Location of saddle points and minimum energy paths by a constrained simplex optimization procedure

Two methods are proposed, one for the location of saddle points and one for the calculation of steepest-descent paths on multidimensional surfaces. Both methods are based on a constrained simplex optimization technique that avoids the evaluation of gradients or second derivative matrices. Three chemical reactions of increasing structural complexity are studied within the PRDDO SCF approximation. Predicted properties of reaction hypersurfaces are in good overall agreement with those determined by gradient minimization and gradient following algorithms in connection with various ab initio SCF methods. Computational efforts required by the new procedures are discussed.     

Solutions of alkali soaps and water in fatty acids IX. The location of theL 2-phase in three-component systems of sodium soap — fatty acid — water,in view of the occurrence of acid soaps

Previous studies of the occurrence of acid soaps in systems containing a longchain sodium soap and the corresponding fatty acid, and the study of phase equilibria in the system sodium octanoate — octanoic acid — water, performed by our group at the beginning of the 1960s, show that the isotropic liquidL ₂-phase of the last mentioned system in its whole region of existence is situated in that part in which acid soaps occur. This provides an explanation for the fact that theL ₂-phase itself contains acid sodium octanoates in all regions. TheL ₂-phase has its origin in the water-free melt of fatty acid and neutral soap in which these components react with each other under the formation of an acid soap. When water is added to the system, this water-free acid soap is transformed into different hydrated acid soaps. In a large region of concentration, there is an extremely close relation between theL ₂-phase and the liquid-crystalline lamellarD-phase, which itself consists of hydrated acid soaps. At its outermost water-rich tip, theL ₂-phase is in equilibrium with theL ₁-phase of the system, just above the+LAC, that is, with the most dilute aqueous soap solution in which acid soap still may be formed in aqueous environment. Formation of acid soap is a fundamental requirement for the existence of this isotropic liquidL ₂-phase.     

High-Throughput Analysis of Sofalcone in Human Plasma by Use of Automated 96-Well Protein Precipitation and LC-MS-MS

A sensitive and selective method for the determination of sofalcone in human plasma was established by use of protein precipitation and liquid chromatography-tandem mass spectrometry. Plasma samples were transferred into 96-well plate using an automated sample handling system and spiked with 10 L of 2 g mL^–1 internal standard solution (d₃-sofalcone). 0.5 mL of acetonitrile was added to the 96-well plate and the plasma samples were then vortexed for 30 sec. After centrifugation, the supernatant was transferred into another 96-well plate and completely evaporated at 40 °C under a stream of nitrogen. The dry residue was reconstituted with mobile phase. All sample transfer and protein precipitation was automated through the application of both the PerkinElmer MultiPROBE II HT and TOMTEC Quadra 96 workstation. The limit of quantitation of sofalcone was 2 ng mL^–1 using a sample volume of 0.2 mL for the analysis. The reproducibility of the method was evaluated by analyzing five samples at nine quality control (QC) levels over the nominal concentration range from 2 ng mL^–1 to 1000 ng mL^–1. Validation of the method showed that the assay has good precision and accuracy. Sofalcone and internal standard produced a protonated precursor ion ([M+H]⁺) at m/z 451 and 454, and both gave a corresponding product ion at m/z 315. The high sample throughput of the method has been successfully applied to a pharmacokinetic study of sofalcone in human plasma.     

Evaluation of phenyldimethylethoxysilane treated high-performance thin-layer chromatographic plates. Application to analysis of flavonoids inScutellariae radix

Summary The retention and selectivity of flavonoids (baicalin, baicalein, wogonin, oroxylin A) inScutellariae radix have been studies by high-performance thin-layer chromatography on phenyldimethylethoxysilane-treated silica plates. The silica plates treated with phenyl groups were used for physical and chemical analysis. From elemental carbon analysis, the maximum number of bonded phenyl surface groups per gram was calculated to be 0.467×10²¹ (Oginal silica plate: Merck Art. 15109, Silica gel 100 F₂₅₄). With methanol-1/15 M phosphate buffer (pH 6.2) mixtures as mobile phase, baicalin, baicalein, wogonin, and oroxylin A inScutellariae radix were separated. It has been shown that phenyl-treated plates are more suitable for selective separation of baicalin, baicalein, wogonin, and oroxylin A than octadecyl-treated plates.     

Surface free energies of styrene-acrylic acid copolymer plates prepared in various frames

Styrene (St)-acrylic acid (AA) copolymer plates were synthesized in the frames made of glass, aluminum (Al) and poly(difluoroethylene) (PDFE). Surface properties of the prepared copolymer plates were characterized with regard to critical surface tension ( _C ), chemical components by IR analysis and surface energies (total energy, _S ; dispersion force components, _S ^d ; polar component, _S ^p ; hydrogen bonding component, _S ^h ) and the following results were obtained.The _C values of the copolymer plates increased with AA content and also depended on the sort of the used frame. The increasing order of the _C values of the copolymer plates corresponded to those of the used frames, namely, PDFE frame < Al frame < Glass frame.The prepared copolymer plates with low AA contents (ca. 10 mol%) were enriched in the AA moiety in the surface layer regardless of the kind of the used frame.The total and the individual components of the surface free energies of the copolymer plates were largely affected by the property of the used frame. The glass frame gave the plate with higher _S ^h values suggesting preferential orientation of the polar site of AA component.     

Facility location in the presence of forbidden regions,I: Formulation and the case of Euclidean distance with one forbidden circle

A constrained form of the Weber problem is formulated in which no path is permitted to enter a prespecified forbidden region $\text{R}$ of the plane. Using the calculus of variations the shortest path between two points $\text{x}\text{,}\text{y}\text{?}\text{R}$ which does not intersect $\text{R}$ is determined. If $\text{d(}\text{x}\text{,}\text{y}\text{)}$ is unconstrained distance, we denote the shortes distance along a feasible path by $\text{d}\text{(}\text{x}\text{y}\text{)}$. The constrained Weber problem is, then: given points $\text{x}{}_{\mathrm{j}}\text{?}\text{R}$ and positive weights w_j, j = 1,2,…,n, find a point $\text{x}\text{?}\text{R}$ such that

$\text{f(}\text{x}\text{)=}\text{Σ}\text{n}\text{j=1}\text{d(}\text{x}\text{,}\text{x}{}_{\mathrm{j}}\text{)}$

is a minimum.An algorithm is formulated for the solution of this problem when $\text{d(}\text{x}\text{,}\text{y}\text{)}$ is Euclidean distance and $\text{R}$ is a single circular region. Numerical results are presented.     

Oblique Perforation of Thick Metallic Plates by Rigid Projectiles

Oblique perforation of thick metallic plates by rigid projectiles with various nose shapes is studied in this paper. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. It is shown that the perforation of a thick plate is dominated by several non-dimensional numbers, i.e., the impact function, the geometry function of projectile, the non-dimensional thickness of target and the impact obliquity. Explicit formulae are obtained to predict the ballistic limit, residual velocity and directional change for the oblique perforation of thick metallic plates. The proposed model is able to predict the critical condition for the occurrence of ricochet. The proposed model is validated by comparing the predictions with other existing models and independent experimental data.The English text was polished by Keren Wang     

沿板平面材料梯度变化功能材料板件分析

本文发展一种功能梯度构件分析的细观元法.细观元法在构件的常规有限元内部设置密集观细单元以反映材料特性变化,又通过协调条件将各细观元结点自由度转换为同一常规有限元自由度,再上机计算.这种细观元法既能充分反映材料功能梯度沿各方向任意变化特性;而其计算单元又和常规有限元一样,是一种针对功能梯度结构分析的有效数值方法.现有功能梯度板件分析中无论对不同形状还是不同边界的功能梯度构件,其材料特性均沿板厚度方向梯度变化,本文用细观元法进行计算与分析,给出了目前尚未得到的沿板平面方向功能梯度变化构件的力学量三维分布形态.     

An FEM approximation for a fourth-order variational inequality of second kind

A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm.