Vanishing Theorems for p-Harmonic Forms on Submanifolds in Spheres

In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.

CONTROLLABILITY CANONICAL FORM FOR NONLINEAR CONTROL SYSTEMS

General nonlinear control systems are studied in this paper with the goal to transform them into the so-called controllability canonteal form via state transformation only. The conditions of transformability are given for both single input and multiple input cases. Besides, by an algebraic approach the procedure for constructing the state transformation is established. This paper is formulated in the framework of calculus rather than differential geometry approach.

THE KILLING FORMS AND DECOMPOSITION THEOREMS OF LIE SUPERTRIPLE SYSTEMS

In this article, the Killing form of a Lie supertriple system （LSTS） and that of its imbedding Lie superalgebra （LSA） are investigated, and a unique decomposition theorem for a quasiclassical LSTS with trivial center is established by means of the parallel decomposition theorem for a quasiclassical LSA.

Lie-form invariance of nonholonomic mechanical systems

The Lie-form invariance of a nonholonomic mechanaical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechaaical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is givea to illustrate the application of the results.

New criterion in predicting glass forming ability of various glass-forming systems

It has been confirmed that glass-forming ability （GFA） of supercooled liquids is related to not only liquid phase stability but also the crystallization resistance. In this paper, it is found that the liquid region interval （T1 - Tg） characterized by the normalized parameter of Tg/T1 could reflect the stability of glass-forming liquids at the equilibrium state, whilst the normalization of supercooled liquid region △Tx=（Tx - Tg）, i.e. △Tx/Tx （wherein T1 is the liquidus temperature, Tg the glass transition temperature, and Tx the onset crystallization temperature） could indicate the crystallization resistance during glass formation. Thus, a new parameter, defined as ζ = Tg/T1＋△Tx/Tx is established to predict the GFA of supercooled liquids. In comparison with other commonly used criteria, this parameter demonstrates a better statistical correlation with the GFA for various glass-forming systems including metallic glasses, oxide glasses and cryoprotectants.

Ore-forming Fluid Systems and Mineralization in the Eastern Jiangnan Uplift in the Border Area of Anhui and Jiangxi Provinces, China

Obvious differences in mineralization characteristics exist between the southern and northern parts of the eastern part of the Jiangnan Uplift in northern Jiangxi Province and southern Anhui Province. The regional metallogeny is discussed, and the ore-forming fluid systems are classified in this article. It is proposed that the fluid ore-forming activities in the Jiangnan Uplift both in northern Jiangxi and southern Anhui have close relationships with the crust-mantle interaction and magmatic-tectonic activities. The types and scales of the mineralization on the both sides of the eastern Jiangnan Uplift were determined by fluid ore-forming systems and geological backgrounds.

Numerical Modelling of Ore-forming Dynamics of Fractal Dispersive Fluid Systems

Based on an analysis of the fractal structures and mass transport mechanism of typical shear-fluid-ore formation system, the fractal dispersion theory of the fluid system was used in the dynamic study of the ore formation system. The model of point-source diffusive illuviation of the shear-fluid-ore formation system was constructed, and the numerical simulation of dynamics of the ore formation system was finished. The result shows that: (1) The metallogenic system have nested fractal structure. Different fractal dimension values in different systems show unbalance and inhomogeneity of ore-forming processes in the geohistory. It is an important parameter to symbolize the process of remobilization and accumulation of ore-forming materials. Also it can indicate the dynamics of the metallogenic system quantitatively to some extent. (2) In essence, the fractal dispersive ore-forming dynamics is a combination of multi-processes dominated by fluid dynamics and supplemented by molecule dispersion in fluids and fluid-rock interaction. It changes components and physico-chemical properties of primary rocks and fluids, favouring deposition and mineralization of ore-forming materials. (3) Gold ore-forming processes in different types of shear zones are quite different. (1) In a metallogenic system with inhomogeneous volumetric change and inhomogeneous shear, mineralization occurs in structural barriers in the centre of a shear zone and in geochemical barriers in the shear zone near its boundaries. But there is little possibility of mineralization out of the shear zone. (2) As to a metallogenic system with inhomogeneous volumetric change and simple shear, mineralization may occur only in structural barriers near the centre of the shear zone. (3) In a metallogenic system with homogeneous volumetric change and inhomogeneous shear, mineralization may occur in geochemical barriers both within and out of the shear zone.

Blow Up of Periodic Solutions to a Class of Quasilinear Hyperbolic Systems in Diagonal Form

In this paper, we discuss the blow-up of periodic solutions to a class of quasilinear hyperbolic systems in diagonal form, and make the accurate estimate of life-span. These results in this paper extend the conclusion [1-3].

Notes on Canonical Forms of Integrable Vector Nonlinear Schr?dinger Systems

We present canonical forms of integrable vector nonlinear Sehr6dinger systems. Mathematically, it is enough to focus on these canonical forms.

On the Form Invariance and Lie Symmetry of Birkhoffian Systems

The Lie symmetry is an invariance of the differential equations of motion under the infinitesimal transformations. The form invariance is an invariance of the form of the mechanical equations of motion under the infinitesimal transformations. In this paper, the relation between form invariance and Lie symmetry of Birkhoffian systems is presented, and the relationship unveil that the form invariance does not always mean Lie symmetry, vice versa.

Thermodynamic model for glass forming ability of ternary metallic glass systems

The thermodynamic model of multicomponent chemical short range order (MCSRO) was established in order to evaluate the glass forming ability (GFA) of ternary alloys. Comprehensive numerical calculations using MSCRO software were conducted to obtain the composition dependence of the MCSRO undercooling in Zr Ni Cu, Zr Si Cu and Pd Si Cu ternary systems. By the MCSRO undercooling principle, the composition range of Zr Ni Cu system with optimum GFA is determined to be 62.5 ～ 75 Zr, 5～ 20 Cu, 12.5 ～ 25 Ni ( n (Ni)/ n (Cu)=1～5). The TTT curves of Zr Ni Cu system were also calculated based on the MCSRO model. The critical cooling rates for Zr based alloy with deep MSCRO undercooling are estimated to be as low as 100?K/s, which is consistent with the practical cooling rate in the preparation of Zr based bulk metallic glass (BMG). The calculation also illustrates that the easy glass forming systems such as Pd based alloys exhibit an extraordinary deep MCSRO undercooling. It is shown that the thermodynamic model of MCSRO provides an effective method for the alloy designing of BMG.

Form Invariance, Noether and Lie Symmetry of Non-conservative Hamiltonian Systems in Phase Space

For the non-conservative holonomic Hamiltonian systems in phase space, the definition and criteria of the form invariance of the generalized Hamilton canonical equations were given. The relations among the form invariance, Noether symmetry and Lie symmetry were studied. The theory of the form invariance for the conservative holonomical systems was worked out. An example was given to illustrate the results.

Analyzing the Form-Finding of a Large-Span Transversely Stiffened Suspended Cable System: A Method Considering Construction Processes

The precise control of the shape of transversely stiffened suspended cable systems is crucial. However, existing form-finding methods primarily rely on iterative calculations that treat loads as fixed known conditions. These methods are inefficient and fail to accurately control shape results. In this study, we propose a form-finding method that analyzes the load response of models under different sag and stress levels, taking into account the construction process. To analyze the system, a structural finite element model was established in ANSYS, and geometric nonlinear analysis was conducted using the Newton-Raphson method. The form-finding analysis results demonstrate that the proposed method achieves precise control of shape, with a maximum shape error ranging from 0.33% to 0.98%. Furthermore, the relationships between loads and tension forces are influenced by the deformed shape of the structures, exhibiting significant geometric nonlinear characteristics. Meanwhile, the load response analysis reveals that the stress level of the self-equilibrium state in the transversely stiffened suspended cable system is primarily governed by strength criteria, while shape is predominantly controlled by stiffness criteria. Importantly, by simulating the initial tensioning process as an initial condition, this method solves for a counterweight that satisfies the requirements and achieves a self-equilibrium state with the desired shape. The shape of the self-equilibrium state is precisely controlled by simulating the construction process. Overall, this work presents a new method for analyzing the form-finding process of large-span transversely stiffened suspended cable system, considering the construction process which was often overlooked in previous studies.

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper,we study the Noether-form invariance of nonholonomic mechanical controllable systems inphase space.Equations of motion of the controllable mechanical systems in phase space are presented.The definitionand the criterion for this system are presented.A new conserved quantity and the Noether conserved quantity deducedfrom the Noether-form invariance are obtained.An example is given to illustrate the application of the results.

FORM INVARIANCE AND NOETHER SYMMETRICAL CONSERVED QUANTITY OF RELATIVISTIC BIRKHOFFIAN SYSTEMS

A form invariance of the relativistic Birkhoffian system is studied, and the conserved quantities of the system are obtained. Under the infinitesimal transformation of groups, the definition and criteria of the form invariance of the system were given. In view of the invariance of relativistic Pfaff_Birkhoff_ D'Alembert principle under the infinitesimal transformation of groups, the theory of Noether symmetries of the relativistic Birkhoffian system were constructed. The relation between the form invariance and the Noether symmetry is studied, and the results show that the form invariance can also lead to the Noether symmetrical conserved quantity of the relativistic Birkhoffian system under certain conditions.

Film-Forming Systems in Topically Administered Pharmaceutical Formulations

The skin is the most extensive and outermost organ in the body and can be greatly exploited both from the point of view of alternative routes of systemic drug delivery and treatment of dermatological diseases. Because of its main function as a barrier against harmful external agents, it also becomes a barrier to drug administration, but there are strategies to reduce this limitation of this promising route of administration. The development of polymer-based film-forming formulations is extensively studied for this purpose, since the formation of a film on the skin increases the contact time of the drug, for this being characterized as a controlled release reservoir system. There are a multitude of possible polymers to compose these formulations and their choice must be made according to the purpose of each application. This work, therefore, aims to study the state of the art of film forming systems for topical application of pharmaceutical formulations.

Global Regularity of Weak Solutions to Degenerate Eliptic Systems in Triangular Form

In this peper, using direct method, we prove the global Holder continuiy of weak solutions to degenerate eliptic systems in triangular form.

Ore Forming Systems (Fe, Ti, Ni, Pb, Zn, Noble Metals) of the Transbaikalia Neoproterozoic Greenstone Belts

It is shown that the ore-forming systems (OFS) of the Vendian-Riphean Greenstone belts (GSB) in the Transbaikalia region were formed in a wide age range: from the Riphean to the Cenozoic. They are grouped into 6 metallogenic types. The noble metal type is divided into 6 metallogenic subtypes differed in time duration intervals of functioning. OFS evolution wore multistage nature inherited from the composition of the GSB primary rocks, with a tendency of the ore generating processes remobilization and regeneration (dynamometamorphism) changing over time by rejuvenation (shoshonite latite and picrobasalt magmatism, mud volcanism).

THE FORM INVARIANCES AND THE HOJMAN CONSERVED QUANTITIES FOR HAMILTON SYSTEMS

The form invariance and the Lie symmetry are defined for Hamilton systems.A relation between the form invariance and the Lie symmetry is derived.The Hojman conserved quantity is constructed by using the generators of Lie symmetry.An approach to find Hojman conserved quantities in terms of the form invariance is presented.An example is given to illustrate the application of the results.

Researching on the Digital Information Systems of Mine and its Applications

The article introduces several digital information systems of mine which established on PC platform by the author using the software package of mathematical economic modal of deposit, GIS software, and furthermore putting them into solving the dynamic management of mine produce, produce programming, produce scheme and decision optimization of systems, rational utilization of the resource, searching ore and increasing reserves on the margin or in the deep part of those old mines .etc, so improving the socialize economic efficiency of mining exploiture.