Fluctuation,thermal impurity depinning and commensurate-incommensurate transition of change density waves on the (100) face of W

Recent experiments on the (100) face of W with and without H is interpreted. The significance of large thermal fluctuation in low dimensionality situation and their observation in the present system is pointed out. A thermal impurity depinning transition is discussed. The existence of a commensurate-incommensurate transition as hydrogen coverage is changed is speculated.     

Structure of 72,74Se at high spin

Lifetimes of high spin states up to { }=22⁺ in the yrast positive parity bands have been measured to investigate the shape evolution with increasing spin in ^{72, 74}Se. The Q _t values derived from these measurements indicate that prolate shape stabilizes for ⁷²Se, while a triaxial shape develops for ⁷⁴Se at higher spins. Comparison of the observed trend in Q _t with spin for ^{72, 74}Se with that of the corresponding kryptones isotones emphasizes the stability provided by N=38 prolate shell gap even at high rotational frequency.     

Statics and dynamics of phase segregation in multicomponent fermion gas

We investigate the statics and dynamics of spatial phase segregation process of a mixture of fermion atoms in a harmonic trap using the density functional theory. The kinetic energy of the fermion gas is written in terms of the density and its gradients. Several cases have been studied by neglecting the gradient terms (the Thomas-Fermi limit) which are then compared with the Monte-Carlo results using the full gradient corrected kinetic energy. A linear instability analysis has been performed using the random-phase approximation. Near the onset of instability, the fastest unstable mode for spinodal decomposition is found to occur at q = 0. However, in the strong coupling limit, many more modes with q ≈ K _F decay with comparable time scales. Received 12 September 2001 Published online 24 September 2002 RID="a" ID="a"e-mail: k1@sharif.edu RID="b" ID="b"Permanent address: Dr. Vijay Kumar Foundation, 45 Bazaar Street, K.K. Nagar (West), Chennai 600 078, India.     

From Bounded Families of Localized Cosines to Bi-Orthogonal Riesz Bases via Shift-Invariance

The notion of bi-inner product functionals generated by two Bessel sequences {f _n } and {g _n } of functions from L ² was introduced in our earlier work as a vehicle to identify dual frames and bi-orthogonal Riesz bases of L ². The objective was to find conditions under which P is a constant mu<iple of the inner product <f,g> of L ². A necessary and suffici condition derived in is that P is both spatial shift-invariant and phase shift-invariant. A<hough these two shift-invariance properties are, in general, unrelated, it could happen that one is a consequence of the other for certain clases of Bessel sequences {f _n } and {g _n }. In this paper, we show that, indeed, for localized cosines with two-overlapping windoes (i.e., only adjacent window functions are allowed to overlap), spatial shift-invariance of P is already sufficient to guarantee that P is a constant mu<iple of the inner product, while phase shift-invariance is not. Hence, phase shift-invariance of P for two-overlapping localized cosine Bessel sequences is a consequence of spatial shift-invariance, but the converse is not valid. As an application, we also show that two families of localized cosines with uniformly bounded and two-overlapping windows are bi-orthogonal Riesz bases of L ², if and only if P is spatial shift-invariant. In addition, we apply this resu< to generalize a resu< on characterization of dual localized cosine bases in our earlier work in to the mu<ivariate setting. A method for computing the dual windows is also given in this paper.     

Understanding the Origins of Nucleophilic Hydride Reactivity of a Sodium Hydride–Iodide Composite

Sodium hydride (NaH) has been commonly used as a Brønsted base in chemical syntheses, while it has rarely been employed to add hydride (H^?) to unsaturated electrophiles. We previously developed a procedure to activate NaH through the addition of a soluble iodide source and found that the new NaH–NaI composite can effect even stereoselective nucleophilic hydride reductions of nitriles, imines, and carbonyl compounds. In this work, we report that mixing NaH with NaI or LiI in tetrahydrofuran (THF) as a solvent provides a new inorganic composite, which consists of NaI interspersed with activated NaH, as revealed by powder X‐ray diffraction, and both solid‐state NMR and X‐ray photoelectron spectroscopies. DFT calculations imply that this remarkably simple inorganic composite, which is comprised of NaH and NaI, gains nucleophilic hydridic character similar to covalent hydrides, resulting in unprecedented and unique hydride donor chemical reactivity.     

Theoretical study of gas phase reactions of important SOA intermediates: (cis‐ and trans‐) BEPOX and β‐IEPOX with OH radical

Mechanisms for hydroxide radicals reacting with 2,3‐epoxy‐1,4‐butanediol (BEPOX) and 2‐methyl‐2,3‐epoxy‐1,4‐butanediol (β‐IEPOX) in the gas phase are investigated using quantum chemistry computations. Geometries of all the structures are optimized at the X3LYP/6‐31+g(d,p) level. The ground‐state energy for each structure is then refined at the CCSD(T)/6‐31+g(d,p) level. All possible reaction paths for BEPOX and β‐IEPOX are analyzed. The results show that during BEPOX and β‐IEPOX gas phase reactions, hydrogen abstractions on C_chain? H are the most energetically favorable reaction paths (S3, S7) while the addition reactions (S6, S9) are not likely to occur. The present theoretical study is consistent with previous experimental results. © 2013 Wiley Periodicals, Inc.     

A General framework for local interpolation

Summary We present a general framework for the construction of local interpolation methods with a given approximation order. Some applications to multivariate spline spaces are presented.Supported by the National Science Foundation, Contract Nos. DMS-8602337 and DMS-8701190Sponsored by Defense Advanced Research Projects Agency (DARPA), under contract No. MDA 972-88-C-0047 for DARPA Initiative in Concurrent Engineering (DICE)     

Constrained best approximation in Hilbert space

In this paper we study the characterization of the solution to the extremal problem inf{‖x‖x ∈C ∩M}, wherex is in a Hilbert spaceH, C is a convex cone, andM is a translate of a subspace ofH determined by interpolation conditions. We introduce a simple geometric property called the “conical hull intersection property” that provides a unifying framework for most of the basic results in the subject of optimal constrained approximation. Our approach naturally lends itself to considering the data cone as opposed to the constraint cone. A nice characterization of the solution occurs, for example, if the data vector associated withM is an interior point of the data cone.     

The Synthesis of a Series of Phosphoryl Coumarins

Different hydroxy substituted coumarins were successfully phosphorylated with diisopropylphophite （DIPPH） by the Atherton-Todd reaction in 76-89% yields. Moreover, the reaction activities of different hydroxys of the coumarins in the Atherton-Todd reaction were studied.