A method for calculation of ion distribution in reaction system forming hydroxide

A formula was proposed to calculate the distribution of metal ions quantitatively in chemical reaction system forming hydroxide where precipitation and complex are formed together. The effects of some factors on formation of precipitation and complex were investigated, and the corresponding precipitation rates of zinc, iron （III）, aluminum, copper and magnesium were calculated. As a result, it shows that the proposed formula is reliable. By the proposed formula, the existence state of metal ions in hydroxides reaction system with any metal ions can be well described and the effects of some factors on the distribution of metal ions were determined.

RESEARCH ON HOT FORMING PROCESS OF A RETAINING RING OF HIGH-NITROGEN STEEL

Mn18Cr18N, the high-nitrogen steel, is the 2nd generation material for manufacturing the retaining ring of firepower generators. In this paper, the hot deformation behavior of the material was investigated by thermo-mechanical modeling tests. And the flow stress curves of the steel were obtained for various combinations of the temperature and strain rate. Based on the results of the tests, the complex forming process of a retaining ring including punching, expanding and extrusion with an enclosure was put forward and simulated by means of numerical simulation method. The results indicate that the process is a novel and force-saved practical technology for manufacturing heavy retaining rings.

SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN'S INEQUALITY

A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions satisfying some additional conditions, such as unfull first normal bundles or Chen’s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen’s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen.

Study on precision cutting technology of complex shape microparts

Relatively to non-traditional and high-energy-beam micro-manufacturing technique, the micro-cutting technology has many merits. For instance, the machining range is bigger, the cost of equipments is much lower, and the productivity and machining accuracy are higher. Therefore, the micro-cutting technology will take an important effect on the machining technique of complex shape microparts. In this paper, based on selfly-developed machine tool, the precision cutting technology of complex shape microparts made of metal material was studied by analyzing the modeling method on complex shape, the means of toolpaths layout and the optimal selection for cutting parameters. On the basis of above work, a typical duralumin specimen of high precision, low surface roughness and complex shape micropart was manufactured. This result will provide favorable technical support for farther research on the micro-cutting technology.

RIGIDITY THEOREMS OF COMPLETE K?HLER-EINSTEIN MANIFOLDS AND COMPLEX SPACE FORMS

We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete K?hler manifolds. We derive some elliptic differential inequalities from Weitzenb?ck formulas for the traceless Ricci tensor of K?hler manifolds with constant scalar curvature and the Bochner tensor of K?hler-Einstein manifolds respectively. Using elliptic estimates and maximum principle, several L^p and L~∞ pinching results are established to characterize K?hler-Einstein manifolds among K?hler manifolds with constant scalar curvature and complex space forms among K?hler-Einstein manifolds.Our results can be regarded as a complex analogues to the rigidity results for Riemannian manifolds. Moreover, our main results especially establish the rigidity theorems for complete noncompact K?hler manifolds and noncompact K?hler-Einstein manifolds under some pointwise pinching conditions or global integral pinching conditions. To the best of our knowledge,these kinds of results have not been reported.

ON THE DECOMPOSITION OF COMPLEX VECTOR SPACES AND THE JORDAN CANONICAL FORM OF COMPLEX LINEAR TRANSFORMATIONS

New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.

Precision Design for Machine Tool Based on Error Prediction

Digitization precision analysis is an important tool to ensure the design precision of machine tool currently. The correlative research about precision modeling and analysis mainly focuses on the geometry precision and motion precision of machine tool, and the forming motion precision of workpiece surface. For the machine tool with complex forming motion, there is not accurate corresponding relationship between the existing criterion on precision design and the machining precision of workpiece. Therefore, a design scheme on machine tool precision based on error prediction is proposed, which is divided into two-stage digitization precision analysis crucially. The first stage aims at the technology system to complete the precision distribution and inspection from the workpiece to various component parts of technology system and achieve the total output precision of machine tool under the specified machining precision; the second stage aims at the machine tool system to complete the precision distribution and inspection from the output precision of machine tool to the machine tool components. This article serves YK3610 gear hobber as the example to describe the error model of two systems and basic application method, and the practical cutting precision of this machine tool achieves to 5-4-4 grade. The proposed method can provide reliable guidance to the precision design of machine tool with complex forming motion.

On the Conjecture of Gackstatter and Laine Concerning Algebraic Differential Equations

In this paper we investigate the form of a class of complex differential equations withadmissible solution and obtain a main result.

2-Harmonic Submanifolds in a Complex Space Form

In the present paper,the authors study totally real 2-harmonic submanifolds in a complex space form and obtain a Simons' type integral inequality of compact submanifolds as well as some relevant conclusions.

Tsallis holographic dark energy under complex form of quintessence model

In this paper,we use a Tsallis holographic dark energy model in two forms,interacting and noninteracting cases,to acquire some parameters as the equation of state for the energy density of the Tsallis model in the FRW Universe concerning the complex form of quintessence model.We will study the cosmology of complex quintessence by revamping the potential and investigating the scalar field dynamics.Then we analyze(w-w’)and stability in two cases,i.e.noninteracting and interacting.We will explore whether these cases describe a real Universe by calculating fractional energy densityΩ_(D)and concerning two parts of the quintessence field effect(complex and real part)by considering the real part of this field to be a slow-roll field.We know that the part in which the fractional energy density(Ω_(D)>1)does not describe a real Universe.Also,we specified an interacting coupling parameter b2that depends on the constant parameter of the Tsallis holographic model(δ)with respect to fractional energy density(0.73).Unlike independence between the fractional energy density and interacting coupling in the real quintessence model,we determine a relationship among these parameters in this theory.Finally,by plotting some figures,we specify the features of(w-w’)and(ν^(2)_(s))in two cases and compare the result with each other.

Conformally flat, minimal, Lagrangian submanifolds in complex space forms

We investigate n-dimensional(n≥4),conformally flat,minimal,Lagrangian submanifolds of the n-dimensional complex space form in terms of the multiplicities of the eigenvalues of the Schouten tensor and classify those that admit at most one eigenvalue of multiplicity one.In the case where the ambient space is Cn,the quasi umbilical case was studied in Blair(2007).However,the classification there is not complete and several examples are missing.Here,we complete(and extend) the classification and we also deal with the case where the ambient complex space form has non-vanishing holomorphic sectional curvature.

Classification of Lagrangian Surfaces of Curvatureε in Non-fiat Lorentzian Complex Space Form ■_1~2(4ε)

It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12（4ε） of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is ＂Besides totally geodesic ones how many Lagrangian surfaces of constant curvature εin M12（46） are there？＂ In an earlier paper an answer to this question was obtained for the case e = 0 by Chen and Fastenakels. In this paper we provide the answer to this question for the case ε≠0. Our main result states that there exist thirty-five families of Lagrangian surfaces of curvature ε in M12（4ε） with ε ≠ 0. Conversely, every Lagrangian surface of curvature ε≠0 in M12（4ε） is locally congruent to one of the Lagrangian surfaces given by the thirty-five families.

Ruled Real Hypersurfaces of A Complex Space Form

The purpose of this paper is to define a ruled real hypersurface of a complex space form M_n(c),c≠0,and to give characterizations of this hypersurface by the infinitesimal affine transformation of the structure vector field induced on the hypersurface.

Crystalline inclusion complexes formed between the drug diflunisal and block copolymers

The solid form of drugs plays a central role in optimizing the physicochemical properties of drugs,and new solid forms will provide more options to achieve the desirable pharmaceutical profiles of drugs.Recently,certain drugs have been found to form crystalline inclusion complexes（ICs） with multiple types of linear polymers,representing a new subcategory of pharmaceutical solids.In this study,we used diflunisal（DIF） as the model drug host and extended the guest of drug/polymer ICs from homopolymers to block copolymers of poly（ethylene glycol）（PEG） and poly（s-caprolactone）（PCL）.The block length in the guest copolymers showed a significant influence on the formation,thermal stability and dissolution behavior of the DIF ICs.Though the PEG block could hardly be included alone,it could indeed be included in the DIF ICs when the PCL block was long enough.The increase of the PCL block length produced IC crystals with improved thermal stability.The dissolution profiles of DIF/block copolymer ICs exhibited gradually decreased aqueous solubility and dissolution rate with the increasing PCL block length.These results demonstrate the possibility of using drug/polymer ICs to modulate the desired pharmaceutical profiles of drugs in a predictable and controllable manner.

Drug-polymer inclusion complex as a new pharmaceutical solid form

The solid forms of drugs play a central role in controlling their physicochemical properties and consequently the bioavailability. Multiple types of drug solid forms have been developed to achieve the desirable pharmaceutical profiles, but new solid forms will provide more options for the solid-state property optimization and hence are highly desirable. This review focuses on a new pharmaceutical solid form, drug-polymer inclusion complexes （ICs）, and summarizes their structural features, structure- property relationships, as well as potential pharmaceutical applications