v15i2.4356.

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Let G be a simple connected graph. For S ⊆ V (G), the weakly connected closed geodetic dominating set S of G is a geodetic closure IG[S] which is between S and is the set of all vertices on geodesics (shortest path) between two vertices of S. We select vertices of Gsequentially as follows: Select a vertex v1 and let S1 = {v1}. Select a vertex v2 ̸= v1 and let S2 = {v1, v2}. Then successively select vertex vi ∈/ IG[Si−1] and let Si = {v1, v2, ..., vi} for i = 1, 2, ..., k until we select a vertex vk in the given manner that yields IG[Sk] = V (G). Also, the subgraph weakly induced ⟨S⟩w by S is c

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8

DeCoste, Rachelle C., Lisa DeMeyer, and Meera G. Mainkar. "Graphs and metric 2-step nilpotent Lie algebras." Advances in Geometry 18, no. 3 (2018): 265–84. http://dx.doi.org/10.1515/advgeom-2017-0052.

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AbstractDani and Mainkar introduced a method for constructing a 2-step nilpotent Lie algebra 𝔫G from a simple directed graph G in 2005. There is a natural inner product on 𝔫G arising from the construction. We study geometric properties of the associated simply connected 2-step nilpotent Lie group N with Lie algebra 𝔫g. We classify singularity properties of the Lie algebra 𝔫g in terms of the graph G. A comprehensive description is given of graphs G which give rise to Heisenberg-like Lie algebras. Conditions are given on the graph G and on a lattice Γ ⊆ N for which the quotient Γ \ N, a compact

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9

Weiss, Richard. "A uniqueness lemma for groups generated by 3-transpositions." Mathematical Proceedings of the Cambridge Philosophical Society 97, no. 3 (1985): 421–31. http://dx.doi.org/10.1017/s030500410006299x.

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Let G be a group. A subset D of G will be called a set of 3-transpositions if |x| =2 for all xεD and |xy| = 3 whenever x, yεD do not commute. We will call the set D closed if xDx = D for each xεD. For each xεD, let

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10

SANKI, BIDYUT. "SYSTOLIC FILLINGS OF SURFACES." Bulletin of the Australian Mathematical Society 98, no. 3 (2018): 502–11. http://dx.doi.org/10.1017/s0004972718000862.

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A filling of a closed hyperbolic surface is a set of simple closed geodesics whose complement is a disjoint union of hyperbolic polygons. The systolic length is the length of a shortest essential closed geodesic on the surface. A geodesic is called systolic, if the systolic length is realised by its length. For every $g\geq 2$, we construct closed hyperbolic surfaces of genus $g$ whose systolic geodesics fill the surfaces with complements consisting of only two components. Finally, we remark that one can deform the surfaces obtained to increase the systole.

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11

Goodaire, Edgar G., and César Polcino Milies. "Involutions and Anticommutativity in Group Rings." Canadian Mathematical Bulletin 56, no. 2 (2013): 344–53. http://dx.doi.org/10.4153/cmb-2011-178-2.

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AbstractLet g denote an involution on a group G. For any (commutative, associative) ring R (with 1), * extends linearly to an involution of the group ring RG. An element α ∊ RG is symmetric if α* = α and skew-symmetric if α* = -α. The skew-symmetric elements are closed under the Lie bracket, [αβ] = αβ - βα. In this paper, we investigate when this set is also closed under the ring product in RG. The symmetric elements are closed under the Jordan product, α˚α = αβ +βα. Here, we determine when this product is trivial. These two problems are analogues of problems about the skew-symmetric and symme

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12

TAL, FÁBIO ARMANDO. "On non-contractible periodic orbits for surface homeomorphisms." Ergodic Theory and Dynamical Systems 36, no. 5 (2015): 1644–55. http://dx.doi.org/10.1017/etds.2014.131.

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In this work we study homeomorphisms of closed orientable surfaces homotopic to the identity, focusing on the existence of non-contractible periodic orbits. We show that, if $g$ is such a homeomorphism, and if ${\hat{g}}$ is its lift to the universal covering of $S$ that commutes with the deck transformations, then one of the following three conditions must be satisfied: (1) the set of fixed points for ${\hat{g}}$ projects to a closed subset $F$ which contains an essential continuum; (2) $g$ has non-contractible periodic points of every sufficiently large period; or (3) there exists a uniform

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13

Bashun, S. Y. "Permutability of the Sylow 2-subgroup with some biprimary subgroups." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 54, no. 4 (2019): 460–67. http://dx.doi.org/10.29235/1561-2430-2018-54-4-460-467.

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In this paper, the compositional structure of a finite group G is investigated, which has the Sylow 2-subgroup that is permutable with some non p-nilpotent biprimary subgroups, which contain the Sylow р-subgroup of G for all odd simple divisors of the р order of the group G, and such biprimary subgroups are taken one by one for each odd р, and mark the set SB(G). In this work, the existence of the subset SB(G)* in SB(G) is proved, which consists of р-closed subgroups. The main result of this paper is as follows: if the Sylow 2-subgroup of the group G is permutable with all subgroups SB(G)*, th

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14

Blass, Andreas, and Claude Laflamme. "Consistency results about filters and the number of inequivalent growth types." Journal of Symbolic Logic 54, no. 1 (1989): 50–56. http://dx.doi.org/10.2307/2275014.

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We use models of set theory described in [2] and [3] to prove the consistency of several combinatorial principles, for example:If ℱ is any filter on N containing all the cofinite sets, then there is a finite-to-one function f: N → N such that f(ℱ) is either the filter of cofinite sets or an ultrafilter.As a consequence of our combinatorial principles, we also obtain the consistency of:The partial ordering P of slenderness classes of abelian groups, denned and studied in [4], is a four-element chain.In the remainder of this Introduction, we shall define our terminology and state the combinatori

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15

RAJEEVSARATHY, KASHYAP. "ROOTS OF DEHN TWISTS ABOUT SEPARATING CURVES." Journal of the Australian Mathematical Society 95, no. 2 (2013): 266–88. http://dx.doi.org/10.1017/s1446788713000190.

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AbstractLet $C$ be a curve in a closed orientable surface $F$ of genus $g\geq 2$ that separates $F$ into subsurfaces $\widetilde {{F}_{i} } $ of genera ${g}_{i} $, for $i= 1, 2$. We study the set of roots in $\mathrm{Mod} (F)$ of the Dehn twist ${t}_{C} $ about $C$. All roots arise from pairs of ${C}_{{n}_{i} } $-actions on the $\widetilde {{F}_{i} } $, where $n= \mathrm{lcm} ({n}_{1} , {n}_{2} )$ is the degree of the root, that satisfy a certain compatibility condition. The ${C}_{{n}_{i} } $-actions are of a kind that we call nestled actions, and we classify them using tuples that we call dat

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16

Cabrera Martínez, Abel, Suitberto Cabrera García, Andrés Carrión García, and Frank A. Hernández Mira. "Total Roman Domination Number of Rooted Product Graphs." Mathematics 8, no. 10 (2020): 1850. http://dx.doi.org/10.3390/math8101850.

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Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. If f satisfies that every vertex in the set {v∈V(G):f(v)=0} is adjacent to at least one vertex in the set {v∈V(G):f(v)=2}, and if the subgraph induced by the set {v∈V(G):f(v)≥1} has no isolated vertex, then we say that f is a total Roman dominating function on G. The minimum weight ω(f)=∑v∈V(G)f(v) among all total Roman dominating functions f on G is the total Roman domination number of G. In this article we study this parameter for the rooted product graphs. Specifically, we obtain closed formulas and tight bounds for the

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17

Ivanov, Alexander A. "Closed Majorana representations of {3, 4}⁺-transposition groups." Advances in Geometry 22, no. 4 (2022): 487–94. http://dx.doi.org/10.1515/advgeom-2022-0015.

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Abstract The paper contributes to Majorana theory. Among the eight non-trivial Norton–Sakuma algebras, four algebras are closed on the set of Majorana generators. These algebras are 2A, 2B, 3C and 4B. The classification of Majorana representations restricted to the closed shapes was anticipated for a long time. In the present article the classification is achieved for shapes restricted to 2A, 3C and 4B and for the set of generating involutions in the target group forming a single conjugacy class. Timmesfeld’s classification of {3, 4}+-transposition groups reduces to consideration of just three

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18

HILDEN, HUGH M., MARIA TERESA LOZANO, and JOSÉ MARIA MONTESINOS-AMILIBIA. "UNIVERSAL 2-BRIDGE KNOT AND LINK ORBIFOLDS." Journal of Knot Theory and Its Ramifications 02, no. 02 (1993): 141–48. http://dx.doi.org/10.1142/s021821659300009x.

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Let (p/q, n) be the orbifold with cyclic isotropy of order n and with singular set the 2-bridge knot or link p/q where p and q are relatively prime numbers, q is odd, q is less than p, and q is not congruent to ±1 mod p (i.e. p/q is any non toroidal 2-bridge knot or link). We show that the orbifold fundamental group π1(p/q, n) is universal for n any multiple of 12. This means that if Γ is any such group, it can be thought of as a discrete group of hyperbolic isometries of hyperbolic 3-space ℍ3, and then, given any closed, oriented 3-manifold M, there exists a subgroup of finite index G of Γ su

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Farahani, Mohammad Reza. "The General Connectivity and General Sum-Connectivity Indices of Nanostructures." International Letters of Chemistry, Physics and Astronomy 44 (January 2015): 73–80. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.44.73.

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Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)

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20

Farahani, Mohammad Reza. "The General Connectivity and General Sum-Connectivity Indices of Nanostructures." International Letters of Chemistry, Physics and Astronomy 44 (January 14, 2015): 73–80. http://dx.doi.org/10.56431/p-892ddt.

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Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)

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21

Kuziak, Dorota, and Ismael G. Yero. "Further new results on strong resolving partitions for graphs." Open Mathematics 18, no. 1 (2020): 237–48. http://dx.doi.org/10.1515/math-2020-0142.

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Abstract A set W of vertices of a connected graph G strongly resolves two different vertices x, y ∉ W if either d G (x, W) = d G (x, y) + d G (y, W) or d G (y, W) = d G (y, x) + d G (x, W), where d G (x, W) = min{d(x,w): w ∈ W} and d(x,w) represents the length of a shortest x − w path. An ordered vertex partition Π = {U 1, U 2,…,U k } of a graph G is a strong resolving partition for G, if every two different vertices of G belonging to the same set of the partition are strongly resolved by some other set of Π. The minimum cardinality of any strong resolving partition for G is the strong partiti

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22

Jabłońska, Eliza. "Characterization of continuous additive set-valued maps “modulo K” on finite dimensional linear spaces." Mathematica Slovaca 74, no. 5 (2024): 1165–72. http://dx.doi.org/10.1515/ms-2024-0084.

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Abstract Let Y be a real vector metric space and K ⊂ Y be a closed convex cone such that K ∩ (− K) = {0}. We prove that a convex compact-valued map F : ℝ → 2 Y ∖ {∅} is K-continuous and K-additive if and only if there are non-empty convex compact sets A, B ⊂ Y such that 0 ∈ A − B ⊂ K and F is equal “modulo K” to the continuous set-valued map G ( t ) = t A , t ≥ 0 , t B , t < 0. $$\begin{array}{} \displaystyle G(t)=\begin{cases} tA,&t\geq0,\\ tB,& t \lt 0. \end{cases} \end{array}$$ Next, we use this result to characterize convex compact-valued maps F : ℝ N → 2 Y ∖ {∅}.

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23

Hofmann, Karl H., Sidney A. Morris, Sheila Oates-Williams, and V. N. Obraztsov. "Locally compact groups with closed subgroups open and p-adic." Mathematical Proceedings of the Cambridge Philosophical Society 118, no. 2 (1995): 303–13. http://dx.doi.org/10.1017/s0305004100073655.

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An open subgroup U of a topological group G is always closed, since U is the complement of the open set . An arbitrary closed subgroup C of G is almost never open, unless G belongs to a small family of exceptional groups. In fact, if G is a locally compact abelian group in which every non-trivial subgroup is open, then G is the additive group δp of p-adic integers or the additive group Ωp of p-adic rationale (cf. Robertson and Schreiber[5[, proposition 7). The fact that δp has interesting properties as a topological group has many roots. One is that its character group is the Prüfer group ℤp∞,

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24

Yin, WanJun, ZhengFeng Ming, and Qun Liu. "Resistance Distance and Kirchhoff Index for a Class of Graphs." Mathematical Problems in Engineering 2018 (December 26, 2018): 1–8. http://dx.doi.org/10.1155/2018/1028614.

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Let G[F,Vk,Hv] be the graph with k pockets, where F is a simple graph of order n≥1, Vk={v1,v2,…,vk} is a subset of the vertex set of F, Hv is a simple graph of order m≥2, and v is a specified vertex of Hv. Also let G[F,Ek,Huv] be the graph with k edge pockets, where F is a simple graph of order n≥2, Ek={e1,e2,…ek} is a subset of the edge set of F, Huv is a simple graph of order m≥3, and uv is a specified edge of Huv such that Huv-u is isomorphic to Huv-v. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of G[F,Vk,Hv] and G[F,Ek,Huv] in terms of the resi

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25

Bresar, Bostjan, and Dasa Mesaric-Stesl. "The competition-independence game with prevention." Filomat 36, no. 18 (2022): 6197–213. http://dx.doi.org/10.2298/fil2218197b.

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The competition-independence game, as introduced by Phillips and Slater, is played on a graph by two players, Diminisher and Sweller, who are taking turns in choosing a vertex that is not in the closed neighborhood of any of the previously chosen vertices. The goal of Diminisher is to minimize the (maximal independent) set of chosen vertices at the end of the game, while Sweller wants just the opposite. Assuming that both players are playing optimally according to their goals, two graph invariants arise depending on who starts the game. In this paper, we introduce a variation of the game in wh

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OKAZAKI, TOKIO, KATSUSHI INOUE, AKIRA ITO, and YUE WANG. "CLOSURE PROPERTY OF SPACE-BOUNDED TWO-DIMENSIONAL ALTERNATING TURING MACHINES, PUSHDOWN AUTOMATA, AND COUNTER AUTOMATA." International Journal of Pattern Recognition and Artificial Intelligence 15, no. 07 (2001): 1143–65. http://dx.doi.org/10.1142/s0218001401001398.

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This paper investigates closure property of the classes of sets accepted by space-bounded two-dimensional alternating Turing machines (2-atm's) and space-bounded two-dimensional alternating pushdown automata (2-apda's), and space-bounded two-dimensional alternating counter automata (2-aca's). Let L(m, n): N2 → N (N denotes the set of all positive integers) be a function with two variables m (= the number of rows of input tapes) and n (= the number of columns of input tapes). We show that (i) for any function f(m) = o( log m) (resp. f(m) = o( log m/ log log m)) and any monotonic nondecreasing f

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Ouatiki, Saliha, and Mohamed Bouzefrane. "A lower bound on the global powerful alliance number in trees." RAIRO - Operations Research 55, no. 2 (2021): 495–503. http://dx.doi.org/10.1051/ro/2021028.

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For a graph G = (V, E), a set D ⊆ V is a dominating set if every vertex in V − D is either in D or has a neighbor in D. A dominating set D is a global offensive alliance (resp. a global defensive alliance) if for each vertex v in V − D (resp. v in D) at least half the vertices from the closed neighborhood of v are in D. A global powerful alliance is both global defensive and global offensive. The global powerful alliance number γpa(G) is the minimum cardinality of a global powerful alliance of G. We show that if T is a tree of order n with l leaves and s support vertices, then $ {\gamma }_{{pa

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Hassan, Javier, and Sergio Canoy, Jr. "Grundy Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 15, no. 4 (2022): 1623–36. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4511.

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Let G be an undirected graph with vertex and edge sets V (G) and E(G), respectively. Let S = (v1, v2, · · · , vk) be a sequence of distinct vertices of G and let Sˆ = {v1, v2, . . . , vk}. Then S is a legal closed hop neighborhood sequence of G if N2 G[vi]\∪i−1j=1N 2 G[vj ] ̸= ∅ for each i ∈ {2, · · · , k}. If, in addition, Sˆ is a hop dominating set of G, then S is called a Grundy hop dominating sequence.The maximum length of a Grundy hop dominating sequence in a graph G, denoted by γ hgr(G), is called the Grundy hop domination number of G. In this paper, we determine some (extreme) values fo

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CECOTTI, SERGIO. "CATEGORICAL TINKERTOYS FOR ${\mathcal N} = 2$ GAUGE THEORIES." International Journal of Modern Physics A 28, no. 05n06 (2013): 1330006. http://dx.doi.org/10.1142/s0217751x13300068.

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In view of classification of the quiver 4d [Formula: see text] supersymmetric gauge theories, we discuss the characterization of the quivers with superpotential [Formula: see text] associated to a [Formula: see text] QFT which, in some corner of its parameter space, looks like a gauge theory with gauge group G. The basic idea is that the Abelian category [Formula: see text] of (finite-dimensional) representations of the Jacobian algebra [Formula: see text] should enjoy what we call the Ringel property of type G; in particular, [Formula: see text] should contain a universal "generic" subcategor

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Schmerl, James H. "Automorphism groups of models of Peano arithmetic." Journal of Symbolic Logic 67, no. 4 (2002): 1249–64. http://dx.doi.org/10.2178/jsl/1190150283.

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Which groups are isomorphic to automorphism groups of models of Peano Arithmetic? It will be shown here that any group that has half a chance of being isomorphic to the automorphism group of some model of Peano Arithmetic actually is.For any structure , let Aut() be its automorphism group. There are groups which are not isomorphic to any model = (N, +, ·, 0, 1, ≤) of PA. For example, it is clear that Aut(N), being a subgroup of Aut((, <)), must be torsion-free. However, as will be proved in this paper, if (A, <) is a linearly ordered set and G is a subgroup of Aut((A, <)), then there

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BOUSQUET-MÉLOU, MIREILLE, and KERSTIN WELLER. "Asymptotic Properties of Some Minor-Closed Classes of Graphs." Combinatorics, Probability and Computing 23, no. 5 (2014): 749–95. http://dx.doi.org/10.1017/s0963548314000303.

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Let${\cal A}$be a minor-closed class of labelled graphs, and let${\cal G}_{n}$be a random graph sampled uniformly from the set ofn-vertex graphs of${\cal A}$. Whennis large, what is the probability that${\cal G}_{n}$is connected? How many components does it have? How large is its biggest component? Thanks to the work of McDiarmid and his collaborators, these questions are now solved when all excluded minors are 2-connected.Using exact enumeration, we study a collection of classes${\cal A}$excluding non-2-connected minors, and show that their asymptotic behaviour may be rather different from th

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32

Zhang, E., and L. Noakes. "Relative geodesics in bi-invariant Lie groups." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2201 (2017): 20160619. http://dx.doi.org/10.1098/rspa.2016.0619.

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Motivated by registration problems, this paper deals with a curve matching problem in homogeneous spaces. Let G be a connected finite-dimensional bi-invariant Lie group and K a closed subgroup. A smooth curve g in G is said to be admissible if it can transform two smooth curves f 1 and f 2 in G / K from one to the other. An ( f 1 , f 2 )- relative geodesic (Holm et al. 2013 Proc. R. Soc. A 469 , 20130297. ( doi:10.1098/rspa.2013.0297 )) is defined as a critical point of the total energy E ( g ) as g varies in the set of all ( f 1 , f 2 )-admissible curves. We obtain the Euler–Lagrange equation

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Shirdel, G. H., M. Ghanbari, and M. Ramezani. "Generalized 3-Rainbow Domination in Graphs and Honeycomb System (HC(n))." Utilitas Mathematica 119, no. 1 (2024): 3–7. http://dx.doi.org/10.61091/um119-01.

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In this paper, we introduce the concept of the generalized 3 -rainbow dominating function of a graph G . This function assigns an arbitrary subset of three colors to each vertex of the graph with the condition that every vertex (including its neighbors) must have access to all three colors within its closed neighborhood. The minimum sum of assigned colors over all vertices of G is defined as the g 3 -rainbow domination number, denoted by γ g 3 r . We present a linear-time algorithm to determine a minimum generalized 3-rainbow dominating set for several graph classes: trees, paths ( P n ) , cyc

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Butkote, R., K. Denecke, and Ch Ratanaprasert. "SEMIGROUP PROPERTIES OF N-ARY OPERATIONS ON FINITE SETS." Asian-European Journal of Mathematics 01, no. 01 (2008): 27–44. http://dx.doi.org/10.1142/s1793557108000047.

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A clone is a set of operations defined on a base set A which is closed under composition and contains all the projection operations. There are several ways to regard a clone as an algebraic structure (see e.g. [3]). If f, g1,…,gn : An → A are n-ary operations defined on A, then by Sn(f, g1 … , gn)(a1 … , an) := f(g1(a1,…,an),…,gn(a1,…,an)) for all a1,…, an ∈ A an (n + 1)-ary operation on the set On(A) of all n-ary operations can be defined. From this operation one can derive a binary operation + defined by f + g := Sn(f, g,…,g) and obtains a semigroup (On(A);+). The collection of all clones of

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35

Balčiūnas, Aidas, Toma Mikalauskaitė, and Darius Šiaučiūnas. "Approximation of analytic functions by generalized shifts of the Lerch zeta-function." Mathematical Modelling and Analysis 30, no. 1 (2025): 142–58. https://doi.org/10.3846/mma.2025.21939.

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In the paper, we approximate analytic functions by generalized shifts $L(\lambda, \alpha, s+ig(\tau))$, $s=\sigma+it$, of the Lerch zeta-function, where $g$ is a certain increasing to $+\infty$ real function having a monotonic derivative. We prove that, for arbitrary parameters $\lambda$ and $\alpha$, there exists a closed set $\FF_{\lambda, \alpha}$ of analytic functions defined in the strip $1/2< \sigma<1$ which functions are approximated by the above shifts. If the set of logarithms $\log(m+\alpha)$, $m\in \NN_0$, is linearly independent over the field of rational numbers, then the se

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Venkatesh, G., M. Govindaraju, P. Vennila, and C. Kamal. "Molecular structure, vibrational spectral assignments (FT-IR and FT-RAMAN), NMR, NBO, HOMO–LUMO and NLO properties of 2-nitroacetophenone based on DFT calculations." Journal of Theoretical and Computational Chemistry 15, no. 01 (2016): 1650007. http://dx.doi.org/10.1142/s0219633616500073.

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The FT-IR and FT-Raman analyses of 2-nitro acetophenone (2NAP) have been carried out by density functional theory (DFT) calculations based on B3LYP level with 6-31G*/6-311[Formula: see text]G** basis set. The gauge-independent atomic orbital (GIAO) method has been used to get 1H NMR and [Formula: see text]C NMR chemical shifts. From DFT calculations, various parameters such as atomic charges, HOMO–LUMO energies and Dipole moment have been obtained. The molecular electronic potential (MEP) has also been derived for 2NAP. In order to find the electronic excitation energies, oscillator strength a

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Liu, Qun. "Resistance distance and Kirchhoff index in generalized R-vertex and R-edge corona for graphs." Filomat 33, no. 6 (2019): 1593–604. http://dx.doi.org/10.2298/fil1906593l.

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For a graph G, the graph R(G) of a graph G is the graph obtained by adding a new vertex for each edge of G and joining each new vertex to both end vertices of the corresponding edge. Let I(G) be the set of newly added vertices, i.e I(G) = V(R(G))\ V(G). The generalized R-vertex corona of G and Hi for i = 1, 2, ?,n, denoted by R(G) ?? ^n i=1 Hi, is the graph obtained from R(G) and Hi by joining the i-th vertex of V(G) to every vertex in Hi. The generalized R-edge corona of G and Hi for i = 1, 2, ?,m, denoted by R(G)?^m i=1 Hi, is the graph obtained from R(G) and Hi by joining the i-th vertex of

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38

Basher, M. "Group vertex magic labeling of some special graphs." Proyecciones (Antofagasta) 43, no. 1 (2024): 119–31. http://dx.doi.org/10.22199/issn.0717-6279-5880.

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For any additive abelian group $A$. Let $\mu$ be an element of $A$, a graph $G=(V,E)$ is said to be $A$-vertex magic graph if there exist a labeling function $f:V(G)\rightarrow A\setminus\{0\}$ such that $\omega(v)=\sum_{u\in N(v)} f(u)=\mu$ for any vertex $v$ of $G$, where $N(v)$ is the set of the open neighborhood of $v$. In this paper, we prove that the graphs such as wheel, Corona $C_{n}\odot mk$, subdivision of ladder and $t$-fold wheel for $t\neq n$ nor $n-2$ are $A$-vertex magic graphs. Also we prove that the subdivide wheel, helm and closed helm are $Z_{k}$-vertex magic graphs. However

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ASTOR, ERIC P., DAMIR DZHAFAROV, ANTONIO MONTALBÁN, REED SOLOMON, and LINDA BROWN WESTRICK. "THE DETERMINED PROPERTY OF BAIRE IN REVERSE MATH." Journal of Symbolic Logic 85, no. 1 (2019): 166–98. http://dx.doi.org/10.1017/jsl.2019.64.

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AbstractWe define the notion of a completely determined Borel code in reverse mathematics, and consider the principle $CD - PB$, which states that every completely determined Borel set has the property of Baire. We show that this principle is strictly weaker than $AT{R_0}$. Any ω-model of $CD - PB$ must be closed under hyperarithmetic reduction, but $CD - PB$ is not a theory of hyperarithmetic analysis. We show that whenever $M \subseteq {2^\omega }$ is the second-order part of an ω-model of $CD - PB$, then for every $Z \in M$, there is a $G \in M$ such that G is ${\rm{\Delta }}_1^1$-generic r

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TATSUMI, TOMOMASA. "Cross-independence closure for statistical mechanics of fluid turbulence." Journal of Fluid Mechanics 670 (January 26, 2011): 365–403. http://dx.doi.org/10.1017/s002211201000532x.

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The infinite set of the Lundgren-Monin equations for the multi-point velocity distributions of fluid turbulence is closed by making use of the cross-independence closure hypothesis proposed by Tatsumi (Geometry and Statistics of Turbulence, 2001, p. 3), and the minimum deterministic set of equations is obtained as the equations for the one-point velocity distribution f, the two-point velocity distribution f(2) and the two-point local velocity distribution f(2)*. In practice, the two-point distributions f(2) and f(2)* are more conveniently expressed in terms of the velocity-sum and -difference

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Sopha, Hanna, and Jan M. Macak. "Bipolar Electrochemistry for the Synthesis of Anodic TiO₂ Nanotube Layers." ECS Meeting Abstracts MA2022-01, no. 47 (2022): 1978. http://dx.doi.org/10.1149/ma2022-01471978mtgabs.

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Self-organized TiO2 nanotube (TNT) layers have attracted considerable scientific and technological interest over the past 17 years motivated for their wide range of applications including (photo-) catalysis, hydrogen generation and biomedical uses [1,2]. The synthesis of these TNT layers is carried out by electrochemical anodization of valve Ti metal substrates in various F--containing electrolytes using a conventional 2-electrode set-up with the Ti substrate as anode and a Pt-foil as cathode. Instead of using a conventional set-up, also bipolar electrochemistry can be employed for the anodiza

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Sopha, Hanna, and Jan M. Macak. "Bipolar Electrochemistry for the Synthesis of Anodic TiO₂ Nanotube Layers." ECS Meeting Abstracts MA2022-02, no. 13 (2022): 782. http://dx.doi.org/10.1149/ma2022-0213782mtgabs.

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Self-organized TiO2 nanotube (TNT) layers have attracted considerable scientific and technological interest over the past 17 years motivated for their wide range of applications including (photo-) catalysis, hydrogen generation and biomedical uses [1,2]. The synthesis of these TNT layers is carried out by electrochemical anodization of valve Ti metal substrates in various F--containing electrolytes using a conventional 2-electrode set-up with the Ti substrate as anode and a Pt-foil as cathode. Instead of using a conventional set-up, also bipolar electrochemistry can be employed for the anodiza

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43

McLarty, Colin. "Failure of Cartesian closedness in NF." Journal of Symbolic Logic 57, no. 2 (1992): 555–56. http://dx.doi.org/10.2307/2275291.

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On any reasonable definition of functions, neither the category of sets nor the category of small categories is cartesian closed in New Foundations (NF). The latter category is sometimes proposed as a foundation for category theory since it is among its own objects. Our result shows it is a poor one.In NF, as in other set theories, a "function" f from a set A to a set B is defined to be a set f of ordered pairs 〈x, y〉 with x in A and y in B, such that (a) if 〈x, y〉 ∈ f and 〈x, y′〉 ∈ f then y = y′, and (b) for every x in A there is some y in B with 〈x, y〉 ∈ f. But in NF different definitions of

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44

Landver, Avner. "Baire numbers, uncountable Cohen sets and perfect-set forcing." Journal of Symbolic Logic 57, no. 3 (1992): 1086–107. http://dx.doi.org/10.2307/2275450.

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The Baire number of the real line (see 1.1(c)) has uncountable cofinality [Mi]. This number is equal to the Baire number of the space 2ω and also to the Baire number (1.1(d)) of every countable partial order. Our research is motivated by the following open question (1.13) (see also [BPS] and [Mi]): can the cofinality of nκ, the Baire number of the space (2κ)κ (1.1(b)), be less than or equal to κ? This question is nontrivial when κ is regular and 2κ = κ (1.3). A. Miller proved that the answer is “no” if κ is strongly inaccessible (see [Mi] and 1.11). Assuming CH, is equal to the Baire number of

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45

Nugrahani, Calista Suci, Christian Constantine, and A. N. M. Salman. "Strong 3-Rainbow Indexes of Closed Helm Graphs." Indonesian Journal of Combinatorics 8, no. 2 (2024): 109. https://doi.org/10.19184/ijc.2024.8.2.5.

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Let <em>G</em> be a nontrivial, edge-colored, and connected graph of order <em>m</em>≥3 where adjacent edges may have the same color. A tree <em>T</em> in graph <em>G</em> is called a rainbow tree if all the edges in <em>T</em> have different colors. For <em>S</em>⊆<em>V</em>(<em>G</em>), the Steiner distance <em>sd</em>(<em>S</em>) of <em>S</em> is the minimum size of a tree in <em>G</em> containing <em>S</em>. Let <em>k</em> b

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DICKS, WARREN, and S. V. IVANOV. "On the intersection of free subgroups in free products of groups." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 3 (2008): 511–34. http://dx.doi.org/10.1017/s0305004107001041.

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AbstractLet (Gi | i ∈ I) be a family of groups, let F be a free group, and let $G = F \ast \mathop{\text{\Large $*$}}_{i\in I} G_i,$ the free product of F and all the Gi.Let $\mathcal{F}$ denote the set of all finitely generated subgroups H of G which have the property that, for each g ∈ G and each i ∈ I, $H \cap G_i^{g} = \{1\}.$ By the Kurosh Subgroup Theorem, every element of $\mathcal{F}$ is a free group. For each free group H, the reduced rank of H, denoted r(H), is defined as $\max \{\rank(H) -1, 0\} \in \naturals \cup \{\infty\} \subseteq [0,\infty].$ To avoid the vacuous case, we make

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47

Gurevich, E. Ya, and D. A. Pavlova. "On embedding of invariant manifolds of the simplest Morse-Smale flows with heteroclinical intersections." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 20, no. 4 (2018): 378–83. http://dx.doi.org/10.15507/2079-6900.20.201804.378-383.

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We study a structure of four-dimensional phase space decomposition on trajectories of Morse-Smale flows admitting heteroclinical intersections. More precisely, we consider a class G(S4) of Morse-Smale flows on the sphere S4 such that for any flow f∈G(S4) its non-wandering set consists of exactly four equilibria: source, sink and two saddles. Wandering set of such flows contains finite number of heteroclinical curves that belong to intersection of invariant manifolds of saddle equilibria. We describe a topology of embedding of saddle equilibria’s invariant manifolds; that is the first step in t

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TAN, SER PEOW. "COMPLEX FENCHEL-NIELSEN COORDINATES FOR QUASI-FUCHSIAN STRUCTURES." International Journal of Mathematics 05, no. 02 (1994): 239–51. http://dx.doi.org/10.1142/s0129167x94000140.

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Let Fg be a closed oriented surface of genus g ≥ 2 and let [Formula: see text] be the space of marked quasi-fuchsian structures on Fg. Let [Formula: see text] be a set of non-intersecting, non-trivial simple closed curves on Fg that cuts Fg into pairs of pants components. In this note, we construct global complex coordinates for [Formula: see text] relative to [Formula: see text] giving an embedding of [Formula: see text] into [Formula: see text]. The totally real subspace of [Formula: see text] with respect to these coordinates is the Teichmüller Space [Formula: see text] of marked hyperbolic

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49

Harris, Morton E. "Isomorphisms of subcategories of fusion systems of blocks and Clifford theory." Journal of Group Theory 23, no. 5 (2020): 925–30. http://dx.doi.org/10.1515/jgth-2019-0153.

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AbstractLet k be an algebraically closed field of prime characteristic p. Let G be a finite group, let N be a normal subgroup of G, and let c be a G-stable block of kN so that {(kN)c} is a p-permutation G-algebra. As in Section 8.6 of [M. Linckelmann, The Block Theory of finite Group Algebras: Volume 2, London Math. Soc. Stud. Texts 92, Cambridge University, Cambridge, 2018], a {(G,N,c)}-Brauer pair {(R,f_{R})} consists of a p-subgroup R of G and a block {f_{R}} of {(kC_{N}(R))}. If Q is a defect group of c and {f_{Q}\in\operatorname{\textit{B}\ell}(kC_{N}(Q))}, then {(Q,f_{Q})} is a {(G,N,c)}

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50

Ballester-Bolinches, A., H. Bechtell, and L. M. Ezquerro. "On Prefrattini residuals." Glasgow Mathematical Journal 40, no. 2 (1998): 187–97. http://dx.doi.org/10.1017/s001708950003250x.

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All groups considered in the sequel are finite. Let (ℭ and denote the formations of groups which consist of collections of groups that respectively either split over each normal subgroup (nC-groups) or for which the groups do not possess nontrivial Frattini chief factors [8]. The purpose of this article is to develop and expand a concept that arises naturally with the residuals for these formations, namely each G-chief factor is non-complemented (Frattini). With respect to a solid set X of maximal subgroups, these properties are generalized respectively to so-called X-parafrattini (X-profratti

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