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Journal articles on the topic 'Translation operator'

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Published: 9 March 2023

Last updated: 11 March 2023

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1

Dales, H. G., and A. Millinoton. "Translation-invariant linear operators." Mathematical Proceedings of the Cambridge Philosophical Society 113, no. 1 (January 1993): 161–72. http://dx.doi.org/10.1017/s030500410007585x.

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The theory of translation-invariant operators on various spaces of functions (or measures or distributions) is a well-trodden field. The problem is to decide, first, whether or not a linear operator between two function spaces on, say, ℝ or ℝ+ which commutes with one or many translations on the two spaces is necessarily continuous, and, second, to give a canonical form for all such continuous operators. In some cases each such operator is zero. The second problem is essentially the ‘multiplier problem’, and it has been extensively discussed; see [7], for example.

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2

Blasco, O., A. Bonilla, and K. G. Grosse-Erdmann. "Rate of growth of frequently hypercyclic functions." Proceedings of the Edinburgh Mathematical Society 53, no. 1 (January 12, 2010): 39–59. http://dx.doi.org/10.1017/s0013091508000564.

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AbstractWe study the rate of growth of entire functions that are frequently hypercyclic for the differentiation operator or the translation operator. Moreover, we prove the existence of frequently hypercyclic harmonic functions for the translation operator and we study the rate of growth of harmonic functions that are frequently hypercyclic for partial differentiation operators.

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3

MAIER, FREDERICK. "Interdefinability of defeasible logic and logic programming under the well-founded semantics." Theory and Practice of Logic Programming 13, no. 1 (August 9, 2011): 107–42. http://dx.doi.org/10.1017/s147106841100041x.

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AbstractWe provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond–Lifschitz (GL) operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.

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4

Miškinis, Paulius. "ON INTEGRAL REPRESENTATION OF THETRANSLATION OPERATOR." Mathematical Modelling and Analysis 17, no. 1 (February 1, 2012): 100–112. http://dx.doi.org/10.3846/13926292.2012.645251.

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The formulation in the explicit form of quantum expression of the one-dimensional translation operator as well as Hermitian operator of momentum and its eigenfunctions are presented. The interrelation between the momentum and the wave number has been generalized for the processes with a non-integer dimensionality α. The proof of the fractional representation of the translation operator is considered. Some aspects of the translations in graduate spaces and their integral representation, as well as applications in physics are discussed. The integral representation of the translation operator is proposed.

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5

Robicheaux, F. "Energy translation operator." Physical Review A 56, no. 5 (November 1, 1997): 4296–99. http://dx.doi.org/10.1103/physreva.56.4296.

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6

LEVENE, R. H., and S. C. POWER. "REFLEXIVITY OF THE TRANSLATION-DILATION ALGEBRAS ON L2(ℝ)." International Journal of Mathematics 14, no. 10 (December 2003): 1081–90. http://dx.doi.org/10.1142/s0129167x03002125.

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The hyperbolic algebra [Formula: see text], studied recently by Katavolos and Power [5], is the weak star closed operator algebra on L2(ℝ) generated by H∞(ℝ), as multiplication operators, and by the dilation operators Vt, t≥0, given by Vtf(x)=et/2f(etx). We show that [Formula: see text] is a reflexive operator algebra and that the four-dimensional manifold [Formula: see text] (with the natural topology) is the reflexive hull of a natural two-dimensional subspace.

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7

Shishkina, E. L. "General Euler-Poisson-Darboux Equation and Hyperbolic B-Potentials." Contemporary Mathematics. Fundamental Directions 65, no. 2 (December 15, 2019): 157–338. http://dx.doi.org/10.22363/2413-3639-2019-65-2-157-338.

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In this work, we develop the theory of hyperbolic equations with Bessel operators. We construct and invert hyperbolic potentials generated by multidimensional generalized translation. Chapter 1 contains necessary notation, deﬁnitions, auxiliary facts and results. In Chapter 2, we study some generalized weight functions related to a quadratic form. These functions are used below to construct fractional powers of hyperbolic operators and solutions of hyperbolic equations with Bessel operators. Chapter 3 is devoted to hyperbolic potentials generated by multidimensional generalized translation. These potentials express negative real powers of the singular wave operator, i. e. the wave operator where the Bessel operator acts instead of second derivatives. The boundedness of such an operator and its properties are investigated and the inverse operator is constructed. The hyperbolic Riesz B-potential is studied as well in this chapter. In Chapter 4, we consider various methods of solution of the Euler-Poisson-Darboux equation. We obtain solutions of the Cauchy problems for homogeneous and nonhomogeneous equations of this type. In Conclusion, we discuss general methods of solution for problems with arbitrary singular operators.

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8

Fishel, B. "Generalized translations associated with an unbounded self-adjoint operator." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 3 (May 1986): 519–28. http://dx.doi.org/10.1017/s030500410006446x.

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Delsarte [2], Povzner [9], Levitan [8], Leblanc [7], Dunford and Schwartz [3] (p. 1626) and Hutson and Pym [5] have discussed generalized translation operators (GTO) ‘associating with a differential operator’. The latter authors have also considered the topic in an abstract setting-the GTO ‘associates’ with a compact operator in a normed space. GTO are to have properties generalizing those of the translation operators defined by members of a group on a vector space E of functions defined on the group:(πεE, s and t are group elements). In the case of a locally compact topological group the integration spaces E = L1,L2,L∞, for a Haar measure of the group, are of especial interest.

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9

Mochow-Grundy, Michelle, and Terence S. Dermody. "The Reovirus S4 Gene 3′ Nontranslated Region Contains a Translational Operator Sequence." Journal of Virology 75, no. 14 (July 15, 2001): 6517–26. http://dx.doi.org/10.1128/jvi.75.14.6517-6526.2001.

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ABSTRACT Reovirus mRNAs are efficiently translated within host cells despite the absence of 3′ polyadenylated tails. The 3′ nontranslated regions (3′NTRs) of reovirus mRNAs contain sequences that exhibit a high degree of gene-segment-specific conservation. To determine whether the 3′NTRs of reovirus mRNAs serve to facilitate efficient translation of viral transcripts, we used T7 RNA polymerase to express constructs engineered with full-length S4 gene cDNA or truncation mutants lacking sequences in the 3′NTR. Full-length and truncated s4 mRNAs were translated using rabbit reticulocyte lysates, and translation product ς3 was quantitated by phosphorimager analysis. In comparison to full-length s4 mRNA, translation of the s4 mRNA lacking the 3′NTR resulted in a 20 to 50% decrease in ς3 produced. Addition to translation reactions of an RNA oligonucleotide corresponding to the S4 3′NTR significantly enhanced translation of full-length s4 mRNA but had no effect on s4 mRNA lacking 3′NTR sequences. Translation of s4 mRNAs with smaller deletions within the 3′NTR identified a discrete region capable of translational enhancement and a second region capable of translational repression. Differences in translational efficiency of full-length and deletion-mutant mRNAs were independent of RNA stability. Protein complexes in reticulocyte lysates that specifically interact with the S4 3′NTR were identified by RNA mobility shift assays. RNA oligonucleotides lacking either enhancer or repressor sequences did not efficiently compete the binding of these complexes to full-length 3′NTR. These results indicate that the reovirus S4 gene 3′NTR contains a translational operator sequence that serves to regulate translational efficiency of the s4 mRNA. Moreover, these findings suggest that cellular proteins interact with reovirus 3′NTR sequences to regulate translation of the nonpolyadenylated reovirus mRNAs.

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10

Prasad, Akhilesh, and U. K. Mandal. "The Kontorovich-Lebedev-Clifford transform." Filomat 35, no. 14 (2021): 4811–24. http://dx.doi.org/10.2298/fil2114811p.

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The Kontorovich-Lebedev-Clifford transform (KLC-transform) as well as its inversion are defined. The useful preliminary results like translation and convolution operators are introduced and their estimates are obtained. Continuity of translation and convolution operators on function spaces F? and G? are discussed. Further, pseudo-differential operator (p.d.o.) associated with the KLC-transform is defined and studied its properties on some function spaces.

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11

Mozhyrovska, Zoryana, and Andriy V. Zagorodnyuk. "Hypercyclic Behavior of Translation Operators on Spaces of Analytic Functions on Hilbert Spaces." Journal of Function Spaces 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/139289.

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We consider special Hilbert spaces of analytic functions of many infinite variables and examine composition operators on these spaces. In particular, we prove that under some conditions a translation operator is bounded and hypercyclic.

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12

Abdelkefi, Chokri. "Maximal functions for Weinstein operator." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 19, no. 1 (December 1, 2020): 105–19. http://dx.doi.org/10.2478/aupcsm-2020-0009.

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AbstractIn the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius ɛ centered at 0 on the upper half space ℝd–1× ]0, +∞ [. Second, we prove weak-type L1-estimates for the uncentered maximal function associated with the Weinstein operator and we obtain the Lp-boundedness of this operator for 1 < p ≤ + ∞. As application, we define a large class of operators such that each operator of this class satisfies these Lp-inequalities. In particular, the maximal operator associated respectively with the Weinstein heat semigroup and the Weinstein-Poisson semigroup belong to this class.

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13

CHOUCHANE, F., M. MILI, and K. TRIMÈCHE. "POSITIVITY OF THE INTERTWINING OPERATOR AND HARMONIC ANALYSIS ASSOCIATED WITH THE JACOBI-DUNKL OPERATOR ON ${\mathbb R}$." Analysis and Applications 01, no. 04 (October 2003): 387–412. http://dx.doi.org/10.1142/s0219530503000247.

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We consider a differential-difference operator Λα,β, [Formula: see text], [Formula: see text] on [Formula: see text]. The eigenfunction of this operator equal to 1 at zero is called the Jacobi–Dunkl kernel. We give a Laplace integral representation for this function and we prove that for [Formula: see text], [Formula: see text], the kernel of this integral representation is positive. This result permits us to prove that the Jacobi–Dunkl intertwining operator and its dual are positive. Next we study the harmonic analysis associated with the operator Λα,β (Jacobi–Dunkl transform, Jacobi–Dunkl translation operators, Jacobi–Dunkl convolution product, Paley–Wiener and Plancherel theorems…).

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14

He, Wen, Bapi Dutta, Rosa M. Rodríguez, Ahmad A. Alzahrani, and Luis Martínez. "Induced OWA Operator for Group Decision Making Dealing with Extended Comparative Linguistic Expressions with Symbolic Translation." Mathematics 9, no. 1 (December 23, 2020): 20. http://dx.doi.org/10.3390/math9010020.

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Nowadays, decision making problems have increased their complexity and a single decision maker cannot handle these problems, with a more diverse and comprehensive view of them being necessary, which results in group decision making (GDM) schemes. The complexity of GDM problems is often due to their inherent uncertainty that is not solved just by using a group. Consequently, different methodologies has been proposed to handle it, in which, the use of the fuzzy linguistic approach stands out. Among the multiple fuzzy linguistic modeling approaches, Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) information has been recently introduced, which enhances classical linguistic modeling that is based on single terms by providing linguistic expressions in a continuous linguistic domain. Its application to decision making is quite promising, but it is necessary to develop enough operators to accomplish aggregation processes in the decision solving scheme. So far, just a small number of aggregation operators have been defined for ELICIT information. Hence, this paper aims at providing new aggregation operators for ELICIT information by developing novel OWA based operators, such as the Induced OWA (IOWA) operator in order to avoid the OWA operator needs of reordering its arguments, because ELICIT information does not have an inherent order due to its fuzzy representation. Our proposal not only consists of extending the definition of an IOWA operator for ELICIT information with crisp weights, but it is also proposed a type-1 IOWA operator for ELICIT information in which both weights and arguments are fuzzy as well as the use of ELICIT information constructing the order inducing variable to reorder the arguments. Additionally, the use of ELICIT information in GDM demands the ability to manage majority based decisions that are better represented in the IOWA operator by linguistic quantifiers. Hence, a majority-driven GDM process for ELICIT information is proposed, which it is the first proposal for fulfilling the majority solving process for GDM while using ELICIT information. Eventually, an illustrative example and a brief comparative analysis are presented in order to show the performance of the proposal and its feasibility.

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15

Borisov, Leonid A., Yuriy N. Orlov, and Vsevolod Zh Sakbaev. "Feynman averaging of semigroups generated by Schrödinger operators." Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, no. 02 (June 2018): 1850010. http://dx.doi.org/10.1142/s0219025718500108.

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The extension of averaging procedure for operator-valued function is defined by means of the integration of measurable map with respect to complex-valued measure or pseudomeasure. The averaging procedure of one-parametric semigroups of linear operators based on Chernoff equivalence for operator-valued functions is constructed. The initial value problem solutions are investigated for fractional diffusion equation and for Schrödinger equation with relativistic Hamiltonian of free motion. It is established that in these examples the solution of evolutionary equation can be obtained by applying the constructed averaging procedure to the random translation operators in classical coordinate space.

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16

Abdelkefi, Chokri, and Mohamed Sifi. "Dunkl Translation and Uncentered Maximal Operator on the Real Line." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–9. http://dx.doi.org/10.1155/2007/87808.

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We establish estimates of the Dunkl translation of the characteristic functionχ[−ɛ,ɛ],ɛ>0, and we prove that the uncentered maximal operator associated with the Dunkl operator is of weak type(1,1). As a consequence, we obtain theLp-boundedness of this operator for1<p≤+∞.

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17

Chin, William. "The Translation Operator for Self-Projective Coalgebras." Communications in Algebra 39, no. 12 (December 2011): 4608–17. http://dx.doi.org/10.1080/00927872.2011.617264.

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18

Girault, Benjamin, Paulo Goncalves, and Eric Fleury. "Translation on Graphs: An Isometric Shift Operator." IEEE Signal Processing Letters 22, no. 12 (December 2015): 2416–20. http://dx.doi.org/10.1109/lsp.2015.2488279.

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19

Hansen, Thorkild B., and Oscar Borries. "Gaussian translation operator in a multilevel scheme." Radio Science 50, no. 8 (August 2015): 754–63. http://dx.doi.org/10.1002/2015rs005686.

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20

Prasad, Akhilesh, and S. K. Verma. "The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces." Filomat 33, no. 8 (2019): 2457–69. http://dx.doi.org/10.2298/fil1908457p.

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In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

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21

Faizi, Shahzad, Wojciech Sałabun, Nisbha Shaheen, Atiq ur Rehman, and Jarosław Wątróbski. "A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment." Mathematics 9, no. 13 (June 24, 2021): 1489. http://dx.doi.org/10.3390/math9131489.

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Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.

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22

Jia, Qi, Rui Feng, Bojian Shi, Yanxia Zhang, Hang Li, Xiaoxin Li, Fangkui Sun, et al. "Universal translation operator for Laguerre–Gaussian mode sorting." Applied Physics Letters 121, no. 19 (November 7, 2022): 191104. http://dx.doi.org/10.1063/5.0123103.

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Laguerre–Gaussian (LG) mode is widely adopted in various applications due to carrying orbital angular momentum (OAM). In practice, it is challenging to sort Laguerre–Gaussian mode according to various features. Traditional fork grating and optical geometric transformations are regarded as convenient methods for sorting LG mode. However, these methods have to destroy the OAM carried by the beam during the sorting process. Here, we demonstrate a nondestructive beam sorting mechanism for LG mode carrying orbital angular momentums based on a translation operator. The numerically solved operator can sort the input beams to pre-defined positions with faithful preservation of all the beam features, which shows good agreement with the experimental results. We believe the proposed translation operator will benefit potential applications in information processing, quantum optics, and optical communications.

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23

Mozhyrovska, Z. G. "Hypercyclic operators on algebra of symmetric analytic functions on $\ell_p$." Carpathian Mathematical Publications 8, no. 1 (June 30, 2016): 127–33. http://dx.doi.org/10.15330/cmp.8.1.127-133.

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In the paper, it is proposed a method of construction of hypercyclic composition operators on $H(\mathbb{C}^n)$ using polynomial automorphisms of $\mathbb{C}^n$ and symmetric analytic functions on $\ell_p.$ In particular, we show that an "symmetric translation" operator is hypercyclic on a Frechet algebra of symmetric entire functions on $\ell_p$ which are bounded on bounded subsets.

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24

Pratama, Dian. "IMAGE DAN PRE-IMAGE TRANSLASI PADA GRUP FUZZY INTUITIONISTIK." Jurnal Ilmiah Matematika dan Pendidikan Matematika 8, no. 2 (December 30, 2016): 41. http://dx.doi.org/10.20884/1.jmp.2016.8.2.2886.

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A intuitionistic fuzzy set in is set gives a membership function and a non-membership function (the complement of membership function) for each with the sum worth one. When it’s applied in group’s theory, it will called intuitionistic fuzzy group with conditions membership function is fuzzy subgroup and non-membership function is anti-fuzzy subgroup. In this research, the operator will be given a fuzzy set is called fuzzy translation operator. This operator is a mapping imposed on membership functions (fuzzy subset) to interval [ 0,1]. This research will discuss the properties homomorphism of translation on intuitionistic fuzzy groups. These properties is the structure of the image and pre-image homomorphism of translation on intuitionistic fuzzy group. We obtain that image and pre-image of translation on intuitionistic fuzzy (normal) groups is also intuitionistic fuzzy (normal) groups.

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25

Jiang, Hongkai, Zheng Jia He, Chendong Duan, and Xue Feng Chen. "Gearbox Fault Diagnosis Using Adaptive Redundant Second Generation Wavelet." Key Engineering Materials 293-294 (September 2005): 95–102. http://dx.doi.org/10.4028/www.scientific.net/kem.293-294.95.

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Vibration signals acquired from a gearbox usually are complex, and it is difficult to detect the symptoms of an inherent fault in a gearbox. In this paper, an adaptive redundant second generation wavelet (ARSGW) based on second generation wavelet (SGW) is developed. It adopts data-based optimization algorithm to design the initial prediction operator and update operator at each scale. The initial operators are interpolated with zero, and then the redundant prediction operator and update operator are obtained. The splitting step in ARSGW is removed, the approximation signal at each scale is predicted and updated with redundant prediction operator and update operator directly, and the length of approximation signal and detail signal at every scale remains the same, ARSGW eliminates translation variance of SGW. Since the redundant prediction operator and update operator lock on to the dominant structure of the signal, ARSGW can well reveal the characteristics of the signal in time domain. ARSGW is found to be very effective in detection of symptoms from the vibration signal of a large air compressor gearbox with impact rub fault. SGW is also used to analyze the same signal for comparison, no modulation signals and periodic impulses appear at any scale.

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26

Menet, Quentin. "Existence of common hypercyclic subspaces for the derivative operator and the translation operators." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113, no. 2 (January 5, 2018): 487–505. http://dx.doi.org/10.1007/s13398-017-0490-8.

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27

Singh, R. K., and W. H. Summers. "Composition operators on weighted spaces of continuous functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 45, no. 3 (December 1988): 303–19. http://dx.doi.org/10.1017/s1446788700031013.

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AbstractWe give algebraic criteria for distinguishing composition operators among all continuous linear operators on spaces of continuous functions with topologies generated by seminorms that are weighted analogues of the supremum norm. In another direction, we also characterize those self maps of the underlying topological space which induce composition operators on such weighted spaces, as well as determine conditions on these self maps which correspond to various basic properties of the induced composition operator. Our results are applied to a question concerning translation invariance which arises in the context of topological dynamics.

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Markin, Marat V. "On the non-hypercyclicity of scalar type spectral operators and collections of their exponentials." Demonstratio Mathematica 53, no. 1 (January 1, 2020): 352–59. http://dx.doi.org/10.1515/dema-2020-0030.

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Abstract Generalizing the case of a normal operator in a complex Hilbert space, we give a straightforward proof of the non-hypercyclicity of a scalar type spectral operator A in a complex Banach space as well as of the collection { e t A } t ≥ 0 {\{{e}^{tA}\}}_{t\ge 0} of its exponentials, which, under a certain condition on the spectrum of the operator A, coincides with the C 0 {C}_{0} -semigroup generated by A. The spectrum of A lying on the imaginary axis, we also show that non-hypercyclic is the strongly continuous group { e t A } t ∈ ℝ {\{{e}^{tA}\}}_{t\in {\mathbb{R}}} of bounded linear operators generated by A. From the general results, we infer that, in the complex Hilbert space L 2 ( ℝ ) {L}_{2}({\mathbb{R}}) , the anti-self-adjoint differentiation operator A ≔ d d x A:= \tfrac{\text{d}}{\text{d}x} with the domain D ( A ) ≔ W 2 1 ( ℝ ) D(A):= {W}_{2}^{1}({\mathbb{R}}) is non-hypercyclic and so is the left-translation strongly continuous unitary operator group generated by A.

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29

Xu, Yuan. "Generalized translation operator and approximation in several variables." Journal of Computational and Applied Mathematics 178, no. 1-2 (June 2005): 489–512. http://dx.doi.org/10.1016/j.cam.2004.02.029.

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30

Jones, Nick G., and Noah Linden. "Integrable spin chains and the Clifford group." Journal of Mathematical Physics 63, no. 10 (October 1, 2022): 101901. http://dx.doi.org/10.1063/5.0095870.

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We construct new families of spin chain Hamiltonians that are local, integrable, and translationally invariant. To do so, we make use of the Clifford group that arises in quantum information theory. We consider translation invariant Clifford group transformations that can be described by matrix product operators (MPOs). We classify translation invariant Clifford group transformations that consist of a shift operator and an MPO of bond dimension two—this includes transformations that preserve locality of all Hamiltonians and those that lead to non-local images of particular operators but, nevertheless, preserve locality of certain Hamiltonians. We characterize translation invariant Clifford group transformations that take single-site Pauli operators to local operators on at most five sites—examples of Quantum Cellular Automata—leading to a discrete family of Hamiltonians that are equivalent to the canonical XXZ model under such transformations. For spin chains solvable by the algebraic Bethe ansatz, we explain how conjugating by an MPO affects the underlying integrable structure. This allows us to relate our results to the usual classifications of integrable Hamiltonians. We also treat the case of spin chains solvable by free fermions.

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31

XU, BIN, ZHAO WEI SHANG, YUAN YAN TANG, BIN FANG, and TAI PING ZHANG. "OCCLUSION ROBUST FACE RECOGNITION WITH SCATTERING OPERATOR IN GRADIENT DOMAIN." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 01 (January 2013): 1350001. http://dx.doi.org/10.1142/s021969131350001x.

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In this paper, we propose a novel occlusion robust face recognition algorithm in gradient direction domain (GDD) using scattering operator. The proposed algorithm transforms image into the GDD to remove pseudo-edges, then scattering operator is used to extract face feature from face image in GDD. Since scattering operators can effectively extract the structural information in face owing to locally translation invariant and deformation stability, the proposed approach is robust to occlusion and varying expression. Our scheme has demonstrated the state-of-the-art performance on several datasets. Especially, our method on the sunglasses images and the scarf in AR database achieves a recognition rate of 100 and 95% respectively, which significantly outperforms most existing methods.

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32

CONRAD, FLORIAN, and TOBIAS KUNA. "A NOTE ON AN INTEGRATION BY PARTS FORMULA FOR THE GENERATORS OF UNIFORM TRANSLATIONS ON CONFIGURATION SPACE." Infinite Dimensional Analysis, Quantum Probability and Related Topics 15, no. 04 (December 2012): 1250028. http://dx.doi.org/10.1142/s0219025712500282.

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An integration by parts formula is derived for the first-order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on ℝd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.

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33

Ould Ahmed Mahmoud, Sid Ahmed. "On Some Normality-Like Properties and Bishop's Property () for a Class of Operators on Hilbert Spaces." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/975745.

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We prove some further properties of the operator (-power quasinormal, defined in Sid Ahmed, 2011). In particular we show that the operator satisfying the translation invariant property is normal and that the operator is not supercyclic provided that it is not invertible. Also, we study some cases in which an operator is subscalar of order ; that is, it is similar to the restriction of a scalar operator of order to an invariant subspace.

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KAYA, Esra. "A different approach to boundedness of the B-maximal operators on the variable Lebesgue spaces." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 3 (September 30, 2022): 710–19. http://dx.doi.org/10.31801/cfsuasmas.1030942.

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By using the Lp(⋅)−Lp(⋅)−boundedness of a maximal operator defined on homogeneous space, it has been shown that the B−B−maximal operator is bounded. In the present paper, we aim to bring a different approach to the boundedness of the B−B−maximal operator generated by generalized translation operator under a continuity assumption on p(⋅)p(⋅). It is noteworthy to mention that our assumption is weaker than uniform Hölder continuity.

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PATHAK, R. S. "CONVOLUTION FOR THE DISCRETE WAVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 06 (November 2011): 905–22. http://dx.doi.org/10.1142/s0219691311004377.

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Translation and convolution associated with the discrete wavelet transform are investigated using properties of Calderón–Zygmund operator and Riesz fractional integral operator. Dual convolution is also studied. The wavelet convolution is applied to approximate functions belonging to certain Lp-spaces.

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Zhao, Zengqin, and Xinsheng Du. "Positive Fixed Points for Semipositone Operators in Ordered Banach Spaces and Applications." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/406727.

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The theory of semipositone integral equations and semipositone ordinary differential equations has been emerging as an important area of investigation in recent years, but the research on semipositone operators in abstract spaces is yet rare. By employing a well-known fixed point index theorem and combining it with a translation substitution, we study the existence of positive fixed points for a semipositone operator in ordered Banach space. Lastly, we apply the results to Hammerstein integral equations of polynomial type.

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Chang, Seung, Jae Choi, and Hyun Chung. "Generalized integral transforms with the translation operator on function space." Filomat 33, no. 3 (2019): 869–80. http://dx.doi.org/10.2298/fil1903869c.

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Main goal of this paper is to establish various basic formulas for the generalized integral transform involving the generalized convolution product. In order to establish these formulas, we use the translation operator which was introduced in [9]. It was not easy to establish basic formulas for the generalized integral transforms because the generalized Brownian motion process used in this paper has the nonzero mean function. In this paper, we can easily establish various basic formulas for the generalized integral transform involving the generalized convolution product via the translation operator.

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MUSIELAK, J., and A. WASZAK. "Generalized variation and translation operator in some sequence spaces." Hokkaido Mathematical Journal 17, no. 3 (October 1988): 345–53. http://dx.doi.org/10.14492/hokmj/1381517818.

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Ceccherini-Silberstein, T. G., and A. Y. Samet-Vaillant. "Gromov's translation algebras, growth and amenability of operator algebras." Expositiones Mathematicae 26, no. 2 (May 2008): 141–62. http://dx.doi.org/10.1016/j.exmath.2007.09.001.

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Hastriter, Michael Larkin, Shinichiro Ohnuki, and Weng Cho Chew. "Error control of the translation operator in 3D MLFMA." Microwave and Optical Technology Letters 37, no. 3 (March 19, 2003): 184–88. http://dx.doi.org/10.1002/mop.10862.

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Du, Guanglong, Ping Zhang, and Xueqian Wang. "Human-Manipulator Interface Using Particle Filter." Scientific World Journal 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/692165.

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This paper utilizes a human-robot interface system which incorporates particle filter (PF) and adaptive multispace transformation (AMT) to track the pose of the human hand for controlling the robot manipulator. This system employs a 3D camera (Kinect) to determine the orientation and the translation of the human hand. We use Camshift algorithm to track the hand. PF is used to estimate the translation of the human hand. Although a PF is used for estimating the translation, the translation error increases in a short period of time when the sensors fail to detect the hand motion. Therefore, a methodology to correct the translation error is required. What is more, to be subject to the perceptive limitations and the motor limitations, human operator is hard to carry out the high precision operation. This paper proposes an adaptive multispace transformation (AMT) method to assist the operator to improve the accuracy and reliability in determining the pose of the robot. The human-robot interface system was experimentally tested in a lab environment, and the results indicate that such a system can successfully control a robot manipulator.

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Fishel, B. "The Fourier–Plancherel transform as a spectral representation of a rigged Hilbert space." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 3 (May 1987): 567–73. http://dx.doi.org/10.1017/s0305004100066925.

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In ‘Generalized Translation Operators…’ [3] algebras associated with a self-adjoint operator were investigated. Examples were given in the cases, inter alia, of the operators Mt and i d/dt in the space L2(ℝ, m) (m = Lebesgue measure). This paper shows that by suitably rigging the space the examples can be seen as natural generalizations of certain familiar algebras. The rigging enables us to introduce, rigorously, into L2(ℝ,m) the improper elements used by Akhiezer and Glazman [1] as cyclic vectors for Mt and i d/dt in order to identify the Fourier–Plancherel transform with a spectral representation of the space.

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Elnaggar, Sameh Y., and Gregory N. Milford. "Properties of translation operator and the solution of the eigenvalue and boundary value problems of arbitrary space–time periodic metamaterials." Royal Society Open Science 8, no. 8 (August 2021): 210367. http://dx.doi.org/10.1098/rsos.210367.

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There is a recent interest in understanding and exploiting the intriguing properties of space–time metamaterials. In the current manuscript, the time periodic circuit theory is exploited to introduce an appropriate translation operator that fully describes arbitrary space–time metamaterials. It is shown that the underlying mathematical machinery is identical to the one used in the analysis of linear time invariant periodic structures, where time and space eigen-decompositions are successively employed. We prove some useful properties the translation operator exhibits. The wave propagation inside the space time periodic metamaterial and the terminal characteristics can be rigorously determined via the expansion in the operators eigenvectors (space–time Bloch waves). Two examples are provided that demonstrate how to apply the framework. In the first, a space time modulated composite right left handed transmission line is studied and results are verified via time domain computations. Furthermore, we apply the theory to explain the non-reciprocal behaviour observed on a nonlinear transmission line manufactured in our lab. Bloch-waves are computed from the extracted circuit parameters. Results predicted using the developed machinery agree with both measurements and time domain analysis. Although the analysis was carried out for electric circuits, the approach is valid for different domains such as acoustic and elastic media.

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Filali, M. "Linear equations in B(ℤ)*." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 123, no. 6 (1993): 1001–9. http://dx.doi.org/10.1017/s030821050002967x.

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SynopsisLet B(ℤ)* be the Banach dual of the space of all bounded complex-valued functions on ℤ. For each n ε ℤ, let Ln be the translation operator on B(ℤ) and Tn be its adjoint operator on B(ℤ)*. This paper concerns itself with equations of the formwhere (an)nεℤ is a sequence of complex numbers.

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Yu, Gyeong-In, Saeed Amizadeh, Sehoon Kim, Artidoro Pagnoni, Ce Zhang, Byung-Gon Chun, Markus Weimer, and Matteo Interlandi. "WindTunnel." Proceedings of the VLDB Endowment 15, no. 1 (September 2021): 11–20. http://dx.doi.org/10.14778/3485450.3485452.

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While deep neural networks (DNNs) have shown to be successful in several domains like computer vision, non-DNN models such as linear models and gradient boosting trees are still considered state-of-the-art over tabular data. When using these models, data scientists often author machine learning (ML) pipelines: DAG of ML operators comprising data transforms and ML models, whereby each operator is sequentially trained one-at-a-time. Conversely, when training DNNs, layers composing the neural networks are simultaneously trained using backpropagation. In this paper, we argue that the training scheme of ML pipelines is sub-optimal because it tries to optimize a single operator at a time thus losing the chance of global optimization. We therefore propose WindTunnel: a system that translates a trained ML pipeline into a pipeline of neural network modules and jointly optimizes the modules using backpropagation. We also suggest translation methodologies for several non-differentiable operators such as gradient boosting trees and categorical feature encoders. Our experiments show that fine-tuning of the translated WindTunnel pipelines is a promising technique able to increase the final accuracy.

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Ravat, Franck, Jiefu Song, and Olivier Teste. "OLAP Analysis Operators for Multi-State Data Warehouses." International Journal of Data Warehousing and Mining 12, no. 4 (October 2016): 20–53. http://dx.doi.org/10.4018/ijdwm.2016100102.

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Data reduction in Multidimensional Data Warehouses (MDWs) allows increasing the efficiency of analysis and facilitating decision-makers' tasks. In this paper, the authors model a MDW containing reduced data through a set of states. Each state is valid for a certain period of time; it contains only useful information according to decision-makers' needs. In order to carry out analyses in a MDW composed of multiple states, an extension of traditional OLAP analysis operators is required. In this paper, the authors define a set of OLAP operators compatible with reduced MDWs. For each operator, they propose a user-oriented definition along with an algorithmic translation. To show the feasibility and the efficiency of the proposed concepts, they implement the analysis operators in an R-OLAP framework.

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Ergul, O., and L. Gurel. "Optimal Interpolation of Translation Operator in Multilevel Fast Multipole Algorithm." IEEE Transactions on Antennas and Propagation 54, no. 12 (December 2006): 3822–26. http://dx.doi.org/10.1109/tap.2006.886562.

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Kaparulin, Dmitry S. "Conservation Laws and Stability of Field Theories of Derived Type." Symmetry 11, no. 5 (May 7, 2019): 642. http://dx.doi.org/10.3390/sym11050642.

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We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another formally self-adjoint operator, while each isometry of space-time gives rise to the series of symmetries of action functional. If the wave operator is given by n-th-order polynomial then this series includes n independent entries, which can be explicitly constructed. The Noether theorem is then used to construct an n-parameter set of second-rank conserved tensors. The canonical energy-momentum tensor is included in the series, while the other entries define independent integrals of motion. The Lagrange anchor concept is applied to connect the general conserved tensor in the series with the original space-time translation symmetry. This result is interpreted as existence of multiple energy-momentum tensors in the class of derived systems. To study stability we seek for bounded-conserved quantities that are connected with the time translations. We observe that the derived theory is stable if its wave operator is defined by a polynomial with simple and real roots. The general constructions are illustrated by the examples of the Pais–Uhlenbeck oscillator, higher-derivative scalar field, and extended Chern–Simons theory.

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Angulo, Jesús, and Santiago Velasco-Forero. "STRUCTURALLY ADAPTIVE MATHEMATICAL MORPHOLOGY BASED ON NONLINEAR SCALE-SPACE DECOMPOSITIONS." Image Analysis & Stereology 30, no. 2 (June 30, 2011): 111. http://dx.doi.org/10.5566/ias.v30.p111-122.

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Standard formulation of morphological operators is translation invariant in the space and in the intensity: the same processing is considered for each point of the image. A current challenging topic in mathematical morphology is the construction of adaptive operators. In previous works, the adaptive operators are based either on spatially variable neighbourhoods according to the local regularity, or on size variable neighbourhoods according to the local intensity. This paper introduces a new framework: the structurally adaptive mathematical morphology. More precisely, the rationale behind the present approach is to work on a nonlinear multi-scale image decomposition, and then to adapt intrinsically the size of the operator to the local scale of the structures. The properties of the derived operators are investigated and their practical performances are compared with respect to standard morphological operators using natural image examples.

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Kryzhevich, Sergey, Viktor Avrutin, Nikita Begun, Dmitrii Rachinskii, and Khosro Tajbakhsh. "Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps." Axioms 10, no. 2 (May 2, 2021): 80. http://dx.doi.org/10.3390/axioms10020080.

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We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.

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