Derived tubular strongly simply connected algebras

Let be a finite dimensional algebra over an algebraically closed field . Assume for a connected quiver and an admissible ideal of . We study algebras which are derived equivalent to tubular algebras. If is strongly simply connected and has more than six vertices, then is derived tubular if and only if (i) the homological quadratic form is a non-negative of corank two and (ii) no vector of is orthogonal (with respect tho the homological bilinear form) to the radical of .

     

Constitutive modeling of the mechanics associated with crystallizable shape memory polymers

Shape memory polymers are novel materials that can be easily formed into complex shapes, retaining memory of their original shape even after undergoing large deformations. The temporary shape is stable and return to the original shape is triggered by a suitable mechanism such as heating. In this paper, we develop constitutive equations to model the mechanical behavior of crystallizable shape memory polymers. Crystallizable shape memory polymers are called crystallizable because the temporary shape is fixed by a crystalline phase, while return to the original shape is due to the melting of this crystalline phase. The modeling is done using a framework that was developed recently for studying crystallization in polymers ([28], [25], [27], [31]) and is based on the theory of multiple natural configurations. In this paper we formulate constitutive equations for the original amorphous phase and the semi-crystalline phase that is formed after the onset of crystallization. In addition we model the melting of the crystalline phase to capture the return of the polymer to its original shape. The model has been used to simulate a typical uni-axial cycle of deformation, the results of this simulation compare very well with experimental data. In addition to this we also simulate circular shear of a hollow cylinder and present results for different cases in this geometry.     

Constitutive modeling of the mechanics associated with crystallizable shape memory polymers

Shape memory polymers are novel materials that can be easily formed into complex shapes, retaining memory of their original shape even after undergoing large deformations. The temporary shape is stable and return to the original shape is triggered by a suitable mechanism such as heating. In this paper, we develop constitutive equations to model the mechanical behavior of crystallizable shape memory polymers. Crystallizable shape memory polymers are called crystallizable because the temporary shape is fixed by a crystalline phase, while return to the original shape is due to the melting of this crystalline phase. The modeling is done using a framework that was developed recently for studying crystallization in polymers ([28], [25], [27], [31]) and is based on the theory of multiple natural configurations. In this paper we formulate constitutive equations for the original amorphous phase and the semi-crystalline phase that is formed after the onset of crystallization. In addition we model the melting of the crystalline phase to capture the return of the polymer to its original shape. The model has been used to simulate a typical uni-axial cycle of deformation, the results of this simulation compare very well with experimental data. In addition to this we also simulate circular shear of a hollow cylinder and present results for different cases in this geometry. Received: January 5, 2005     

Scattering of N(2)O on electron impact over an extensive energy range (0.1 eV-2000 eV)

We report electron impact total cross sections, Q(T), for e-N(2)O scattering over an extensive range of impact energies approximately from 0.1 eV to 2000 eV. We employ an ab initio calculation using R-matrix formalism below the ionization threshold of the target and above it we use the well established spherical complex optical potential to compute the cross sections. Total cross section is obtained as a sum of total elastic and total electronic excitation cross sections below the ionization threshold and above the ionization threshold as a sum of total elastic and total inelastic cross sections. Ample cross section data for e-N(2)O scattering are available at low impact energies and hence meaningful comparisons are made. Good agreement is observed with the available theoretical as well as experimental results over the entire energy range studied here.     

Ultrasonic Agitation in Basic Alumina Catalyzed Aldol Condensation of Ketones

The use of ultrasonic irradiation to improve the yield and to shorten the reaction time of aldol dimerization of ketones catalyzed with basic alumina is described.     

Estimating the size of a union of random subsets of fixed cardinality

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Estimating the size of a union of random subsets of fixed cardinality

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Cluster Tilted Algebras with a Cyclically Oriented Quiver

In association with a finite dimensional algebra A of global dimension two, we consider the endomorphism algebra of A, viewed as an object in the triangulated hull of the orbit category of the bounded derived category, in the sense of Amiot. We characterize the algebras A of global dimension two such that its endomorphism algebra is isomorphic to a cluster-tilted algebra with a cyclically oriented quiver. Furthermore, in the case that the cluster tilted algebra with a cyclically oriented quiver is of Dynkin or extended Dynkin type then A is derived equivalent to a hereditary algebra of the same type.     

A comparative study of novel chalcone derivative by X-ray and quantum chemical calculations (Ab-initio and DFT): Experimental and theoretical approach

A novel bio-organic molecule, 3-(3-chloro-4-methoxy-phenyl)-1-(4,5-dimethoxy-2-methyl phenyl) prop-2-en-1-one (I), has been synthesized and characterized by FTIR, ¹H, and ¹³C NMR. To understand the role of solvents, UV-vis absorption, and fluorescence study has been carried out using different solvents. The single-crystal X-ray diffraction technique has been studied to confirm the three dimensional structure of the compound and the hydrogen bond interactions involved in the stability of the structure. The ab-initio and density functional theory (DFT) are used to optimize the molecular structure. The calculated results show that the predicted geometry can well reproduce structural parameters. In addition, frontier molecular orbitals and Mullikan charge distributions are carried out by using RHF and B3LYP methods. The synthesized compound has been screened for its antimicrobial and antifungal activities against different panel of organisms.     

Modeling the film casting process using a continuum model for crystallization in polymers

In this paper, the film casting process has been simulated using a new model developed recently using the framework of multiple natural configurations to study crystallization in polymers (see Rao and Rajagopal Z. Angew. Math. Phys. 53 (2002) 265; Polym. Eng. Sci. 44(1) (2004) 123; Simulation of the film blowing process for semicrystalline polymers, in press, 2004). In the film casting process, the material starts out as a viscoelastic melt and undergoes deformation and cooling, resulting in a semi-crystalline solid. In order to model the complex changes taking place in the material and predict the behavior of the final solid it is important to use models that are capable of describing these changes. The model used here has been formulated within a general thermodynamic framework that is capable of describing dissipative processes. In addition it handles in a direct manner the change of symmetry in the material; it thus provides a good basis for studying the crystallization process in polymers. The polymer melt is modeled as a rate type viscoelastic fluid and the crystalline solid polymer is modeled as an anisotropic elastic solid. The initiation criterion, marking the onset of crystallization and equations governing the crystallization kinetics arise naturally in this setting in terms of the appropriate thermodynamic functions. The mixture region, wherein the material transitions from a melt to a semi-crystalline solid, is modeled as a mixture of a viscoelastic fluid and an elastic solid. This is in marked contrast to earlier approaches where in the simulation has been done assuming that the material was a viscous fluid and the transition to a solid like behavior is achieved by increasing the viscosity to a large value resulting in a highly viscous fluid and not an elastic solid. The results of our simulations compare well against experimental data available in literature. In addition to these quantitative comparisons have carried out parametric study to study the influence of the different parameters on the film casting process.