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Articoli di riviste sul tema "Numerial semigroup"

Autore: Grafiati

Pubblicato: 4 giugno 2021

Ultima modifica: 1 febbraio 2022

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1

Robles-Pérez, Aureliano M., and José Carlos Rosales. "The enumeration of the set of atomic numerical semigroups with fixed Frobenius number." Journal of Algebra and Its Applications 19, no. 08 (2019): 2050144. http://dx.doi.org/10.1142/s0219498820501443.

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A numerical semigroup is irreducible if it cannot be obtained as an intersection of two numerical semigroups containing it properly. If we only consider numerical semigroups with the same Frobenius number, that concept is generalized to atomic numerical semigroup. Based on a previous one developed to obtain all irreducible numerical semigroups with a fixed Frobenius number, we present an algorithm for computing all atomic numerical semigroups with a fixed Frobenius number.

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2

BRAS-AMORÓS, MARIA, PEDRO A. GARCÍA-SÁNCHEZ, and ALBERT VICO-OTON. "NONHOMOGENEOUS PATTERNS ON NUMERICAL SEMIGROUPS." International Journal of Algebra and Computation 23, no. 06 (2013): 1469–83. http://dx.doi.org/10.1142/s0218196713500306.

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Patterns on numerical semigroups are multivariate linear polynomials, and they are said to admit a numerical semigroup if evaluating the pattern at any nonincreasing sequence of elements of the semigroup gives integers belonging to the semigroup. In a first approach, only homogeneous patterns were analyzed. In this contribution we study conditions for a nonhomogeneous pattern to admit a nontrivial numerical semigroup, and particularize this study to the case the independent term of the pattern is a multiple of the multiplicity of the semigroup. Moreover, for the so-called strongly admissible patterns, the set of numerical semigroups admitting these patterns with fixed multiplicity m forms an m-variety, which allows us to represent this set in a tree and to describe minimal sets of generators of the semigroups in the variety with respect to the pattern. Furthermore, we characterize strongly admissible patterns having a finite associated tree.

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3

Moreno, M. A., J. Nicola, E. Pardo, and H. Thomas. "Numerical Semigroups That Are Not Intersections ofd-Squashed Semigroups." Canadian Mathematical Bulletin 52, no. 4 (2009): 598–612. http://dx.doi.org/10.4153/cmb-2009-059-4.

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AbstractWe say that a numerical semigroup isd-squashedif it can be written in the formforN,a1, … ,adpositive integers with gcd(a1, … ,ad) = 1. Rosales and Urbano have shown that a numerical semigroup is 2-squashed if and only if it is proportionally modular.Recent works by Rosaleset al.give a concrete example of a numerical semigroup that cannot be written as an intersection of 2-squashed semigroups. We will show the existence of infinitely many numerical semigroups that cannot be written as an intersection of 2-squashed semigroups. We also will prove the same result for 3-squashed semigroups. We conjecture that there are numerical semigroups that cannot be written as the intersection ofd-squashed semigroups for any fixedd, and we prove some partial results towards this conjecture.

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4

Singhal, Deepesh. "Numerical semigroups of small and large type." International Journal of Algebra and Computation 31, no. 05 (2021): 883–902. http://dx.doi.org/10.1142/s0218196721500417.

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A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. Some of the key properties of a numerical semigroup are its Frobenius number [Formula: see text], genus [Formula: see text] and type [Formula: see text]. It is known that for any numerical semigroup [Formula: see text]. Numerical semigroups with [Formula: see text] are called almost symmetric, we introduce a new property that characterizes them. We give an explicit characterization of numerical semigroups with [Formula: see text]. We show that for a fixed [Formula: see text] the number of numerical semigroups with Frobenius number [Formula: see text] and type [Formula: see text] is eventually constant for large [Formula: see text]. The number of numerical semigroups with genus [Formula: see text] and type [Formula: see text] is also eventually constant for large [Formula: see text].

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5

BLANCO, V., and J. C. ROSALES. "IRREDUCIBILITY IN THE SET OF NUMERICAL SEMIGROUPS WITH FIXED MULTIPLICITY." International Journal of Algebra and Computation 21, no. 05 (2011): 731–44. http://dx.doi.org/10.1142/s0218196711006492.

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In this paper we introduce the notion of m-irreducibility that extends the standard concept of irreducibility of a numerical semigroup when the multiplicity is fixed. We analyze the structure of the set of m-irreducible numerical semigroups, we give some properties of these numerical semigroups and we present algorithms to compute the decomposition of a numerical semigroup with multiplicity m into m-irreducible numerical semigroups.

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6

García-Sánchez, P. A., B. A. Heredia, H. İ. Karakaş, and J. C. Rosales. "Parametrizing Arf numerical semigroups." Journal of Algebra and Its Applications 16, no. 11 (2017): 1750209. http://dx.doi.org/10.1142/s0219498817502097.

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We present procedures to calculate the set of Arf numerical semigroups with given genus, given conductor and given genus and conductor. We characterize the Kunz coordinates of an Arf numerical semigroup. We also describe Arf numerical semigroups with fixed Frobenius number and multiplicity up to 7.

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7

Rosales, J. C. "Numerical Semigroups that Differ from a Symmetric Numerical Semigroup in One Element." Algebra Colloquium 15, no. 01 (2008): 23–32. http://dx.doi.org/10.1142/s1005386708000035.

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Given two numerical semigroups S and S', the distance between S and S' is the cardinality of S\S' plus the cardinality of S'\S. In this paper we study those numerical semigroups S for which there is a symmetric numerical semigroup whose distance to S is one.

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8

Delgado, M., P. A. García-Sánchez, and A. M. Robles-Pérez. "Numerical semigroups with a given set of pseudo-Frobenius numbers." LMS Journal of Computation and Mathematics 19, no. 1 (2016): 186–205. http://dx.doi.org/10.1112/s1461157016000061.

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The pseudo-Frobenius numbers of a numerical semigroup are those gaps of the numerical semigroup that are maximal for the partial order induced by the semigroup. We present a procedure to detect if a given set of integers is the set of pseudo-Frobenius numbers of a numerical semigroup and, if so, to compute the set of all numerical semigroups having this set as set of pseudo-Frobenius numbers.

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9

García-García, J. I., M. A. Moreno-Frías, and A. Vigneron-Tenorio. "Proportionally modular affine semigroups." Journal of Algebra and Its Applications 17, no. 01 (2018): 1850017. http://dx.doi.org/10.1142/s0219498818500172.

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This work introduces a new kind of semigroup of [Formula: see text] called proportionally modular affine semigroup. These semigroups are defined by modular Diophantine inequalities and they are a generalization of proportionally modular numerical semigroups. We give an algorithm to compute their minimal generating sets, and we specialize when [Formula: see text]. For this case, we also provide a faster algorithm to compute their minimal system of generators, prove they are Cohen–Macaulay and Buchsbaum, and determinate their (minimal) Frobenius vectors. Besides, Gorenstein proportionally modular affine semigroups are characterized.

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10

Zito, Giuseppe. "Arf good semigroups." Journal of Algebra and Its Applications 17, no. 10 (2018): 1850182. http://dx.doi.org/10.1142/s0219498818501827.

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In this paper, we study the property of the Arf good subsemigroups of [Formula: see text], with [Formula: see text]. We give a way to compute all the Arf semigroups with a given collection of multiplicity branches. We also deal with the problem of determining the Arf closure of a set of vectors and of a good semigroup, extending the concept of characters of an Arf numerical semigroup to Arf good semigroups.

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11

LEHER, ELI. "BOUNDS FOR THE GENUS OF NUMERICAL SEMIGROUPS." International Journal of Number Theory 04, no. 05 (2008): 827–34. http://dx.doi.org/10.1142/s1793042108001699.

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12

Robles-Pérez, Aureliano M., and José Carlos Rosales. "The Frobenius number in the set of numerical semigroups with fixed multiplicity and genus." International Journal of Number Theory 13, no. 04 (2017): 1003–11. http://dx.doi.org/10.1142/s1793042117500531.

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13

Bras-Amorós, Maria, Hebert Pérez-Rosés, and José Miguel Serradilla-Merinero. "Quasi-Ordinarization Transform of a Numerical Semigroup." Symmetry 13, no. 6 (2021): 1084. http://dx.doi.org/10.3390/sym13061084.

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In this study, we present the notion of the quasi-ordinarization transform of a numerical semigroup. The set of all semigroups of a fixed genus can be organized in a forest whose roots are all the quasi-ordinary semigroups of the same genus. This way, we approach the conjecture on the increasingness of the cardinalities of the sets of numerical semigroups of each given genus. We analyze the number of nodes at each depth in the forest and propose new conjectures. Some properties of the quasi-ordinarization transform are presented, as well as some relations between the ordinarization and quasi-ordinarization transforms.

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14

Moreno-Frías, M. A., and José Carlos Rosales. "Counting the Ideals with a Given Genus of a Numerical Semigroup with Multiplicity Two." Symmetry 13, no. 5 (2021): 794. http://dx.doi.org/10.3390/sym13050794.

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Let S and T be two numerical semigroups. We say that T is an I(S)-semigroup if T∖{0} is an ideal of S. Given k a positive integer, we denote by Δ(k) the symmetric numerical semigroup generated by {2,2k+1}. In this paper we present a formula which calculates the number of I(S)-semigroups with genus g(Δ(k))+h for some nonnegative integer h and which we will denote by i(Δ(k),h). As a consequence, we obtain that the sequence {i(Δ(k),h)}h∈N is never decreasing. Besides, it becomes stationary from a certain term.

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15

ROSALES, J. C., and P. VASCO. "OPENED MODULAR NUMERICAL SEMIGROUPS WITH A GIVEN MULTIPLICITY." International Journal of Algebra and Computation 19, no. 02 (2009): 235–46. http://dx.doi.org/10.1142/s0218196709005056.

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Let ℕ be the set of nonnegative integers and let I be an interval of positive rational numbers. Then [Formula: see text] is a numerical semigroup. In this paper we study the multiplicity of the numerical semigroups of the form [Formula: see text], where a and b are integers such that 2 ≤ a < b. We also see the connection between the multiplicity and the Frobenius number of this type of semigroups.

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16

Şahi̇n, Mesut, and Leah Gold Stella. "Gluing semigroups and strongly indispensable free resolutions." International Journal of Algebra and Computation 29, no. 02 (2019): 263–78. http://dx.doi.org/10.1142/s0218196719500012.

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We study strong indispensability of minimal free resolutions of semigroup rings focusing on the operation of gluing used in the literature to take examples with a special property and produce new ones. We give a naive condition to determine whether gluing of two semigroup rings has a strongly indispensable minimal free resolution. As applications, we determine simple gluings of [Formula: see text]-generated non-symmetric, [Formula: see text]-generated symmetric and pseudo symmetric numerical semigroups as well as obtain infinitely many new complete intersection semigroups of any embedding dimensions, having strongly indispensable minimal free resolutions.

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17

Robles-Pérez, Aureliano M., and José Carlos Rosales. "The genus, Frobenius number and pseudo-Frobenius numbers of numerical semigroups of type 2." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 146, no. 5 (2016): 1081–90. http://dx.doi.org/10.1017/s0308210515000840.

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We study some questions on numerical semigroups of type 2. On the one hand, we investigate the relation between the genus and the Frobenius number. On the other hand, for two fixed positive integers g1, g2, we give necessary and sufficient conditions in order to have a numerical semigroup S such that {g1, g2} is the set of its pseudo-Frobenius numbers and, moreover, we explicitly build families of such numerical semigroups.

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18

Baeth, Nicholas R., and Matthew Enlow. "Multiplicative factorization in numerical semigroups." International Journal of Algebra and Computation 30, no. 02 (2019): 419–30. http://dx.doi.org/10.1142/s0218196720500058.

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A numerical semigroup is a nonempty additively closed subset [Formula: see text] with [Formula: see text]. The arithmetic, that is the additive factorization properties, of numerical semigroups has been well studied. Their multiplicative properties, on the other hand, have received little, if any, attention. If [Formula: see text] or [Formula: see text], then multiplicative factorization (as products of primes) in [Formula: see text] is unique. However, if there is [Formula: see text] with [Formula: see text], then multiplicative factorization in [Formula: see text] is no longer unique. The purpose of this paper is to introduce this previously unstudied structure of numerical semigroups. Specifically, we classify the irreducible elements and provide a description of how non-unique multiplicative factorization can be in numerical semigroups. In addition, we show that multiplicative numerical semigroups belong to the class of [Formula: see text]-monoids, but yet are not Krull.

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19

ARVESON, WILLIAM. "ON THE INDEX AND DILATIONS OF COMPLETELY POSITIVE SEMIGROUPS." International Journal of Mathematics 10, no. 07 (1999): 791–823. http://dx.doi.org/10.1142/s0129167x99000343.

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It is known that every semigroup of normal completely positive maps P = {Pt:t≥ 0} of ℬ(H), satisfying Pt(1) = 1 for every t ≥ 0, has a minimal dilation to an E0 acting on ℬ(K) for some Hilbert space K⊇H. The minimal dilation of P is unique up to conjugacy. In a previous paper a numerical index was introduced for semigroups of completely positive maps and it was shown that the index of P agrees with the index of its minimal dilation to an E0-semigroup. However, no examples were discussed, and no computations were made. In this paper we calculate the index of a unital completely positive semigroup whose generator is a bounded operator [Formula: see text] in terms of natural structures associated with the generator. This includes all unital CP semigroups acting on matrix algebras. We also show that the minimal dilation of the semigroup P={ exp tL:t≥ 0} to an E0-semigroup is is cocycle conjugate to a CAR/CCR flow.

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20

ASSI, ABDALLAH. "THE FROBENIUS VECTOR OF A FREE AFFINE SEMIGROUP." Journal of Algebra and Its Applications 11, no. 04 (2012): 1250065. http://dx.doi.org/10.1142/s021949881250065x.

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21

OJEDA, I., and A. VIGNERON-TENORIO. "THE SHORT RESOLUTION OF A SEMIGROUP ALGEBRA." Bulletin of the Australian Mathematical Society 96, no. 3 (2017): 400–411. http://dx.doi.org/10.1017/s0004972717000612.

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This work generalises the short resolution given by Pisón Casares [‘The short resolution of a lattice ideal’, Proc. Amer. Math. Soc.131(4) (2003), 1081–1091] to any affine semigroup. We give a characterisation of Apéry sets which provides a simple way to compute Apéry sets of affine semigroups and Frobenius numbers of numerical semigroups. We also exhibit a new characterisation of the Cohen–Macaulay property for simplicial affine semigroups.

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22

Sun, Guangren, and Zhengjun Zhao. "Generalizing strong admissibility of patterns of numerical semigroups." International Journal of Algebra and Computation 27, no. 01 (2017): 107–19. http://dx.doi.org/10.1142/s0218196717500060.

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A homogeneous pattern is a linear multivariate polynomial without constant term. Bras-Amorós and García-Sánchez introduced the notion of pattern for numerical semigroups, which generalizes the definition of Arf numerical semigroups. The notion of pattern for numerical semigroups is extended in this paper into a family of homogeneous patterns [Formula: see text]. A numerical semigroup admitting a family of homogeneous patterns [Formula: see text] at [Formula: see text]-level is characterized. We pay our attention in this paper to the families with the action of some permutation groups, especially those consisting of certain partition stabilizers. Stable or sensitive patterns are focused on and we characterize them for several specific permutation groups.

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23

Butko, Yana A. "Chernoff approximation of subordinate semigroups." Stochastics and Dynamics 18, no. 03 (2018): 1850021. http://dx.doi.org/10.1142/s0219493718500211.

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This note is devoted to the approximation of evolution semigroups generated by some Markov processes and hence to the approximation of transition probabilities of these processes. The considered semigroups correspond to processes obtained by subordination (i.e. by a time-change) of some original (parent) Markov processes with respect to some subordinators, i.e. Lévy processes with a.s. increasing paths (they play the role of the new time). If the semigroup, corresponding to a parent Markov process, is not known explicitly then neither the subordinate semigroup, nor even the generator of the subordinate semigroup are known explicitly too. In this note, some (Chernoff) approximations are constructed for subordinate semigroups (in the case when subordinators have either known transitional probabilities, or known and bounded Lévy measure) under the condition that the parent semigroups are not known but are already Chernoff-approximated. As it has been shown in the recent literature, this condition is fulfilled for several important classes of Markov processes. This fact allows, in particular, to use the constructed Chernoff approximations of subordinate semigroups, in order to approximate semigroups corresponding to subordination of Feller processes and (Feller type) diffusions in Euclidean spaces, star graphs and Riemannian manifolds. Such approximations can be used for direct calculations and simulation of stochastic processes. The method of Chernoff approximation is based on the Chernoff theorem and can be interpreted also as a construction of Markov chains approximating a given Markov process and as the numerical path integration method of solving the corresponding PDE/SDE.

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24

Spirito, Dario. "Embedding the set of nondivisorial ideals of a numerical semigroup into ℕn". Journal of Algebra and Its Applications 17, № 11 (2018): 1850205. http://dx.doi.org/10.1142/s0219498818502055.

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The set [Formula: see text] of the classes of nondivisorial ideals of a numerical semigroup [Formula: see text] can be endowed with a natural partial order induced by the set of star operations on [Formula: see text]. We study embeddings of [Formula: see text] into [Formula: see text], specializing on three families of numerical semigroups with radically different behavior.

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25

ŞAHİN, MESUT, and NİL ŞAHİN. "BETTI NUMBERS FOR CERTAIN COHEN–MACAULAY TANGENT CONES." Bulletin of the Australian Mathematical Society 99, no. 1 (2018): 68–77. http://dx.doi.org/10.1017/s0004972718000898.

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We compute Betti numbers for a Cohen–Macaulay tangent cone of a monomial curve in the affine $4$-space corresponding to a pseudo-symmetric numerical semigroup. As a byproduct, we also show that for these semigroups, being of homogeneous type and homogeneous are equivalent properties.

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26

Korbelář, Miroslav, and Günter Landsmann. "One-generated semirings and additive divisibility." Journal of Algebra and Its Applications 16, no. 02 (2017): 1750038. http://dx.doi.org/10.1142/s0219498817500384.

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We study the structure of one-generated semirings from the symbolical point of view and their connections to numerical semigroups. We prove that such a semiring is additively divisible if and only if it is additively idempotent. We also show that every at most countable commutative semigroup is contained in the additive part of some one-generated semiring.

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Rosales, J. C., and M. B. Branco. "Decomposition of a numerical semigroup as an intersection of irreducible numerical semigroups." Bulletin of the Belgian Mathematical Society - Simon Stevin 9, no. 3 (2002): 373–81. http://dx.doi.org/10.36045/bbms/1102715062.

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Rosales, J. C., and P. A. García-Sánchez. "Every Numerical Semigroup is One Half of Infinitely Many Symmetric Numerical Semigroups." Communications in Algebra 36, no. 8 (2008): 2910–16. http://dx.doi.org/10.1080/00927870802108171.

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Robles-Pérez, Aureliano M., and José Carlos Rosales. "Numerical semigroups in a problem about cost-effective transport." Forum Mathematicum 29, no. 2 (2017): 329–45. http://dx.doi.org/10.1515/forum-2015-0123.

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AbstractLet ${{\mathbb{N}}}$ be the set of nonnegative integers. A problem about how to transport profitably an organized group of persons leads us to study the set T formed by the integers n such that the system of inequalities, with nonnegative integer coefficients,$a_{1}x_{1}+\cdots+a_{p}x_{p}<n<b_{1}x_{1}+\cdots+b_{p}x_{p}$has at least one solution in ${{\mathbb{N}}^{p}}$. We will see that ${T\cup\{0\}}$ is a numerical semigroup. Moreover, we will show that a numerical semigroup S can be obtained in this way if and only if ${\{a+b-1,a+b+1\}\subseteq S}$, for all ${a,b\in S\setminus\{0\}}$. In addition, we will demonstrate that such numerical semigroups form a Frobenius variety and we will study this variety. Finally, we show an algorithmic process in order to compute T.

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Moreno-Frías, M. A., and J. C. Rosales. "Numerical semigroups bounded by the translation of a plane monoid." Aequationes mathematicae 95, no. 5 (2021): 915–29. http://dx.doi.org/10.1007/s00010-021-00837-3.

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AbstractLet $$\mathbb {N}$$ N be the set of nonnegative integer numbers. A plane monoid is a submonoid of $$(\mathbb {N}^2,+)$$ ( N 2 , + ) . Let M be a plane monoid and $$p,q\in \mathbb {N}$$ p , q ∈ N . We will say that an integer number n is M(p, q)-bounded if there is $$(a,b)\in M$$ ( a , b ) ∈ M such that $$a+p\le n \le b-q$$ a + p ≤ n ≤ b - q . We will denote by $${\mathrm A}(M(p,q))=\{n\in \mathbb {N}\mid n \text { is } M(p,q)\text {-bounded}\}.$$ A ( M ( p , q ) ) = { n ∈ N ∣ n is M ( p , q ) -bounded } . An $$\mathcal {A}(p,q)$$ A ( p , q ) -semigroup is a numerical semigroup S such that $$S= {\mathrm A}(M(p,q))\cup \{0\}$$ S = A ( M ( p , q ) ) ∪ { 0 } for some plane monoid M. In this work we will study these kinds of numerical semigroups.

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Hellus, M., A. Rechenauer, and R. Waldi. "On the Frobenius number of certain numerical semigroups." International Journal of Algebra and Computation 31, no. 03 (2021): 519–32. http://dx.doi.org/10.1142/s0218196721500259.

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Let [Formula: see text], [Formula: see text], be a real and [Formula: see text] a prime number, with [Formula: see text] containing at least two primes. Denote by [Formula: see text] the largest integer which cannot be written as a sum of primes from [Formula: see text]. Then [Formula: see text] Further a question of Wilf about the “Money-Changing Problem” has a positive answer for all semigroups of multiplicity [Formula: see text] containing the primes from [Formula: see text]. In particular, this holds for the semigroup generated by all primes not less than [Formula: see text]. The latter special case was already shown in a previous paper.

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Kehinde, R., and O. H. Abdulazeez. "NUMERICAL AND GRAPHICAL RESULTS OF FINITE SYMMETRIC INVERSE (I_{n}) AND FULL (T_{n}) TRANSFORMATION SEMIGROUPS." FUDMA JOURNAL OF SCIENCES 4, no. 4 (2021): 443–53. http://dx.doi.org/10.33003/fjs-2020-0404-501.

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Supposed is a finite set, then a function is called a finite partial transformation semigroup , which moves elements of from its domain to its co-domain by a distance of where . The total work done by the function is therefore the sum of these distances. It is a known fact that and . In this this research paper, we have mainly presented the numerical solutions of the total work done, the average work done by functions on the finite symmetric inverse semigroup of degree , and the finite full transformation semigroup of degree , as well as their respective powers for a given fixed time in space. We used an effective methodology and valid combinatorial results to generalize the total work done, the average work done and powers of each of the transformation semigroups. The generalized results were tested by substituting small values of and a specified fixed times in space. Graphs were plotted in each case to illustrate the nature of the total work done and the average work done. The results obtained in this research article have an important application in some branch of physics and theoretical computer science

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Martinez-Moreno, J., and A. Rodriguez-Palacios. "Imbedding elements whose numerical range has a vertex at zero in holomorphic semigroups." Proceedings of the Edinburgh Mathematical Society 28, no. 1 (1985): 91–95. http://dx.doi.org/10.1017/s0013091500003229.

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If a is an element of a complex unital Banach algebra whose numerical range is confined to a closed angular region with vertex at zero and angle strictly less than π, we imbed a in a holomorphic semigroup with parameter in the open right half plane.There has been recently a great development in the theory of semigroups in Banach algebras (see [6]), with attention focused on the relation between the structure of a given Banach algebra and the existence of continuous or holomorphic non-trivial semigroups with certain properties with range in this algebra. The interest of this paper arises from the fact that we relate in it, we think for the first time, this new point of view in the theory of Banach algebras with the already classic one of numerical ranges [2,3]. The proofs of our results use, in addition to some basic ideas from numerical ranges in Banach algebras, the concept of extremal algebra Ea(K) of a compact convex set K in ℂ due to Bollobas [1] and concretely the realization of Ea(K) achieved by Crabb, Duncan and McGregor [4].

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34

Huang, I.-Chiau, and Mee-Kyoung Kim. "Numerical semigroup algebras." Communications in Algebra 48, no. 3 (2019): 1079–88. http://dx.doi.org/10.1080/00927872.2019.1677686.

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35

Cusimano, Nicole, Félix del Teso, and Luca Gerardo-Giorda. "Numerical approximations for fractional elliptic equations via the method of semigroups." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 3 (2020): 751–74. http://dx.doi.org/10.1051/m2an/2019076.

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Abstract (sommario):

We provide a novel approach to the numerical solution of the family of nonlocal elliptic equations (−Δ)su = f in Ω, subject to some homogeneous boundary conditions B on ∂Ω, where s ∈ (0,1), Ω ⊂ ℝn is a bounded domain, and (-Δ)s is the spectral fractional Laplacian associated to B on ∂Ω. We use the solution representation (−Δ)−s f together with its singular integral expression given by the method of semigroups. By combining finite element discretizations for the heat semigroup with monotone quadratures for the singular integral we obtain accurate numerical solutions. Roughly speaking, given a datum f in a suitable fractional Sobolev space of order r ≥ 0 and the discretization parameter h > 0, our numerical scheme converges as O(hr+2s), providing super quadratic convergence rates up to O(h4) for sufficiently regular data, or simply O(h2s) for merely f ∈ L2 (Ω). We also extend the proposed framework to the case of nonhomogeneous boundary conditions and support our results with some illustrative numerical tests.

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36

Bras-Amorós, Maria. "The ordinarization transform of a numerical semigroup and semigroups with a large number of intervals." Journal of Pure and Applied Algebra 216, no. 11 (2012): 2507–18. http://dx.doi.org/10.1016/j.jpaa.2012.03.011.

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37

Rosales, J. C., and P. A. García-Sánchez. "Every numerical semigroup is one half of a symmetric numerical semigroup." Proceedings of the American Mathematical Society 136, no. 02 (2007): 475–77. http://dx.doi.org/10.1090/s0002-9939-07-09098-3.

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38

Barucci, Valentina, and Faten Khouja. "On the class semigroup of a numerical semigroup." Semigroup Forum 92, no. 2 (2014): 377–92. http://dx.doi.org/10.1007/s00233-014-9679-8.

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39

Rosales, J. C., and P. A. García-Sánchez. "Constructing Almost Symmetric Numerical Semigroups from Irreducible Numerical Semigroups." Communications in Algebra 42, no. 3 (2013): 1362–67. http://dx.doi.org/10.1080/00927872.2012.740117.

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40

Tizziotti, Guilherme, та Juan Villanueva. "On κ-sparse numerical semigroups". Journal of Algebra and Its Applications 17, № 11 (2018): 1850209. http://dx.doi.org/10.1142/s0219498818502092.

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Abstract (sommario):

Given a positive integer [Formula: see text], we investigate the class of numerical semigroups verifying the property that every two subsequent non-gaps are spaced by at least [Formula: see text]. These semigroups will be called [Formula: see text]-sparse and generalize the concept of sparse numerical semigroups.

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41

Nathan Kaplan. "Counting Numerical Semigroups." American Mathematical Monthly 124, no. 9 (2017): 862. http://dx.doi.org/10.4169/amer.math.monthly.124.9.862.

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42

İLHAN, Sedat, and Halil İbrahim KARATAŞ. "Arf numerical semigroups." TURKISH JOURNAL OF MATHEMATICS 41 (2017): 1448–57. http://dx.doi.org/10.3906/mat-1512-46.

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43

MORENO FRÍAS, María Ángeles, and José Carlos ROSALES. "Perfect numerical semigroups." TURKISH JOURNAL OF MATHEMATICS 43, no. 3 (2019): 1742–54. http://dx.doi.org/10.3906/mat-1901-111.

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44

Ciolan, Emil-Alexandru, Pedro A. García-Sánchez, and Pieter Moree. "Cyclotomic Numerical Semigroups." SIAM Journal on Discrete Mathematics 30, no. 2 (2016): 650–68. http://dx.doi.org/10.1137/140989479.

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45

Thompson, Jeremy, Kurt Herzinger, and Trae Holcomb. "Balanced numerical semigroups." Semigroup Forum 94, no. 3 (2017): 632–49. http://dx.doi.org/10.1007/s00233-016-9816-7.

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46

Jafari, Raheleh, and Santiago Zarzuela Armengou. "Homogeneous numerical semigroups." Semigroup Forum 97, no. 2 (2018): 278–306. http://dx.doi.org/10.1007/s00233-018-9941-6.

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47

Fröberg, R., C. Gottlieb, and R. Häggkvist. "On numerical semigroups." Semigroup Forum 35, no. 1 (1986): 63–83. http://dx.doi.org/10.1007/bf02573091.

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48

Rosales, J. C. "On numerical semigroups." Semigroup Forum 52, no. 1 (1996): 307–18. http://dx.doi.org/10.1007/bf02574106.

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49

Rosales, J. C., P. A. Garcı́a-Sánchez, J. I. Garcı́a-Garcı́a, and M. B. Branco. "Arf numerical semigroups." Journal of Algebra 276, no. 1 (2004): 3–12. http://dx.doi.org/10.1016/j.jalgebra.2004.03.007.

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50

Rosales, J. C., and M. B. Branco. "Irreducible numerical semigroups." Pacific Journal of Mathematics 209, no. 1 (2003): 131–43. http://dx.doi.org/10.2140/pjm.2003.209.131.

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