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Journal articles on the topic 'Lattice naturale'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Bělohlávek, Radim. "Reduction and a Simple Proof of Characterization of Fuzzy Concept Lattices." Fundamenta Informaticae 46, no. 4 (2001): 277–85. https://doi.org/10.3233/fun-2001-46401.

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Presented is a reduction of fuzzy Galois connections and fuzzy concept lattices to (crisp) Galois connections and concept lattices: each fuzzy concept lattice can be viewed as a concept lattice (in a natural way). As a result, a simple proof of the characterization theorem for fuzzy concept lattices is obtained. The reduction enables us to apply the results worked out for concept lattices to fuzzy concept lattices.

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2

Guo, Heng, Fengxia Liu, Linlin Wang, and Kun Tian. "New bounds of the smoothing parameter for lattices." PLOS One 20, no. 7 (2025): e0328688. https://doi.org/10.1371/journal.pone.0328688.

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The smoothing parameter on lattices is crucial for lattice-based cryptographic design. In this study, we establish a new upper bound for the lattice smoothing parameter, which represents an improvement over several significant classical findings. For one-dimensional integer lattices, under specific and optimized conditions, we have achieved a more precise upper bound compared to previous research. Regarding general high-dimensional lattices, when the lattice dimension is large enough and the error parameter is within a particular range, we have derived a new upper bound. In the practical appli

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3

Grabowski, Adam. "Stone Lattices." Formalized Mathematics 23, no. 4 (2015): 387–96. http://dx.doi.org/10.1515/forma-2015-0031.

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Summary The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the other which is dense. The core of the paper is of course the idea of Stone identity $$a^* \sqcup a^{**}

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4

Alvarado-García, Alejandro, César Cejudo-Castilla, Hugo Alberto Rincón-Mejía, and Ivan Fernando Vilchis-Montalvo. "Pseudocomplements and strong pseudocomplements in lattices of module classes." Journal of Algebra and Its Applications 17, no. 01 (2018): 1850016. http://dx.doi.org/10.1142/s0219498818500160.

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In this work, we consider the existence and construction of pseudocomplements in some lattices of module classes. The classes of modules belonging to these lattices are defined via closure under operations such as taking submodules, quotients, extensions, injective hulls, direct sums or products. We characterize the rings for which the lattices [Formula: see text]-tors (of hereditary torsion classes), [Formula: see text]-nat (the lattice of natural classes) and [Formula: see text]-conat (the lattice of conatural classes) coincide.

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Chajda, Ivan, and Helmut Länger. "Left residuated lattices induced by lattices with a unary operation." Soft Computing 24, no. 2 (2019): 723–29. http://dx.doi.org/10.1007/s00500-019-04461-x.

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Abstract In a previous paper, the authors defined two binary term operations in orthomodular lattices such that an orthomodular lattice can be organized by means of them into a left residuated lattice. It is a natural question if these operations serve in this way also for more general lattices than the orthomodular ones. In our present paper, we involve two conditions formulated as simple identities in two variables under which this is really the case. Hence, we obtain a variety of lattices with a unary operation which contains exactly those lattices with a unary operation which can be conver

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6

BÉTERMIN, LAURENT. "ON A LATTICE GENERALISATION OF THE LOGARITHM AND A DEFORMATION OF THE DEDEKIND ETA FUNCTION." Bulletin of the Australian Mathematical Society 102, no. 1 (2020): 118–25. http://dx.doi.org/10.1017/s000497272000012x.

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We consider a deformation $E_{L,\unicode[STIX]{x1D6EC}}^{(m)}(it)$ of the Dedekind eta function depending on two $d$-dimensional simple lattices $(L,\unicode[STIX]{x1D6EC})$ and two parameters $(m,t)\in (0,\infty )$, initially proposed by Terry Gannon. We show that the minimisers of the lattice theta function are the maximisers of $E_{L,\unicode[STIX]{x1D6EC}}^{(m)}(it)$ in the space of lattices with fixed density. The proof is based on the study of a lattice generalisation of the logarithm, called the lattice logarithm, also defined by Terry Gannon. We also prove that the natural logarithm is

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Longstaff, W. E., J. B. Nation, and Oreste Panaia. "Abstract reflexive sublattices and completely distributive collapsibility." Bulletin of the Australian Mathematical Society 58, no. 2 (1998): 245–60. http://dx.doi.org/10.1017/s0004972700032226.

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There is a natural Galois connection between subspace lattices and operator algebras on a Banach space which arises from the notion of invariance. If a subspace lattice ℒ is completely distributive, then ℒ is reflexive. In this paper we study the more general situation of complete lattices for which the least complete congruence δ on ℒ such that ℒ/δ is completely distributive is well-behaved. Our results are purely lattice theoretic, but the motivation comes from operator theory.

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8

Trubin, A. A. "Scattering of Plane Electromagnetic Waves by Lattices of Spherical Dielectric Resonators with Degenerate Lower Types of Natural Oscillations." Visnyk NTUU KPI Seriia - Radiotekhnika Radioaparatobuduvannia, no. 91 (March 30, 2023): 12–17. https://doi.org/10.20535/radap.2023.91.12-17.

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The problem of scattering of plane electromagnetic waves on lattices of spherical dielectric resonators (DRs) with low magnetic oscillations is considered. The results of theoretical calculations of complex coefficients of mutual coupling of spherical dielectric resonators in open space for cases of excitation of degenerate types of oscillations are presented. The expressions found coincide with those obtained earlier for the special case of oscillations of resonators excited along or perpendicular to the line connecting their centers. The main regularities of the change in the coupling coeffi

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9

Aydın, A., and F. Temizsu. "Statistical convergence in vector lattices." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 111, no. 3 (2023): 4–10. http://dx.doi.org/10.31489/2023m3/4-10.

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The statistical convergence is defined for sequences with the asymptotic density on the natural numbers, in general. In this paper, we introduce the statistical convergence in vector lattices by using the finite additive measures on directed sets. Moreover, we give some relations between the statistical convergence and the lattice properties such as the order convergence and lattice operators.

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10

Restall, Greg, and Francesco Paoli. "The geometry of non-distributive logics." Journal of Symbolic Logic 70, no. 4 (2005): 1108–26. http://dx.doi.org/10.2178/jsl/1129642117.

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AbstractIn this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems for classical logic and Girard's proofnets for linear log

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11

Chen, Zai Liang, Luo Hong Deng, and Cong Jing. "Dynamic Performance and Structural Optimization of Large-Scale Machine Table." Applied Mechanics and Materials 615 (August 2014): 313–16. http://dx.doi.org/10.4028/www.scientific.net/amm.615.313.

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Designed new table for large floor boring and milling machine, used ANSYS to optimize the structure of the table as a whole. According to the contours of removable material the materials which can be removed, obtained the inner ribs layout of table and the sand holes location of rib plate. Dynamic optimization variables on basic ribs cell, studied the effect of steel lattice structure parameters influenced on the natural frequency of the lattices and the related parameter of lattices influenced on whole table, to get the ideal rib lattice structure after optimizing again. Optimized bench can r

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Várilly-Alvarado, Anthony, and David Zywina. "Arithmetic E8 Lattices with Maximal Galois Action." LMS Journal of Computation and Mathematics 12 (2009): 144–65. http://dx.doi.org/10.1112/s1461157000001479.

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AbstractWe construct explicit examples of E8 lattices occurring in arithmetic for which the natural Galois action is equal to the full group of automorphisms of the lattice, i.e., the Weyl group of E8. In particular, we give explicit elliptic curves over Q(t) whose Mordell-Weil lattices are isomorphic to E8 and have maximal Galois action.Our main objects of study are del Pezzo surfaces of degree 1 over number fields. The geometric Picard group, considered as a lattice via the negative of the intersection pairing, contains a sublattice isomorphic to E8. We construct examples of such surfaces fo

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13

ADARICHEVA, KIRA, and J. B. NATION. "LATTICES OF QUASI-EQUATIONAL THEORIES AS CONGRUENCE LATTICES OF SEMILATTICES WITH OPERATORS: PART I." International Journal of Algebra and Computation 22, no. 07 (2012): 1250065. http://dx.doi.org/10.1142/s0218196712500658.

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We show that for every quasivariety 𝒦 of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of 𝒦 (the dual of the lattice of sub-quasivarieties of 𝒦) is isomorphic to Con(S, +, 0, 𝒡. As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found.

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Kirsanov, M. N. "Analytical Estimation of the Natural Oscillation Frequency of a Planar Lattice." Advanced Engineering Research 22, no. 4 (2023): 315–22. http://dx.doi.org/10.23947/2687-1653-2022-22-4-315-322.

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Introduction. A new scheme of a flat statically determinate regular lattice is proposed. The lattice rods are hinged. The study aims at deriving a formula for the dependence on the number of panels of the first natural oscillation frequency of nodes endowed with masses, each of which has two degrees of freedom in the lattice plane. The rigidity of all rods is assumed to be the same, the supports (movable and fixed hinges) — nondeformable. Another objective of the study is to find the dependence of the stresses in the most compressed and stretched rods on the number of panels in an analytical f

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15

Kroc, Jiří. "Influence of Lattice Anisotropy on Models Formulated by Cellular Automata in Presence of Grain Boundary Movement: A Case Study." Materials Science Forum 482 (April 2005): 195–98. http://dx.doi.org/10.4028/www.scientific.net/msf.482.195.

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This paper continues in the previous research focussed to two simple questions. The first one reads: ”What is the influence of anisotropy of computational lattice on simulations of boundary movement?” where grain boundary movement typically appears in simulations of grain boundary migration and static/dynamic recrystallization. The second question reads: ”How is the computational anisotropy related to natural anisotropy of the material lattice itself?” This study is focussed on the influence of change of the computational algorithm and/or lattice on the grain boundary movement. Two algorithms,

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Couch, W. E., M. Surovy, and R. J. Torrence. "Some singular motions of non-Abelian Toda lattices." Canadian Journal of Physics 78, no. 2 (2000): 99–112. http://dx.doi.org/10.1139/p00-025.

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Motions of finite Toda lattices are known to be associated with linear wave equations whose general solutions can be expressed in terms of progressing waves, and this association is known to generalize to finite non-Abelian Toda lattices of n x n matrices and systems of n coupled linear wave equations. We present a nontrivial family of non-Abelian Toda lattice motions that can be specialized to ones that are not finite, but not infinitely extendible either, as they contain nonvanishing but singular matrices of rank (n s). In these cases we give a natural continuation of the lattice dynamics

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17

de Viola-Prioli, Ana M., and Jorge E. Viola-Prioli. "Asymmetry in the lattice of kernel functors." Glasgow Mathematical Journal 33, no. 1 (1991): 95–97. http://dx.doi.org/10.1017/s0017089500008089.

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Much of the research done by different authors on the lattice of kernel functors (equivalently, linear topologies) has been summarized by Golan in [2]. More recently, the rings whose lattices of kernel functors are linearly ordered were introduced in [3] as a categorical generalization of valuation rings in the non-commutative case. Results (and examples) in [3] show that there is an abundance of non-commutative rings R whose lattices (R), both in Mod-R and R-Mod, are simultaneously linearly ordered; however, the question of the symmetry of this condition remained open. Here we will prove that

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18

Grätzer, G., H. Lakser, and E. T. Schmidt. "Congruence Representations of Join-homomorphisms of Finite Distributive Lattices: Size and Breadth." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 1 (2000): 85–103. http://dx.doi.org/10.1017/s1446788700001592.

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AbstractLet K and L be lattices, and let ϕ be a homomorphism of K into L.Then ϕ induces a natural 0-preserving join-homomorphism of Con K into Con L.Extending a result of Huhn, the authors proved that if D and E are finite distributive lattices and ψ is a 0-preserving join-homomorphism from D into E, then D and E can be represented as the congruence lattices of the finite lattices K and L, respectively, such that ψ is the natural 0-preserving join-homomorphism induced by a suitable homomorphism ϕ: K → L. Let m and n denote the number of join-irreducible elements of D and E, respectively, and l

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19

Niederle, Josef. "Natural generalization of some lattice theory concepts to partially ordered sets." Czechoslovak Mathematical Journal 41, no. 2 (1991): 297–99. http://dx.doi.org/10.21136/cmj.1991.102463.

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20

Chajda, Ivan, and Helmut Länger. "When does a semiring become a residuated lattice?" Asian-European Journal of Mathematics 09, no. 04 (2016): 1650088. http://dx.doi.org/10.1142/s1793557116500881.

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It is an easy observation that every residuated lattice is in fact a semiring because multiplication distributes over join and the other axioms of a semiring are satisfied trivially. This semiring is commutative, idempotent and simple. The natural question arises if the converse assertion is also true. We show that the conversion is possible provided the given semiring is, moreover, completely distributive. We characterize semirings associated to complete residuated lattices satisfying the double negation law where the assumption of complete distributivity can be omitted. A similar result is o

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21

BUNIMOVICH, LEONID A. "MANY-DIMENSIONAL LORENTZ CELLULAR AUTOMATA AND TURING MACHINES." International Journal of Bifurcation and Chaos 06, no. 06 (1996): 1127–35. http://dx.doi.org/10.1142/s0218127496000618.

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We study the class of cellular automata that generalizes the Lorentz lattice gases in statistical mechanics, the models of industrious ants in the theory of an artificial life and the so-called Tur-mites (many-dimensional Turing machines). We prove that on the square lattice ℤd, d = 2, the existence of a bounded orbit of a particle (ant, machine) determines all nondegenerate local scattering rules (states of a machine). For higher dimensional (d ≥ 3) cubic lattices we show that under some natural conditions all possible bounded orbits (vortices) can live only in some “vortex sheets” that have

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22

GEERSE, C. P. M., and A. HOF. "LATTICE GAS MODELS ON SELF-SIMILAR APERIODIC TILINGS." Reviews in Mathematical Physics 03, no. 02 (1991): 163–221. http://dx.doi.org/10.1142/s0129055x91000072.

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We discuss lattice gas models on the vertices of tilings in arbitrary dimension that are self-similar in the way Penrose tilings of the plane are self-similar. Among these, there are systems that fundamentally lack translation invariance. Under natural hypotheses on the interactions and the states, we prove the existence of thermodynaraic functions — the mean pressure, the mean energy and the mean entropy — and derive the variational principle. The relation between Gibbs states and tangent functionals to the mean pressure is investigated. Generalizations to quantum systems are also discussed.

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23

Craig, Andrew, Miroslav Haviar, and Klarise Marais. "Dual digraphs of finite meet-distributive and modular lattices." Cubo (Temuco) 26, no. 2 (2024): 279–302. http://dx.doi.org/10.56754/0719-0646.2602.279.

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We describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph representation of finite lattices by Craig, Gouveia and Haviar (2015). These digraphs, known as TiRS digraphs, have their origins in the dual representations of lattices by Urquhart (1978) and Ploščica (1995). We describe two properties of finite lattices which are weakenings of (upper) semimodularity and lower semimodularity respectively, and then show how these properties have a simple description in the dual digrap

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Chajda, Ivan, and Helmut Länger. "Adjoint Operations in Twist-Products of Lattices." Symmetry 13, no. 2 (2021): 253. http://dx.doi.org/10.3390/sym13020253.

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Given an integral commutative residuated lattices L=(L,∨,∧), its full twist-product (L2,⊔,⊓) can be endowed with two binary operations ⊙ and ⇒ introduced formerly by M. Busaniche and R. Cignoli as well as by C. Tsinakis and A. M. Wille such that it becomes a commutative residuated lattice. For every a∈L we define a certain subset Pa(L) of L2. We characterize when Pa(L) is a sublattice of the full twist-product (L2,⊔,⊓). In this case Pa(L) together with some natural antitone involution ′ becomes a pseudo-Kleene lattice. If L is distributive then (Pa(L),⊔,⊓,′) becomes a Kleene lattice. We presen

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Conrad, Jonathan, Jens Eisert, and Francesco Arzani. "Gottesman-Kitaev-Preskill codes: A lattice perspective." Quantum 6 (February 10, 2022): 648. http://dx.doi.org/10.22331/q-2022-02-10-648.

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We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of stabilizer codes. We derive formal bounds on code parameters, show how different decoding strategies are precisely related, propose new ways to obtain GKP codes by means of glued lattices and the tensor product of lattices and point to natural resource savings that have remained hidden in recent approaches. We present general results that we illustrate through

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WEHRUNG, FRIEDRICH. "FROM JOIN-IRREDUCIBLES TO DIMENSION THEORY FOR LATTICES WITH CHAIN CONDITIONS." Journal of Algebra and Its Applications 01, no. 02 (2002): 215–42. http://dx.doi.org/10.1142/s0219498802000148.

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For a finite lattice L, the congruence lattice Con L of L can be easily computed from the partially ordered set J (L) of join-irreducible elements of L and the join-dependency relation DL on J (L). We establish a similar version of this result for the dimension monoid Dim L of L, a natural precursor of Con L. For L join-semidistributive, this result takes the following form: Theorem 1. Let L be a finite join-semidistributive lattice. Then Dim L is isomorphic to the commutative monoid defined by generators Δ(p), for p ∈ J(L), and relations [Formula: see text] As a consequence of this, we obtain

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27

Rump, Wolfgang. "Von Neumann algebras, L-algebras, Baer *-monoids, and Garside groups." Forum Mathematicum 30, no. 4 (2018): 973–95. http://dx.doi.org/10.1515/forum-2017-0108.

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AbstractIt is shown that the projection lattice of a von Neumann algebra, or more generally every orthomodular latticeX, admits a natural embedding into a group{G(X)}with a lattice ordering so that{G(X)}determinesXup to isomorphism. The embedding{X\hookrightarrow G(X)}appears to be a universal (non-commutative) group-valued measure onX, while states ofXturn into real-valued group homomorphisms on{G(X)}. The existence of completions is characterized by a generalized archimedean property which simultaneously applies toXand{G(X)}. By an extension of Foulis’ coordinatization theorem, the negative

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Xu, Xiaoping. "Theta Series of Unimodular Lattices, Combinatorial Identities and Weighted Symmetric Polynomials." Algebra Colloquium 13, no. 01 (2006): 67–86. http://dx.doi.org/10.1142/s1005386706000101.

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Hecke proved that the theta series of a positive definite even unimodular lattice is a polynomial of the well-known Essenstein series E4(z) and the Ramanujan series Δ24(z). A natural question is what kind of polynomials in E4(z) and Δ24(z) could be the theta series of positive definite even unimodular lattices. In this paper, we find two combinatorial identities on the theta series of the root lattices of the finite-dimensional simple Lie algebras of type D4n and the cosets in their integral duals, in terms of E4(z) and Δ24(z). Using these two identities, we prove that three families of weight

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Semenov, Alexei, and Sergei Soprunov. "Automorphisms and Definability (of Reducts) for Upward Complete Structures." Mathematics 10, no. 20 (2022): 3748. http://dx.doi.org/10.3390/math10203748.

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The Svenonius theorem establishes the correspondence between definability of relations in a countable structure and automorphism groups of these relations in extensions of the structure. This may help in finding a description of the lattice constituted by all definability spaces (reducts) of the original structure. Results on definability lattices were previously obtained only for ω-categorical structures with finite signature. In our work, we introduce the concept of an upward complete structure and define the upward completion of a structure. For upward complete structures, the Galois corres

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Vanwelde, Marion, Cédric Hernalsteens, S. Alex Bogacz, Shinji Machida, and Nicolas Pauly. "Parametrizations of coupled betatron motion for strongly coupled lattices." Journal of Instrumentation 18, no. 10 (2023): P10012. http://dx.doi.org/10.1088/1748-0221/18/10/p10012.

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Abstract The coupling of transverse motion is a natural occurrence in particle accelerators, either in the form of a residual coupling arising from imperfections or originating by design from strong systematic coupling fields. While the first can be treated perturbatively, the latter requires a robust approach adapted to strongly coupled optics, and a parametrization of the linear optics must be performed to explore beam dynamics in such peculiar lattices. This work highlights the key physical interpretations of the main parametrization formalisms to describe linear coupled optics, along with

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31

HUANG, HAIBO, T. S. LEE, and C. SHU. "THERMAL CURVED BOUNDARY TREATMENT FOR THE THERMAL LATTICE BOLTZMANN EQUATION." International Journal of Modern Physics C 17, no. 05 (2006): 631–43. http://dx.doi.org/10.1142/s0129183106009059.

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In this paper, a recent curved non-slip wall boundary treatment for isothermal Lattice Boltzmann equation (LBE) [Z. Guo, C. Zheng and B. Shi, Phys. Fluids14(6) (2002)] is extended to handle the thermal curved wall boundary for a double-population thermal lattice Boltzmann equation (TLBE). The unknown distribution population at a wall node which is necessary to fulfill streaming step is decomposed into its equilibrium and non-equilibrium parts. The equilibrium part is evaluated according to Dirichlet and Neumann boundary constraints, and the non-equilibrium part is obtained using a first-order

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Alemayehu, Dawit Bogale, Masahiro Todoh, and Song-Jeng Huang. "Hybrid Biomechanical Design of Dental Implants: Integrating Solid and Gyroid Triply Periodic Minimal Surface Lattice Architectures for Optimized Stress Distribution." Journal of Functional Biomaterials 16, no. 2 (2025): 54. https://doi.org/10.3390/jfb16020054.

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Background: Dental implantology has evolved significantly since the introduction of additive manufacturing, which allows for the reproduction of natural bone’s porous architecture to improve bone tissue compatibility and address stress distribution issues important to long-term implant success. Conventional solid dental implants frequently cause stress shielding, which compromises osseointegration and reduces durability. Aim: The current research proposes to examine the biomechanical efficacy of fully and hybrid gyroid triply periodic minimum surface (TPMS) latticed implants across different c

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Gu, Anhui, and Peter E. Kloeden. "Asymptotic Behavior of a Nonautonomous p-Laplacian Lattice System." International Journal of Bifurcation and Chaos 26, no. 10 (2016): 1650174. http://dx.doi.org/10.1142/s0218127416501741.

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The existence of a pullback attractor for the nonautonomous [Formula: see text]-Laplacian type equations on infinite lattices is established under certain natural dissipative conditions. In particular, there is no restriction on the power index [Formula: see text] of the nonlinearity relative to the index [Formula: see text]. The forward limiting behavior is also discussed and, under suitable assumptions on the time dependent terms, the lattice system is shown to be asymptotically autonomous with its pullback attractor component sets converging upper semi-continuously to the autonomous global

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Obaton, Anne-Françoise, Jacques Fain, Dietmar Meinel, et al. "In Vivo Bone Progression in and around Lattice Implants Additively Manufactured with a New Titanium Alloy." Applied Sciences 13, no. 12 (2023): 7282. http://dx.doi.org/10.3390/app13127282.

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The osseointegration in/around additively manufactured (AM) lattice structures of a new titanium alloy, Ti–19Nb–14Zr, was evaluated. Different lattices with increasingly high sidewalls gradually closing them were manufactured and implanted in sheep. After removal, the bone–interface implant (BII) and bone–implant contact (BIC) were studied from 3D X-ray computed tomography images. Measured BII of less than 10 µm and BIC of 95% are evidence of excellent osseointegration. Since AM naturally leads to a high-roughness surface finish, the wettability of the implant is increased. The new alloy posse

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GONZÁLEZ-FÉREZ, JUAN, and LEANDRO MARÍN. "MONOMORPHISMS AND KERNELS IN THE CATEGORY OF FIRM MODULES." Glasgow Mathematical Journal 52, A (2010): 83–91. http://dx.doi.org/10.1017/s0017089510000224.

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AbstractIn this paper we consider for a non-unital ring R, the category of firm R-modules for a non-unital ring R, i.e. the modules M such that the canonical morphism μM : R ⊗RM → M given by r ⊗ m ↦ rm is an isomorphism. This category is a natural generalization of the usual category of unitary modules for a ring with identity and shares many properties with it. The only difference is that monomorphisms are not always kernels. It has been proved recently that this category is not Abelian in general by providing an example of a monomorphism that is not a kernel in a particular case. In this pap

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Czédli, Gábor. "SPERNER THEOREMS FOR UNRELATED COPIES OF POSETS AND GENERATING DISTRIBUTIVE LATTICES." Ural Mathematical Journal 10, no. 1 (2024): 44. http://dx.doi.org/10.15826/umj.2024.1.004.

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For a finite poset (partially ordered set) \(U\) and a natural number \(n\), let \(S(U,n)\) denote the largest number of pairwise unrelated copies of \(U\) in the powerset lattice (AKA subset lattice) of an \(n\)-element set. If \(U\) is the singleton poset, then \(S(U,n)\) was determined by E. Sperner in 1928; this result is well known in extremal combinatorics. Later, exactly or asymptotically, Sperner's theorem was extended to other posets by A.P. Dove, J.R. Griggs, G.O.H. Katona, D.J. Stahl, and W.T.Jr. Trotter. We determine \(S(U,n)\) for all finite posets with 0 and 1, and we give reason

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BAYRAK, Özgü. "Finite element simulation of femoral stems lightweighted with re-entrant honeycomb lattice structure." European Mechanical Science 7, no. 3 (2023): 128–37. http://dx.doi.org/10.26701/ems.1287321.

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Artificial hip joints are used to replace damaged or diseased natural joints. When the stress that is typically applied to the bone changes because the implant and bone are different in stiffness, a phenomenon known as stress shielding occurs. Stress shielding can lead to bone weakening through reduced density and aseptic loosening in the long term. Studies are ongoing to overcome this phenomenon through geometric design, the use of materials with a low modulus of elasticity, or latticed implants. In this study, the effect of lightening the hip prosthesis with lattice structures on stress shie

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Chajda, Ivan, and Helmut Länger. "Residuation in non-associative MV-algebras." Mathematica Slovaca 68, no. 6 (2018): 1313–20. http://dx.doi.org/10.1515/ms-2017-0181.

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Abstract It is well known that every MV-algebra can be converted into a residuated lattice satisfying divisibility and the double negation law. In a previous paper the first author and J. Kühr introduced the concept of an NMV-algebra which is a non-associative modification of an MV-algebra. The natural question arises if an NMV-algebra can be converted into a residuated structure, too. Contrary to MV-algebras, NMV-algebras are not based on lattices but only on directed posets and the binary operation need not be associative and hence we cannot expect to obtain a residuated lattice but only an

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Revol, J. F. "Lattice resolution in natural polymers." Proceedings, annual meeting, Electron Microscopy Society of America 47 (August 6, 1989): 748–49. http://dx.doi.org/10.1017/s0424820100155712.

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Recent developments in low-dose electron microscopy have led to reports of crystal lattice fringes in natural polymers extremely sensitive to damage by electron irradiation. In one of these studies, lattice images of (β-chitin from the diatom Thalassiosira-fluviatilis were obtained and subsequent computer processing produced the molecular projection of this biopolymer crystal along its b-axis at 0.35 nm resolution. Similar direct structural studies have not been done yet on the α-chitin which is far the most abundant polymorphic form found in nature. The present work reports the direct imaging

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Graña, Manuel. "Lattice computing and natural computing." Neurocomputing 72, no. 10-12 (2009): 2065–66. http://dx.doi.org/10.1016/j.neucom.2008.11.021.

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Danso, Larry, and Eduard Karpov. "Reprogramming Static Deformation Patterns in Mechanical Metamaterials." Materials 11, no. 10 (2018): 2050. http://dx.doi.org/10.3390/ma11102050.

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This paper discusses an x-braced metamaterial lattice with the unusual property of exhibiting bandgaps in their deformation decay spectrum, and, hence, the capacity for reprogramming deformation patterns. The design of polarizing non-local lattice arising from the scenario of repeated zero eigenvalues of a system transfer matrix is also introduced. We develop a single mode fundamental solution for lattices with multiple degrees of freedom per node in the form of static Raleigh waves. These waves can be blocked at the material boundary when the solution is constructed with the polarization vect

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MUSCH, B. U., and A. PROKUDIN. "(BESSEL-)WEIGHTED ASYMMETRIES." International Journal of Modern Physics: Conference Series 04 (January 2011): 126–34. http://dx.doi.org/10.1142/s2010194511001632.

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Semi-inclusive deep inelastic scattering experiments allow us to probe the motion of quarks inside the proton in terms of so-called transverse momentum dependent parton distribution functions (TMD PDFs), but the information is convoluted with fragmentation functions (TMD FFs) and soft factors. It has long been known that weighting the measured event counts with powers of the hadron momentum before forming angular asymmetries de-convolutes TMD PDFs and TMD FFs in an elegant way, but this also entails an undesirable sensitivity to high momentum contributions. Using Bessel functions as weights, w

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Aoki, Hideo, Takahiro Fukui, and Yasuhiro Hatsugai. "Topological Aspects of Quantum Hall Effect in Graphene." International Journal of Modern Physics B 21, no. 08n09 (2007): 1133–39. http://dx.doi.org/10.1142/s0217979207042562.

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We study the recently observed quantum Hall effect (QHE) in graphene from a theoretical viewpoint of topological nature of the QHE to pose questions: (i) The zero-mass Dirac dispersion, which is the origin of the anomalous QHE, exists only around the zero gap, so a natural question is what happens to the QHE topological numbers over the entire energy spectrum. (ii) How the property that the bulk QHE topological number is equal to the edge QHE topological number, shown for the ordinary QHE, applies to the honeycomb lattice. We have shown that (a) the anomalous QHE ∝ (2N + 1) persists, surprisin

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Gunaydin, Kadir, Orhan Gülcan, and Aykut Tamer. "Application of Homogenization Method in Free Vibration of Multi-Material Auxetic Metamaterials." Vibration 8, no. 1 (2025): 2. https://doi.org/10.3390/vibration8010002.

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Different additive manufacturing modalities enable the production of multi-material components which can be used in a wide range of industrial applications. The prediction of the mechanical properties of these components via finite element modelling rather than through testing is critical in terms of cost and time. However, due to the higher computational time spent on the modelling of lattice structures, different methods have been investigated to accurately predict mechanical properties. For this purpose, this study proposes the use of a homogenization method in the two most common types of

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Mahalank, Pushpalatha, Seyma Ozon Yildirim, Fikriye Ersoy Zihni, Bhairaba Kumar Majhi, and Ismail Naci Cangul. "Some topological indices of pentagonal double chains." ITM Web of Conferences 49 (2022): 01004. http://dx.doi.org/10.1051/itmconf/20224901004.

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In graph theory, lattices are used when some structural part of the graph repeats itself finitely or infinitely many times. They have applications in complex analysis and geometry in mathematics, and also natural applications in chemical graph theory. As a lattice can be taken as a graph, it is also possible to use them in the study of large networks. Recently, some topological graph indices of pentagonal chains is studied and here, we study some topological graph indices of pentagonal double chains similarly to that work. We make use of the vertex and edge partitions of these graphs and calcu

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Aguilera, Michel, Sergio Pino-Alarcón, Francisco J. Peña, Eugenio E. Vogel, Natalia Cortés, and Patricio Vargas. "Magnetocaloric Effect for a Q-Clock-Type System." Entropy 27, no. 1 (2024): 11. https://doi.org/10.3390/e27010011.

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In this work, we study the magnetocaloric effect (MCE) in a working substance corresponding to a square lattice of spins with Q possible orientations, known as the “Q-state clock model”. When the Q-state clock model has Q≥5 possible configurations, it presents the famous Berezinskii–Kosterlitz–Thouless (BKT) phase associated with vortex states. We calculate the thermodynamic quantities using Monte Carlo simulations for even Q numbers, ranging from Q=2 to Q=8 spin orientations per site in a lattice. We use lattices of different sizes with N=L×L=82,162,322,642,and1282 sites, considering free bou

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Kladovasilakis, Nikolaos, Sotirios Pemas, and Eleftheria Maria Pechlivani. "Computer-Aided Design of 3D-Printed Clay-Based Composite Mortars Reinforced with Bioinspired Lattice Structures." Biomimetics 9, no. 7 (2024): 424. http://dx.doi.org/10.3390/biomimetics9070424.

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Towards a sustainable future in construction, worldwide efforts aim to reduce cement use as a binder core material in concrete, addressing production costs, environmental concerns, and circular economy criteria. In the last decade, numerous studies have explored cement substitutes (e.g., fly ash, silica fume, clay-based materials, etc.) and methods to mimic the mechanical performance of cement by integrating polymeric meshes into their matrix. In this study, a systemic approach incorporating computer aid and biomimetics is utilized for the development of 3D-printed clay-based composite mortar

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Tang, Juan, Yong Fang, and Jian-Gang Tang. "The Lattice-Valued Turing Machines and the Lattice-Valued Type 0 Grammars." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/291870.

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Purpose.The purpose of this paper is to study a class of the natural languages called the lattice-valued phrase structure languages, which can be generated by the lattice-valued type 0 grammars and recognized by the lattice-valued Turing machines.Design/Methodology/Approach.From the characteristic of natural language, this paper puts forward a new concept of the l-valued Turing machine. It can be used to characterize recognition, natural language processing, and dynamic characteristics.Findings.The mechanisms of both the generation of grammars for the lattice-valued type 0 grammar and the dyna

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Kamozina, Olesia. "Boolean Lattices of n-multiply ωσ-fibered Fitting Classes". Bulletin of Irkutsk State University. Series Mathematics 40 (2022): 34–48. http://dx.doi.org/10.26516/1997-7670.2022.40.34.

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Let N be the set of all natural numbers. Consider all definitions and results taking into account the partitioning of the area for determining satellites and directions. An arbitrary Fitting class is considered a 0-multiply fibered Fitting class; for n equal to or greater than 1, a Fitting class is said to be n-multiply fibered if it has at least one satellite f, all non-empty values which are (n-1)-multiply fibered Fitting classes. The main result of this work is a description of n-multiply fibered Fitting classes, for which the lattice of all n-multiply fibered Fitting subclasses is Boolean.

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Gao, Niushan, and Cosimo Munari. "Surplus-Invariant Risk Measures." Mathematics of Operations Research 45, no. 4 (2020): 1342–70. http://dx.doi.org/10.1287/moor.2019.1035.

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This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far, this notion has been investigated in the setting of some special spaces of random variables. In this paper, we develop a theory of surplus invariance in its natural framework, namely, that of vector lattices. Besides providing a unifying perspective on the existing literature, we establish a variety of new results including dual representations and extensions of surplus-invariant risk measures and structural result

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