Optimization of the locations of the loudspeaker and absorption material in a small room

The sound field both in the loudspeaker box and in the room is calculated by an analytical solution of three-dimensional wave equation. It is shown in theory that the amplitude response in small rooms is affected by the following positions: driver position on the front panel of the box, box position in the room, absorption material position in the box and absorption material position on the interior walls of the room. Both our computer prediction and experiments prove that the optimum positions are beneficial to the amplitude response.     

小波包去噪信号的分形特征

将分形理论与小波包滤波相结合，用盒维数的大小来评判信号曲线的滤波情况。随着小波包分解尺度的增大，滤波后信号曲线的盒维数逐渐减小，并最后趋于稳定值。因此可以根据盒维数-分解尺度曲线来选择最佳分解尺度。对仿真含噪信号进行了滤波实验，结果表明：即使在信噪比低至0．5时仍能得到较好的结果，并且该法用于毛细管电泳实验数据的处理结果同样令人满意。     

Stereochemistry of cyclic ether formation—II : Intramolecular cyclisation of secondary aliphatic alcohols to tetrahydrofuran-type ethers

The mechanism and stereochemistry of δ-C atom functionalisation in the reactions of secondary straight-chain aliphatic alcohols with lead tetraacetate, ceric ammonium nitrate, and heavy metal (Pb⁴⁺, Hg²⁺, Ag⁺) salts (AcO)^?1, O^2?, CO₃^2?-halogen (I₂, Br₂, Cl₂) combinations are discussed. By demonstrating the intermediacy of 5-bromo-2-hexanol, it was confirmed that the dark silver oxidebromine induced cyclisation of 2-hexanol (and alcohols in general) involves (as the other hypohalite reactions) intramolecular 1,5-hydrogen abstraction by alkoxy radicals and formation of δ-bromohydrins. A novel and simple procedure for obtaining tetrahydrofurans from alcohols by way of the hypochlorite reaction, using silver or mercuric salts and chlorine, is described.     

A decomposition procedure for the determination of arsenic in marine samples

The use of wet and dry ashing procedures to decompose marine biological tissues and to degrade organoarsenic compounds to inorganic arsenic for analysis by zinc-column arsine generation and atomic-absorption spectrophotometry was investigated. Wet ashing with nitric, sulphuric and perchloric acids (10:2:3 v/v) released the largest percentage of arsenic from fish tissue and quantitatively degraded methylated and other organoarsenic compounds to inorganic arsenic. The arsenic concentrations found when standard reference materials were ashed with this acid mixture were in agreement with the certified values.     

Oxidative cyclization of 2-pyrrolidinyl-acetamide and 2-pyrrolidinyl-propionamide local anaesthetics

2 - Pyrrolidinyl - acetamide and -propionamide local anaesthetics (1a–d) on oxidation with mercuric acetate, potassium hexacyanoferrate(III) and potassium permanganate underwent oxidative cyclization to give new bicyclic compounds, hexahydro - 1H - pyrrolo[1,2 - a]imidazolin - 2 - ones (2a–d). The propionamides (1c–d) yielded mixtures of the two possible diastereoisomers of 2c and 2d. These were separated; in solution and above their melting points they epimerized via ring opening and reclosure between the 7a-carbon and 1-nitrogen atoms.     

On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds

We consider a new algorithm, an interior-reflective Newton approach, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generatesstrictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths (reflection paths). The interior-reflective approach does not require identification of an activity set. In this paper we establish that the interior-reflective Newton approach is globally and quadratically convergent. Moreover, we develop a specific example of interior-reflective Newton methods which can be used for large-scale and sparse problems.Research partially supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG02-86ER25013.A000, and in part by NSF, AFOSR, and ONR through grant DMS-8920550, and by the Advanced Computing Research Institute, a unit of the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of its Corporate Research Institute.Corresponding author.     

Conformational studies of 1,2,3-trichloro- and 1,2,3-tribromopropane by nuclear magnetic resonance spectroscopy: attractive parallel (1:3) halogen-hydr

Analysis of the NMR spectra of 1,2,3-trichloropropane and 1,2,3-tribromopropane in various media shows the most stable conformer to be AG_-. The populations of several conformera have been estimated by using pure trans and gauche coupling constants obtained from closely similar molecules. The calculated populations found in non-polar solvents agree well with those obtained by electron diffraction studies in the gas phase. It is suggested that the AG_- form is stabilised relative to AG₊ by the former having two parallel (1:3) halogen-hydrogen attractions against one in the AG₊ form. Comparison is made to related molecules where the most stable conformers also have the greatest number of parallel (1:3) halogen-hydrogen interactions.     

Photochemistry of β, γ-unsaturated ketones-V: The direct irradiation of some γ-phenyl β, γ-enones

The photochemistry of some members of the two series of γ-phenyl substituted acyclic β, γ-unsaturated ketones 1 and 2 upon direct irradiation with γ 310nm has been investigated, viz 1c–1h and 2b+2c.The alkyl substituted (E)-5-phenyl-4-penten-2-ones 1c–1h yield the corresponding 1,3-acyl shift products and (Z)-isomers, and 1g and 1h in addition two decarbonylated products. 2b only yields the (Z)-isomer and some benzaldehyde, but 2c yields the 1,3-acyl shift product, the ODPM product, three hydrocarbons formed by disproportionation of the allyl radical, and some benzaldehyde. The β-phenyl β, γ-UK 3a proved to be photostable. The 1,3-acyl shift products of 1c–1h result mainly from the singlet excited state in a cage radical process. The exclusive formation of the (E)-configuration of the 1,3-acyl shift product is explained in terms of conformational preference of the intermediate allyl radical. It is proposed that the formation of the (Z)-isomer proceeds from ¹T(π -π^*) which is populated according to

. Evidence is presented which supports the proposed mechanism.The β,γ-UK 2b containing a benzoyl moiety leads to a higher degree of (E)-(Z) isomerization than the corresponding 1d which has an acetyl moiety.The triplet energies of (E)- and (Z)-1h are 56 and ca 70 kcal/mol respectively.     

Some Remarks on One-dimensional Functions and Their Riemann–Liouville Fractional Calculus

A one-dimensional continuous function of unbounded variation on [0,1] has been constructed.The length of its graph is infnite,while part of this function displays fractal features.The Box dimension of its Riemann–Liouville fractional integral has been calculated.     

On the symmetry of three identical interacting particles in a one-dimensional box

We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group D_3d$D_{3d}$. Group theory greatly facilitates the application of perturbation theory and the Rayleigh–Ritz variational method. A great advantage is that every irreducible representation can be treated separately. Group theory enables us to predict the connection between the states for the small box length and large box length regimes of the system. We discuss the crossings and avoided crossings of the energy levels as well as other interesting features of the spectrum of the system.