Prediction of flow stress at hot working condition

A mathematical model has been developed to determine flow stress at hot deformation condition. The proposed model is capable of including work softening due to dynamic phase transformations as well as the effect of temperature and strain rate variation on flow stress utilizing the additivity rule for strain. To verify the model, hot compression tests for two grades of steels has been carried out. The comparison between the experimental and theoretical results confirms the validity of the model.     

Sulfonyl Ketenimines as Key Intermediates in One‐Pot Synthesis of N‐Sulfonyl‐2‐alkaneimidoyl Selenocyanates

Sulfonyl‐ketenimine intermediates, generated by the addition of Cu acetylides to sulfonyl azides, are trapped by KSeCN to afford N‐sulfonyl‐2‐alkaneimidoyl selenocyanates in moderate‐to‐good yields.     

A new scheme for solving nonlinear Stratonovich Volterra integral equations via Bernoulli’s approximation

In this paper, an efficient method for solving nonlinear Stratonovich Volterra integral equations is proposed. By using Bernoulli polynomials and their stochastic operational matrix of integration, these equations can be reduced to the system of nonlinear algebraic equations with unknown Bernoulli coefficient which can be solved by numerical methods such as Newton’s method. Also, an error analysis is valid under fairly restrictive conditions. Furthermore, in order to show the accuracy and reliability of the proposed method, the new approach is compared with the block pulse functions method by some examples. The obtained results reveal that the proposed method is more accurate and efficient than the block pulse functions method.     

Simple and efficient one-pot synthesis of N-phenyl-3,5-difunctionalized pyrazoles

A facile one-pot synthesis of N-phenyl-3,5-difunctionalized pyrazoles is described. The dialkyl 2-[(Z)-phenylhydrazono]succinate intermediate, which is prepared in situ from the mixture of phenylhydrazine and dialkyl acetylenedicarboxylate reacts with aroyl chloride or fumaryl chloride to afford the title compounds. Different types of compounds containing COCl functional group were used to investigate the scope and limitation of the reaction. Two -CO₂R and -O₂C groups at 3- and 5-position are potentially capable to convert to other functional groups. The reaction conditions are relatively mild and the yields are good.     

A novel isocyanide-based three-component synthesis of benzimidazo[1,2-a][1,4]diazepinones

3-(2-Formyl-1H-benzimidazol-1-yl)propanoic acid, as a bifunctional formyl acid was prepared in four steps. This compound underwent a one-pot reaction with amines and alkyl isocyanides via the Ugi 4-center-3-component condensation. A series of novel benzimidazole-fused 1,4-diazepine-5-ones were obtained via this method in moderate to excellent yields.     

A numerical approach for solving weakly singular partial integro‐differential equations via two‐dimensional‐orthonormal Bernstein polynomials with the convergence analysis

In this paper, we develop an efficient matrix method based on two‐dimensional orthonormal Bernstein polynomials (2D‐OBPs) to provide approximate solution of linear and nonlinear weakly singular partial integro‐differential equations (PIDEs). First, we approximate all functions involved in the considerable problem via 2D‐OBPs. Then, by using the operational matrices of integration, differentiation, and product, the solution of Volterra singular PIDEs is transformed to the solution of a linear or nonlinear system of algebraic equations which can be solved via some suitable numerical methods. With a small number of bases, we can find a reasonable approximate solution. Moreover, we establish some useful theorems for discussing convergence analysis and obtaining an error estimate associated with the proposed method. Finally, we solve some illustrative examples by employing the presented method to show the validity, efficiency, high accuracy, and applicability of the proposed technique.     

Strong versus weak local minimizers for the perturbed Dirichlet functional

Let be a bounded domain and . In this paper we consider functionals of the form where the admissible function belongs to the Sobolev space of vector-valued functions and is such that the integral on the right is well defined. We state and prove a sufficiency theorem for local minimizers of where . The exponent is shown to depend on the dimension and the growth condition of and an exact expression is presented for this dependence. We discuss some examples and applications of this theorem. Received: 20 July 2000 / Accepted: 7 June 2001 / Published online: 19 October 2001     

Geometry of Coadjoint Orbits and Multiplicity-one Branching Laws for Symmetric Pairs

Consider the restriction of an irreducible unitary representation π of a Lie group G to its subgroup H. Kirillov’s revolutionary idea on the orbit method suggests that the multiplicity of an irreducible H-module ν occurring in the restriction π|_H could be read from the coadjoint action of H on \(\mathcal {O}^{G} \cap \text {pr}^{-1}({\mathcal {O}}^{H})\), provided π and ν are ‘geometric quantizations’ of a G-coadjoint orbit \(\mathcal {O}^{G}\) and an H-coadjoint orbit \(\mathcal {O}^{H}\), respectively, where \(\text {pr} \colon \sqrt {-1}\mathfrak {g}^{\ast } \to \sqrt {-1}\mathfrak {h}^{\ast }\) is the projection dual to the inclusion \(\mathfrak {h} \subset \mathfrak {g}\) of Lie algebras. Such results were previously established by Kirillov, Corwin and Greenleaf for nilpotent Lie groups. In this article, we highlight specific elliptic orbits \(\mathcal {O}^{G}\) of a semisimple Lie group G corresponding to highest weight modules of scalar type. We prove that the Corwin–Greenleaf number \(\sharp (\mathcal {O}^{G} \cap \text {pr}^{-1}({\mathcal {O}}^{H}))/H\) is either zero or one for any H-coadjoint orbit \(\mathcal {O}^{H}\), whenever (G,H) is a symmetric pair of holomorphic type. Furthermore, we determine the coadjoint orbits \(\mathcal {O}^{H}\) with nonzero Corwin–Greenleaf number. Our results coincide with the prediction of the orbit philosophy, and can be seen as ‘classical limits’ of the multiplicity-free branching laws of holomorphic discrete series representations (Kobayashi [Progr. Math. 2007]).     

Observation of turbulent-driven shear flow in a cylindrical laboratory plasma device

An azimuthally symmetric radially sheared plasma fluid flow is observed to spontaneously form in a cylindrical magnetized helicon plasma device with no external sources of momentum input. A turbulent momentum conservation analysis shows that this shear flow is sustained by the Reynolds stress generated by collisional drift turbulence in the device. The results provide direct experimental support for the basic theoretical picture of drift-wave-shear-flow interactions.     

Correlation Between Segmental Dynamics,Glass Transition,and Lithium Ion Conduction in Poly(Methyl Methacrylate)/Ionic Liquid Mixture

A solid-state membrane of a polymer/ionic liquid miscible mixture, poly(methyl methacrylate) (PMMA) and 1-butyl-3-methylimidazolium hexafluorophosphate (BMIMPF₆) doped with lithium perchlorate (LiClO₄), was prepared and characterized. Miscibility, segmental dynamics, glass transition and ionic conductivity were investigated. Based on the results from differential scanning calorimetry (DSC) and dynamic mechanical thermal analysis (DMTA), the system is fully miscible and of single phase. Broadening of the glass transition was observed when increasing the amount of ionic liquid, which can be attributed to mobility and flexibility differences between the polymer and ionic liquid. A large dynamical asymmetry and intrinsic mobility difference allow segmental and structural motion/relaxation over a wider temperature range by increasing the amount of ionic liquid. Saturation recovery spin–lattice relaxation time (T₁) versus temperature obtained from ⁷Li nuclear magnetic resonance (NMR) showed high mobility of lithium ions, which was almost temperature independent. Lithium ion conductivity significantly increases with increasing ionic liquid amount. It is concluded that lithium ion mobility and its conduction is positively correlated to segmental dynamics of ion carriers in this model system, which is more noticeable in mixtures with higher amounts of the ionic liquid.