Interaction between high-level and low-level image analysis for semantic video object extraction

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Free Rota-Baxter algebras and rooted trees

A Rota-Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota-Baxter relation, that generalizes the integration by parts formula. Most of the studies on Rota-Baxter algebras have been for commutative algebras. Two constructions of free commutative Rota-Baxter algebras were obtained by Rota and Cartier in the 1970s and a third one by Keigher and one of the authors in the 1990s in terms of mixable shuffles. Recently, noncommutative Rota-Baxter algebras have appeared both in physics in connection with the work of Connes and Kreimer on renormalization in perturbative quantum field theory, and in mathematics related to the work of Loday and Ronco on dendriform dialgebras and trialgebras. This paper uses rooted trees and forests to give explicit constructions of free noncommutative Rota--Baxter algebras on modules and sets. This highlights the combinatorial nature of Rota--Baxter algebras and facilitates their further study. As an application, we obtain the unitarization of Rota-Baxter algebras.Comment: 23 page

Combinatorics of renormalization as matrix calculus

We give a simple presentation of the combinatorics of renormalization in perturbative quantum field theory in terms of triangular matrices. The prescription, that may be of calculational value, is derived from first principles, to wit, the ``Birkhoff decomposition'' in the Hopf-algebraic description of renormalization by Connes and Kreimer.Comment: 10 pages, revised version, typos corrected, to appear in Phys. Lett.

Effect of Sintering Atmosphere on Phase Evolution of Hydroxyapatite Nanocomposite Powders

In the present work, pure hydroxyapatite, hydroxyapatite-20 wt% alumina and hydroxyapatite-20 wt% titanium mixtures were pressed and sintered in air, moist, and reduction atmospheres at 1200 C for 2 h. XRD investigations of sintered samples showed that, pure hydroxyapatite is stable in all three atmospheres. But, moist and reduction atmospheres were preferred to suppress the hydroxyapatite decomposition in hydroxyapatite -alumina and hydroxyapatite – titanium nanocomposites, respectively. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3494

Мерчандайзинг як партнерська взаємодія виробника та роздробу

У даній статті розглянуто мерчандайзинг як елемент комплексу маркетингових комунікацій, задачі та функції мерчандайзингу для виробника та для роздрібного торговця, їх точки пересічення та розбіжності, висувається припущення про їх взаємодію по цьому питанню, що може збільшити ефект, що очікується від використання методів мерчандайзингу в місцях продажу, як для виробника, так і для магазину.In this article merchandising is considered. Its task and functions for a producer and for a retail dealer, their intersection and divergence. There are also pulled out supposition about their cooperation in this field, what can increase an effect, which is expected from merchandising methods using to both in the places of sale

Renormalization of gauge fields using Hopf algebras

We describe the Hopf algebraic structure of Feynman graphs for non-abelian gauge theories, and prove compatibility of the so-called Slavnov-Taylor identities with the coproduct. When these identities are taken into account, the coproduct closes on the Green's functions, which thus generate a Hopf subalgebra.Comment: 16 pages, 1 figure; uses feynmp. To appear in "Recent Developments in Quantum Field Theory". Eds. B. Fauser, J. Tolksdorf and E. Zeidler. Birkhauser Verlag, Basel 200

The shape of invasion perclation clusters in random and correlated media

The shape of two-dimensional invasion percolation clusters are studied numerically for both non-trapping (NTIP) and trapping (TIP) invasion percolation processes. Two different anisotropy quantifiers, the anisotropy parameter and the asphericity are used for probing the degree of anisotropy of clusters. We observe that in spite of the difference in scaling properties of NTIP and TIP, there is no difference in the values of anisotropy quantifiers of these processes. Furthermore, we find that in completely random media, the invasion percolation clusters are on average slightly less isotropic than standard percolation clusters. Introducing isotropic long-range correlations into the media reduces the isotropy of the invasion percolation clusters. The effect is more pronounced for the case of persisting long-range correlations. The implication of boundary conditions on the shape of clusters is another subject of interest. Compared to the case of free boundary conditions, IP clusters of conventional rectangular geometry turn out to be more isotropic. Moreover, we see that in conventional rectangular geometry the NTIP clusters are more isotropic than TIP clusters

An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions

A well-known ansatz (`trace method') for soliton solutions turns the equations of the (noncommutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We develop an algebraic formalism, in particular involving a (mixable) shuffle product, to explore their structure. More precisely, we show that the equations of the noncommutative KP hierarchy and its extension (xncKP) in the case of a Moyal-deformed product, as derived in previous work, correspond to identities in this algebra. Furthermore, the Moyal product is replaced by a more general associative product. This leads to a new even more general extension of the noncommutative KP hierarchy. Relations with Rota-Baxter algebras are established.Comment: 59 pages, relative to the second version a few minor corrections, but quite a lot of amendments, to appear in J. Phys.

Tuning electronic properties and contact type in van der Waals heterostructures of bilayer SnS and graphene

Using first-principles calculations, we study the structural and electronic properties of the bilayer SnS/graphene, bilayer SnS/bilayer graphene (AA-stacked), bilayer SnS/bilayer graphene (AB-stacked) and monolayer SnS/graphene/monolayer SnS van der Waals (vdW) heterostructures. Electronic properties of all components of the vdW heterostructures are well preserved, which reflects the weakness of the vdW interaction. In the cases of bilayer SnS/graphene and bilayer SnS/bilayer graphene (AA-stacked), an Ohmic contact is formed which can be turned first into p-type and then into n-type Schottky contacts via application of an external electric field. Calculations show that an Ohmic contact is also formed at the interface of bilayer SnS/bilayer graphene (AB-stacked) heterostructure, but interestingly, by applying the perpendicular electric field a transition from semimetal/semiconductor contact to semiconductor/semiconductor one occurs which can enhance its optical properties. Alternatively, in the monolayer SnS/graphene/monolayer SnS vdW heterosructure, a p-type Schottky contact is established that changes into Ohmic contact under an applied electric field. Our results clearly indicate that the electronic properties of the vdW heterostructures can be tuned efficiently by external electric field, which is important in designing of new nanoelectronic devices.Comment: 12 pages, 11 figure