Representation Theory of Three-Dimensional Elliptical Crack Under Dynamic Loading

The relation between the normal displacement on the surface of a dynamical elliptical crack and the normal stress over the crack surface was studied. The three dimensional elastodynamic equations and Fourier Laplace transforms are used. Based on the influence function and the inversion of integral transforms, one can find that if the distribution of normal displacement on the surface of a dynamic elliptical crack is a polynomial of degree n in x 1 and x 2 , then the normal pressure acting over the ellipse is also a polynomial P n(x 1,x 2) of the same degree in x 1 and x 2 .

Rankin-Cohen Deformations and Representation Theory

The author uses the unitary representation theory of SL2(R) to understand the Rankin-Cohen brackets for modular forms. Then this interpretation is used to study the corresponding deformation problems that Paula Cohen, Yuri Manin and Don Zagier initiated. Two uniqueness results are established.

A NEW MODELLING METHOD FOR EVALUATING EXTERNAL DISTURBING POTENTIAL BASED ON THEORY OF UNIFIED REPRESENTATION OF GRAVITATIONAL FIELD

For a special use a new modelling method of evaluating external disturbing potential is presented in this paper.Being different from classical methods in physical geodesy this method is grounded upon the theory of unified representation of gravitational field.The models created in this way are particularly satisfactory for a high_speed computation of gravitational field in low altitude because they take account of topographic effects and have their kernel functions with simple structure and weak singularity.

Parseval Theory of Complex Wavelet Transform for Wavelet Family Including Rotational Parameters

A rotational parameter Rθ has been introduced to complex wavelet transform （CWT）. The rotational CWT （RCWT） corresponds to a matrix element 〈φ｜U2（θ;μ;κ）[F〉 in the context of quantum mechanics, where U2（θ;μ;κ） is a two-mode rotational displacing-squeezing operator in the 〈η｜ representation. Based on this, the Parseval theorem and the inversion formula of RCWT have been proved. The concise proof not only manifestly shows the merit of Dirac＇s representation theory but also leads to a new orthogonal property of complex mother wavelets in parameter space.

The social representation of fintech from the perspective of traditional financial sector professionals:evidence from Brazil

This study aims to reveal the social representation of fintech from the perspective of traditional financial sector professionals in Brazil—herein used as a proxy for emerging markets—to interpret and compare it with the scientific literature on the concept of fintech.To achieve this,we applied the social representations theory associated with the word evocation test,similarity analysis,and descending hierarchical classification.After analyzing the results,we perceived a partial misalignment between the existing literature on the concept of fintech and the perspective of traditional financial sector professionals concerning this construct.In contrast to the literature surveyed,the respondents lack perception regarding the potential of fintech to constitute disruptive technology for the traditional financial sector—radically transforming or even eliminating it.In addition,traditional financial sector professionals have little insight into the potential of fintech to financially include the low-income population,owing to their lower costs and greater ease of use.Finally,traditional financial sector professionals failed to appreciate the need to develop a legal and regulatory framework for the performance of fintech in emerging markets.This is a subject that has also been scantly addressed by academia.

Reduction of truss topology optimization

A reduction of truss topology design problem formulated by semidefinite optimization （SDO） is considered. The finite groups and their representations are introduced to reduce the stiffness and mass matrices of truss in size. Numerical results are given for both the original problem and the reduced problem to make a comparison.

SIMULATION OF FABRIC DRAPE USING A THIN PLATE ELEMENT WITH FINITE ROTATION

The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated. (Author abstract) 9 Refs.

Remedial Use of Gastronomic Products: Case Study of Manavgat

In the treatment of diseases or illnesses,modern medicine is used as well as traditional medicine practices.Medicinal plants are commonly used in traditional medicine.For this reason,it is seen in the literature that this subject is generally studied from pharmacology or ethnobotanical perspective.However,in-home practices,it is seen that gastronomic products are also used for healing purposes,along with medicinal and aromatic plants.This research is conducted in order to identify the remedial use of food/beverages and to evaluate them within the scope of social representation theory.The qualitative research method was preferred as the best way to observe social representations and semi-structured interviews were conducted with 20 people.As a result of the interviews,it was determined that 107 different practices were applied in the treatment of 35 diseases.These practices have been evaluated in the context of social representations,and it was concluded that scientific knowledge and common-sense.

Representations of coherent and squeezed states in an extended two-parameter Fock space

Recently an f -deformed Fock space which is spanned by ｜ n λ was introduced. These bases are the eigenstates of a deformed non-Hermitian Hamiltonian. In this contribution, we will use rather new nonorthogonal basis vectors for the construction of coherent and squeezed states, which in special case lead to the earlier known states. For this purpose, we first generalize the previously introduced Fock space spanned by ｜ n λ bases, to a new one, spanned by extended two-parameters bases ｜ n λ 1 ,λ 2 . These bases are now the eigenstates of a non-Hermitian Hamiltonian H λ 1 ,λ 2 = a λ 1 ,λ 2 a ＋ 1 2 , where a λ 1 ,λ 2 = a ＋ λ 1 a ＋ λ 2 and a are, respectively, the deformed creation and ordinary bosonic annihilation operators. The bases ｜ n λ 1 ,λ 2 are nonorthogonal （squeezed states）, but normalizable. Then, we deduce the new representations of coherent and squeezed states in our two-parameter Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states numerically.

Differential equations and Lie group representations

We discuss the role of diflterential equations in Lie group representation theory.We use Kashiwara's pentagon as a reference frame for the real representation theory and then report on some work arising from its p-adic analogue by Emerton,Kisin,Patel,Huyghe,Schmidt,Strauch using Berthelofs theory of arithmetic D-modules and Schneider-Stuhler theory of sheaves on buildings.

Convergence in Conformal Field Theory

Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory.The author reviews some main convergence results,conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras.He also reviews the related analytic extension results,conjectures and problems.He discusses the convergence and analytic extensions of products of intertwining operators(chiral conformal fields)and of q-traces and pseudo-q-traces of products of intertwining operators.He also discusses the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result.He then explains conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.

Lyric Poem as Representation： From Plato to the New Criticism

This essay treats the understanding of poetry, especially lyric poetry, as representation. The theme is developed partly as a historical survey, from the Classical Age to Romanticism and to Modernism, and through the history of aesthetics in Western terms. It offers critical scrutiny with the intention to explore a more justifiable theory of representation. Hopefully it may help to understand lyric poetry in historical contexts from Plato and Aristotle＇s imitation theories, to Beardsley＇s theory of illocutionary action and New Criticism. It is the image in lyric poetry that accounts for human action＇s being represented. Poetic beauty is an illusionary reality, as that in painting, and the role of image has been widely appreciated in producing this beauty as verbal icon. Finally, I mention the connection between Western theorizing of poetry as representation and Chinese poetry and poetics in general. We see the possibility that the importance of lyric poetry as representation can encourage comparative literature and world literature, and a general theory of representation. These might be informative in Chinese literary studies, from a theoretical point of view.

Restricting Specht modules of cyclotomic Hecke algebras

This paper proves that the restriction of a Specht module for a(degenerate or non-degenerate)cyclotomic Hecke algebra, or KLR(Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration.

Lie Invariants in Two and Three Variables

We use computer algebra to determine the Lie invariants of degree ≤ 12 in the free Lie algebra on two generators corresponding to the natural representation of the simple 3-dimensional Lie algebra sl2（C）. We then consider the free Lie algebra on three generators, and compute the Lie invariants of degree ≤ 7 corresponding to the adjoint representation of sl2（C）, and the Lie invariants of degree ≤ 9 corresponding to the natural representation of sl3（C）. We represent the action of sl2（C） and sl3（C） on Lie polynomials by computing the coefficient matrix with respect to the basis of Hall words.

Estimates of the Isovariant Borsuk–Ulam Constants of Connected Compact Lie Groups

The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ： S（V） → S（W） between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk-Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk-Ulam constant c^-G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.

Harmonic Analysis for Real Spherical Spaces

We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces Z = G/H attached to a real reductive Lie group G. A special emphasis is made to the case where Z is real spherical.

Eigenvalues of the Manifold Sp（n）/U（n）

In this paper, we give the eigenvalues of the manifold Sp（n）/U（n）. We prove that an eigenvalue λs（f1,f2,...,fn） of the Lie group Sp（n）, corresponding to the representation with label （f1, f2,..., fn）, is an eigenvalue of the manifold Sp（n）/U（n）, if and only if f1, f2,..., fn are all even.

Erdoes-Ko-Rado theorem for irreducible imprimitive reflection groups

Let Ω be a finite set, and let G be a permutation group on Ω. A subset H of G is called intersecting if for any a, 7r H, they agree on at least one point. We show that a maximal intersecting subset of an irreducible imprimitive reflection group G（m,p,n） is a coset of the stabilizer of a point in {1,... ,n} provided n is sufficiently large.

Valued Gabriel quiver of a wedge product and semiprime coalgebras

We describe the valued Gabriel quiver of a wedge product of coalgebras and study the category of comodules of a semiprime coalgebra. In particular, we prove that any monomial semiprime k-tame fc-tame coalgebra is string. We also prove a version of Eisenbud-Griffith theorem for coalgebras, namely, any hereditary semiprime strictly quasi-finite coalgebra is serial.

Clustered Hyperbolic Categories

We introduce a class of categories, called clustered hyperbolic categories, which are constructed from a categorized version of preseeds called categorical preseeds using categorical mutations that are a ＂functorial＂ edition of preseed mutations. Every Weyl preseed p gives rise to a categorical preseed P which generates a clustered hyperbolic category; this is formed by copies of categories each one of which is equivalent to the category of representations of the Weyl cluster algebra H（p）. A ＂categorical realization＂ of Weyl cluster algebra is provided in the sense of defining a map Fp from any clustered hyperbolic category induced from p to the Weyl cluster algebra H（p）, where the image of Fp generates H（p）.