scholarly journals Comultiplication Rules for the Double Schur Functions and Cauchy Identities

10.37236/102 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
A. I. Molev
Keyword(s):  
Symmetric Functions ◽  
Schur Functions ◽  
Primitive Elements ◽  
Expansion Formula ◽  
New Family ◽  
Dual Object ◽  
Multiplication Rule ◽  
Distinguished Basis ◽  
Natural Way

The double Schur functions form a distinguished basis of the ring $\Lambda(x\!\parallel\!a)$ which is a multiparameter generalization of the ring of symmetric functions $\Lambda(x)$. The canonical comultiplication on $\Lambda(x)$ is extended to $\Lambda(x\!\parallel\!a)$ in a natural way so that the double power sums symmetric functions are primitive elements. We calculate the dual Littlewood–Richardson coefficients in two different ways thus providing comultiplication rules for the double Schur functions. We also prove multiparameter analogues of the Cauchy identity. A new family of Schur type functions plays the role of a dual object in the identities. We describe some properties of these dual Schur functions including a combinatorial presentation and an expansion formula in terms of the ordinary Schur functions. The dual Littlewood–Richardson coefficients provide a multiplication rule for the dual Schur functions.

scholarly journals Noncommutative Symmetric Hall-Littlewood Polynomials

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Lenny Tevlin
Keyword(s):  
Symmetric Functions ◽  
Schur Functions ◽  
Monomial Basis ◽  
Noncommutative Symmetric Functions ◽  
New Family ◽  
Littlewood Polynomials ◽  
International Audience ◽  
Noncommutative Setting

International audience Noncommutative symmetric functions have many properties analogous to those of classical (commutative) symmetric functions. For instance, ribbon Schur functions (analogs of the classical Schur basis) expand positively in noncommutative monomial basis. More of the classical properties extend to noncommutative setting as I will demonstrate introducing a new family of noncommutative symmetric functions, depending on one parameter. It seems to be an appropriate noncommutative analog of the Hall-Littlewood polynomials. Les fonctions symétriques non commutatives ont de nombreuses propriétés analogues à celles des fonctions symétriques classiques (commutatives). Par exemple, les fonctions de Schur en rubans (analogues de la base de Schur classique) admettent des développements à coefficients positifs dans la base des monômes non commutatifs. La plupart des propriétés classiques s'étendent au cas non commutatif, comme je le montrerai en introduisant une nouvelle famille de fonctions symétriques non commutatives, dépendant d'un paramètre. Cette famille semble être un analogue non commutatif approprié de la famille des polynômes de Hall-Littlewood.

scholarly journals The Role of Global Appearance of Omnidirectional Images in Relative Distance and Orientation Retrieval

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3327
Author(s):  
Vicente Román ◽  
Luis Payá ◽  
Adrián Peidró ◽  
Mónica Ballesta ◽  
Oscar Reinoso
Keyword(s):  
Mobile Robotics ◽  
A Priori ◽  
Computational Cost ◽  
Relevant Information ◽  
Local Features ◽  
New Family ◽  
Lighting Conditions ◽  
Omnidirectional Images ◽  
Great Development

Over the last few years, mobile robotics has experienced a great development thanks to the wide variety of problems that can be solved with this technology. An autonomous mobile robot must be able to operate in a priori unknown environments, planning its trajectory and navigating to the required target points. With this aim, it is crucial solving the mapping and localization problems with accuracy and acceptable computational cost. The use of omnidirectional vision systems has emerged as a robust choice thanks to the big quantity of information they can extract from the environment. The images must be processed to obtain relevant information that permits solving robustly the mapping and localization problems. The classical frameworks to address this problem are based on the extraction, description and tracking of local features or landmarks. However, more recently, a new family of methods has emerged as a robust alternative in mobile robotics. It consists of describing each image as a whole, what leads to conceptually simpler algorithms. While methods based on local features have been extensively studied and compared in the literature, those based on global appearance still merit a deep study to uncover their performance. In this work, a comparative evaluation of six global-appearance description techniques in localization tasks is carried out, both in terms of accuracy and computational cost. Some sets of images captured in a real environment are used with this aim, including some typical phenomena such as changes in lighting conditions, visual aliasing, partial occlusions and noise.

scholarly journals Oxidation of Terpenoids to Achieve High-Value Flavor and Fragrances—Questioning Microalgae Oxidative Capabilities in the Biotransformation of the Sesquiterpene Valencene and of Selected Natural Apocarotenoids

Chemistry ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 821-830
Author(s):  
Davide De Simeis ◽  
Stefano Serra ◽  
Alessandro Di Fonzo ◽  
Francesco Secundo
Keyword(s):  
Experimental Data ◽  
Natural Products ◽  
Aqueous Medium ◽  
Photochemical Reaction ◽  
Substrate Oxidation ◽  
Market Size ◽  
Chlorella Sp ◽  
General Opinion ◽  
Natural Way

Natural flavor and fragrance market size is expected to grow steadily due to the rising consumer demand of natural ingredients. This market request is guided by the general opinion that the production of natural compounds leads to a reduction of pollution, with inherent advantages for the environment and people’s health. The biotransformation reactions have gained high relevance in the production of natural products. In this context, few pieces of research have described the role of microalgae in the oxidation of terpenoids. In this present study, we questioned the role of microalgal based oxidation in the synthesis of high-value flavors and fragrances. This study investigated the role of three different microalgae strains, Chlorella sp. (211.8b and 211.8p) and Chlorococcum sp. (JB3), in the oxidation of different terpenoid substrates: α-ionone, β-ionone, theaspirane and valencene. Unfortunately, the experimental data showed that the microalgal strains used are not responsible for the substrate oxidation. In fact, our experiments demonstrate that the transformation of the four starting compounds is a photochemical reaction that involves the oxygen as oxidant. Even though these findings cast a shadow on the use of these microorganisms for an industrial purpose, they open a new possible strategy to easily obtain nootkatone in a natural way by just using an aqueous medium, oxygen and light.

Mothering from a Distance: The Lived Experiences of Filipina Transnational Mothers in Singapore

2021 ◽  
pp. 106648072110618
Author(s):  
Jeffrey R. Ballaret ◽  
Jonel P. Lanada
Keyword(s):  
Labor Migration ◽  
Lived Experiences ◽  
Positive Thinking ◽  
Economic Prosperity ◽  
Virtual Communication ◽  
The Past ◽  
New Family ◽  
Transnational Mothers

Transnational motherhood continues to grow among Filipina mothers. It resulted in economic prosperity and quality of life of Filipino families but caused family pressures within the sphere of motherhood. This qualitative study is grounded through the philosophical lens of phenomenology aimed to explore the lived experiences of transnational mothers. It seeks to understand their life history, present experiences that redefined their motherhood, and reflections of the future. The lived experiences of transnational mothers began with the experience of the personal and structural dimensions of poverty in the past. Their decision to embark on labor migration was primarily instrumental to alleviate their life condition. However, mothering from a distance has ensued emotional, social, and psychological strains. To cope with the situation, they observed four central coping ways: the role of faith and prayer; the repression of emotional strains through work and friends; focus and positive thinking; and the rationalization of distance by way of regular virtual communication and remittances. The hopes of transnational mothers revealed their yearning for family reunification predicated on improving their family life through financial security, savings, and children's education. This intersection between motherhood and labor migration has therefore created new family forms, structures, roles, meaning, and expectations.

scholarly journals Peran Penyuluh Agama dalam Kehidupan Beragama guna Meningkatkan Keluarga Sakinah (Studi Kasus pada Majelis Ta'lim Al-Muhajirin Sukarame II Bandar Lampung)

2019 ◽  
Vol 1 (1) ◽  
pp. 92-108
Author(s):  
Rahmat Hidayat
Keyword(s):  
Religious Language ◽  
Community Leaders ◽  
Religious Leaders ◽  
Government Program ◽  
New Family ◽  
Strategic Role ◽  
The Government ◽  
Negative Impacts

ABSTRACT  Islamic Religious Instructor has a quite strategic role in the midst of society. besides he is a preacher of Islam, also the Islamic Religious Instructor, according to his function as a guide, illuminator, and community builder with religious language. The role of religious counselors in addition to functioning as an impetus for the community to actively participate in development also plays a role in overcoming obstacles that build the course of development, particularly overcoming negative impacts. Religious instructors as religious leaders always guide, nurture, and move the community to do good and stay away from prohibited acts, inviting something that is needed by the community in fostering its territory both for the purposes of social facilities and worship. The Religious Instructor is a place to ask questions and a place to complain for his community to solve and resolve with his advice. Religious Instructors as community leaders act as priests in matters of religion and social problems as well as in matters of state by an effort to succeed the government program. The role of religious instructors in improving and creating the quality of sakinah families in the Muhajirin AL Muhajirin voluntary II Ta'lim Assembly group in Teluk Betung Barat Subdistrict, Bandar Lampung City, it can be concluded that religious counselors play an important role in improving the quality of sakinah families, one of which is in terms of worship , and also able to improve the quality of a new family and has long become a sakinah family.

scholarly journals Combinatorial Expansions in $K$-Theoretic Bases

10.37236/2320 ◽  
2012 ◽  
Vol 19 (4) ◽  
Author(s):  
Jason Bandlow ◽  
Jennifer Morse
Keyword(s):  
Generating Functions ◽  
Symmetric Functions ◽  
Schur Functions ◽  
Geometric Information ◽  
Combinatorial Description ◽  
Littlewood Polynomials ◽  
Stanley Symmetric Functions ◽  
K Theory ◽  
Combinatorial Representation

We study the class $\mathcal C$ of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape.  Included in this class are the Hall-Littlewood polynomials, $k$-Schur functions, and Stanley symmetric functions; functions whose Schur coefficients encode combinatorial, representation theoretic and geometric information. While Schur functions represent the cohomology of the Grassmannian variety of $GL_n$, Grothendieck functions $\{G_\lambda\}$ represent the $K$-theory of the same space.  In this paper, we give a combinatorial description of the coefficients when any element of $\mathcal C$ is expanded in the $G$-basis or the basis dual to $\{G_\lambda\}$.

π-TYPE FERMIONS AND π-TYPE KP HIERARCHY

2018 ◽  
Vol 61 (03) ◽  
pp. 601-613
Author(s):  
NA WANG ◽  
CHUANZHONG LI
Keyword(s):  
Symmetric Functions ◽  
Schur Functions ◽  
Kp Hierarchy ◽  
Tau Functions ◽  
The Way

AbstractIn this paper, we first construct π-type Fermions. According to these, we define π-type Boson–Fermion correspondence which is a generalization of the classical Boson–Fermion correspondence. We can obtain π-type symmetric functions Sλπ from the π-type Boson–Fermion correspondence, analogously to the way we get the Schur functions Sλ from the classical Boson–Fermion correspondence (which is the same thing as the Jacobi–Trudi formula). Then as a generalization of KP hierarchy, we construct the π-type KP hierarchy and obtain its tau functions.

scholarly journals Silicon Meets Graphene for a New Family of Near-Infrared Schottky Photodetectors

2019 ◽  
Vol 9 (18) ◽  
pp. 3677 ◽  
Author(s):  
Maurizio Casalino
Keyword(s):  
Near Infrared ◽  
Infrared Photodetectors ◽  
Strong Light ◽  
Broadband Absorption ◽  
New Family ◽  
High Carrier Mobility ◽  
Light Matter Interaction ◽  
High Carrier ◽  
Schottky Junctions

In recent years, graphene has attracted much interest due to its unique properties of flexibility, strong light-matter interaction, high carrier mobility and broadband absorption. In addition, graphene can be deposited on many substrates including silicon with which is able to form Schottky junctions, opening the path to the realization of near-infrared photodetectors based on the internal photoemission effect where graphene plays the role of the metal. In this work, we review the very recent progress of the near-infrared photodetectors based on Schottky junctions involving graphene. This new family of device promises to overcome the limitations of the Schottky photodetectors based on metals showing the potentialities to compare favorably with germanium photodetectors currently employed in silicon photonics.

scholarly journals κ-DEFORMED STATISTICS AND CLASSICAL FOUR-MOMENTUM ADDITION LAW

2008 ◽  
Vol 23 (09) ◽  
pp. 653-665 ◽  
Author(s):  
MARCIN DASZKIEWICZ ◽  
JERZY LUKIERSKI ◽  
MARIUSZ WORONOWICZ
Keyword(s):  
Minkowski Space ◽  
Fock Space ◽  
Scalar Fields ◽  
Cross Product ◽  
Creation And Annihilation Operators ◽  
Multiplication Rule ◽  
Symmetry Properties ◽  
Deformed Algebra ◽  
Free Scalar

We consider κ-deformed relativistic symmetries described algebraically by modified Majid–Ruegg bi-cross-product basis and investigate the quantization of field oscillators for the κ-deformed free scalar fields on κ-Minkowski space. By modification of standard multiplication rule, we postulate the κ-deformed algebra of bosonic creation and annihilation operators. Our algebra permits one to define the n-particle states with classical addition law for the four-momentum in a way which is not in contradiction with the nonsymmetric quantum four-momentum co-product. We introduce κ-deformed Fock space generated by our κ-deformed oscillators which satisfy the standard algebraic relations with modified κ-multiplication rule. We show that such a κ-deformed bosonic Fock space is endowed with the conventional bosonic symmetry properties. Finally we discuss the role of κ-deformed algebra of oscillators in field-theoretic noncommutative framework.

Coverings of Bipartite Graphs

1958 ◽  
Vol 10 ◽  
pp. 517-534 ◽  
Author(s):  
A. L. Dulmage ◽  
N. S. Mendelsohn
Keyword(s):  
Bipartite Graphs ◽  
The Core ◽  
Natural Way

For the purpose of analysing bipartite graphs (hereinafter called simply graphs) the concept of an exterior covering is introduced. In terms of this concept it is possible in a natural way to decompose any graph into two parts, an inadmissible part and a core. It is also possible to decompose the core into irreducible parts and thus obtain a canonical reduction of the graph. The concept of irreducibility is very easily and naturally expressed in terms of exterior coverings. The role of the inadmissible edges of a graph is to obstruct certain natural coverings of the graph.

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