Uniqueness of Positive Radial Solutions for a Class of Semipositone Systems on the Exterior of a Ball

In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP: , where Δu = div (∇u) and Δv = div (∇v) are the Laplacian of u, λ is a positive parameter, Ω = {x ∈ Rn : N > 2, |x| > r0, r0 > 0}, let i = [1,2] then Ki :[r0,∞] → (0,∞) is a continuous function such that limr→∞ ki(r) = 0 and is The external natural derivative, and : [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of f with a) fi > 0, b) fi < 0, and c) fi = 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings.

Interior and Exterior Differential Systems for Lie Algebroids

A theorem of Maurer-Cartan type for Lie algebroids is presented. Suppose that any vector subbundle of a Lie algebroid is called interior differential system (IDS) for that Lie algebroid. A theorem of Frobenius type is obtained. Extending the classical notion of exterior diffential system (EDS) to Lie algebroids, a theorem of Cartan type is obtained.

An impact sensitivity assessment method of spacecraft based on virtual exterior wall

The impact sensitivity assessment of spacecraft is to obtain the probability of spacecraft encountering the OD/M(orbital debris or meteoroid),which is a prerequisite for survivability assessment of on-orbit spacecraft.An impact sensitivity assessment method of spacecraft based on virtual exterior wall was proposed to improve the computational efficiency.This method eliminates determination of the outermost surface elements of the spacecraft before generating the debris rays,which are assumed to originate from a non-concave virtual wall that completely wraps the spacecraft.The Dist Mesh method was adopted for the generating of the virtual wall to ensure its mesh quality.The influences of the sizes,mesh densities,shapes of the virtual wall on the efficiency and accuracy were considered to obtain the best combination of the size and mesh density of the wall and spacecraft.The results of this method were compared with those of S3DE(Survivability of Spacecraft in Space Debris Environment),BUMPER,MDPANTO,ESABASE2/Debris to verify the feasibility of the method.The PCHIP(Piecewise Cubic Hermite Interpolating Polynomial)was used to fit the size vs.flux relationship of the space debris to acquire the impact probability of OD/M with arbitrary size on the spacecraft.

Exterior Quality and Physical Properties of Hongda Tobacco in Yunnan Province

[Objective] The aim was to analyze the exterior quality and physical prop- erties of Hongda Tobacco in Yunnan Province, thus providing references for planting planning, technology and selection of raw materials. [Method] Hongda C3F progenies were chosen from 24 villages and towns in Qujing, Kunming, Baoshan and Dali, and the concerning exterior quality and physical properties were analyzed through cluster analysis. [Result] The openness and width of C3F differed significantly among Qujing, Kunming, Baoshan and Dali. The thickness, stem content, equilibrium moisture con- tent extremely differed, and density and filling power varied significantly. Most physi- cal properties, such as equilibrium moisture content and density, of Dali Hongda were quite different from those in Qujing, Kunming and Baoshan, indicating that Dali Hongda enjoys special characteristics in physical properties. In addition, stem content in east, center and west areas of Yunnan Province differed significantly and Hongda in Yunnan could be classified into four species according to physical property. [Conclusion] The research has laid basis for planting planning, technology and raw mate- rials selection of Hongda tobacco.

Measurement of bullet impact conditions using automated in-flight photography system

Knowledge of impact conditions is critical to evaluating the terminal impact performance of a projectile.For a small caliber bullet,in-flight velocity has been precisely measured for decades using detection screens,but accurately quantifying the orientation of the bullet on a target has been more challenging.This report introduces the Automated Small-Arms Photogrammetry(ASAP)analysis method used to measure,model,and predict the orientation of a small caliber bullet before reaching an impact surface.ASAP uses advanced hardware developed by Sydor Technologies to record a series of infrared digital photographs.Individual images(four orthogonal pairs)are processed using computer vision algorithms to quantify the orientation of the projectile and re-project its precise position and orientation into a three-dimensional muzzle-fixed coordinate system.An epicyclic motion model is fit to the measured data,and the epicyclic motion is extrapolated to the target location.Analysis results are fairly immediate and may be reviewed during testing.Prove-out demonstrations have shown that the impact-angle prediction capability is less than six hundredths of a degree for the 5.56 mm ball round tested.Keywords:Yaw,Terminal ballistics,Exterior ballistics,Test&evaluation,Computer vision,Image processing,Angle of

Control of exterior ballistic properties of spin-stabilized bullet by optimizing internal mass distribution

This paper introduces a novel approach for controlling the exterior ballistic properties of spin-stabilized bullets by optimizing their internal mass distributions. Specifically, the properties of interest are the bullets’ stability characteristics that are examined through dynamic and gyroscopic stability parameters.New analytical expressions for aerodynamic quantities are also derived to address the compressibility of air. These expressions are utilized in a bullet model that enables efficient computation of the stability parameters for a given mass distribution. The bullet model is used in the formulation of nonlinear optimization problems that provide optimal mass distributions with respect to given goals, i.e., desired stability characteristics. The bullet types investigated in this paper are a long range bullet and a limited range training bullet. In the optimization of the mass distribution of the long range bullet, the goal is that the bullet stays stable for as long as possible. The mass distribution of the training bullet is optimized such that the bullet is stable at launch but becomes unstable shortly afterwards. The global optimal solutions obtained with the new approach fulfill the desired stability characteristics better than currently used uniformly filled bullets. Overall, the optimization approach reveals a new goal focused philosophy for bullet design compared to current trial and error design practices.

Numerical Simulation of Antennae by Discrete Exterior Calculus

Numerical simulation of antennae is a topic in computational electromagnetism,which is concerned withthe numerical study of Maxwell equations.By discrete exterior calculus and the lattice gauge theory with coefficient R,we obtain the Bianchi identity on prism lattice.By defining an inner product of discrete differential forms,we derivethe source equation and continuity equation.Those equations compose the discrete Maxwell equations in vacuum caseon discrete manifold,which are implemented on Java development platform to simulate the Gaussian pulse radiation onantennaes.

PANSYSTEMS LOGIC:A NEW LOGIC FRAMEWORK FOR ARTIFICIAL INTELLIGENCE

Zan Tingquan and Wu Xuemou, Pansystems logic: a new logic fra-mework for AI.In this artic1e, we take a step towards providing a new logic fra-mework as a basis for human and artificial intelligence.We unite logic,epistemology, cognitive science, methodology and s ystems sciences tostudy cognitive processes and forms of thought and try to construct anew logic framework by use of pansystems metllodology.The new logicframework is called pansystems Logic.Included are:(1)propose the concepts of generalized. subjects and generalizedobjects, articulate the pansystems observocontrol relativity principle asa new model of cognitive foundations for artifitial intelligence.(2)present fifteen layer-parts of artifitial intelligence researchfrom the new view, i.e.AI concerns with five aspects of man, things,the relations between man and things, artificial systems, the relations be-tween the former three and the latter one,which should be studied fromthree levels of philosophical, mathematical and technical researches.

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = （σ ＋ m ）n / （ n-σ- 2 ） is its critical exponent provided max{-1, [ （1- m ）n- 2] / （ n ＋ l ） } 〈 σ 〈 n- 2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Futhermore, we demonstrate that if max（1, σ ＋ m） 〈 p 〈 pc, then every positive solution of the equations blows up in finite time; whereas for p 〉 pc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n〈σ＋2.

ON THE UNIQUENESS OF BOUNDARY INTEGRAL EQUATION FOR THE EXTERIOR HELMHOLTZ PROBLEM

From the point of view of energy analysis, the cause that the uniqueness of the boundary integral equation induced from the exterior Helmholtz problem does not hold is investigated in this paper. It is proved that the Sommerfeld's condition at the infinity is changed so that it is suitable not only for the radiative wave but also for the absorptive wave when we use the boundary integral equation to describe the exterior Helmholtz problem. There fore, the total energy of the system is conservative. The mathematical dealings to guarantee the uniqueness are discussed based upon this explanation.

FAST AND SLOW DECAY SOLUTIONS FOR SUPERCRITICAL FRACTIONAL ELLIPTIC PROBLEMS IN EXTERIOR DOMAINS

1 Introduction and Main Results We construct classic solutions of the following supercritical nonlinear fractional exterior problem.

Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

Abstract We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling(SECS)absorbing method and Arnoldi propagation method.Such combination has not been reported in the literature.The proposed scheme is particularly useful in the applications involving long-time wave propagation.The SECS is a wonderful absorber,but its application results in a non-Hermitian Hamiltonian,invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian.We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian.The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet(XUV)and strong infrared(IR)laser pulses.Both perfect absorption and stable propagation are observed.

THE COUPLING OF BOUNDARY ELEMENT AND FINITE ELEMENT METHODS FOR THE EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS

In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variational formulation and well posedness of the coupling method are obtained. The convergence and optimal estimates for the approximation solution are provided.

LARCH BARK TANNIN ADHESIVE FOR EXTERIOR PARTICLEBOARD

The larch bark tannins were used to make adhesive for particleboard. The tanninadhesive in which 60% phcnol was replaced by tannin has 1 - 1 .5 month storage life and its cost is lower than that of PF resin. At the 10% and 9% rcsin solids content on dry wood chips, larch particleboard and poplar particleboard were made respectively. The physical properties of boards can meet the nccds of cxterior particleboard in German Standard DIN68763 V 100.

Three dimensional simulation of electromagnetic railgun's exterior ballistics

In order to evaluate the electromagnetic railgun＇ s practical combat capability as well as its tactic application prospects, a three dimensional simulation model of electromagnetic railgun＇ s exterior ballistics is presented. On the hypothesis of the Earth＇ s being round and ignoring the influ- ence of rotation, the railgun＇ s atmospheric environment and its motion equations are established by the Simulink Module of Matlab. And the railgun＇ s characteristics of exterior ballistic under different muzzle energy and emission inclinations are discussed. Results show that its incomparable superiori- ty in improving range and lethality to conventional artillery under the same launch condition based on railgun＇ s range and variation of velocities. It is useful for the efficacy evaluation of railgun＇ s combat capability and its practical applications in fields such as ground war, missile interception and so on.

Experimental Studies on Seismic Behavior of Exterior SRUHSC Joints

To investigate the seismic behavior of the joints,six steel reinforced ultra high strength concrete( SRUHSC) frame exterior joints were tested. Three levels of axial compressive ratio varying from 0.25 to 0.45 were investigated to determine how this variable might influence the performance of the joints including failure mode,ductility,energy dissipation capacity,stiffness degradation,shear strength and shear deformation by the quasi-static cyclic test on SRUHSC exterior joints. This research program suggests that the design of joint should make full use of the joint panel deformation to dissipate energy of earthquake. It is tested that the value of 0.38 as a dividing point about the effect of axial compression ratio on the seismic performance of SRUHSC exterior joints should be taken into account in design. In addition,the increase of volumetric ratio of stirrup could possess the ductility for adequate response to unexpected strong earthquakes and a recommended value of minimum volumetric ratio of stirrup with high axial-load level is pointed out.

Fitting on elements of exterior orientation utilizing SPOT-5 raw data file

In traditional pattern, the calculation of elements of exterior orientation is to calculate the elements of image forming moment by using fundamental ground control points. Utilizing satellite raw data file directly, which holds abundant information and using the numerical analysis methods of modern mathematics, the parameter equations about each element of exterior orientation are adjused and the elements of image forming moment under some precision are calculated.

Exteriorized colon anastomosis for unprepared bowel: An alternative to routine colostomy

AIM: To see the possibility of avoiding routine colostomy in patients presenting with unprepared bowel. METHODS: The cohort is composed of 103 patients, of these, 86 patients presented as emergencies (self- inflected and iatrogenic colon injuries, stab wounds and blast injury of the colon, volvulus sigmoid, obstructing left colon cancer, and strangulated ventral hernia). Another 17 patients were managed electively for other colon pathologies. During laparotomy, the involved segment was resected and the two ends of the colon were brought out via a separate colostomy wound. One layer of interrupted 3/0 silk was used for colon anastomosis. The exteriorized segment was immediately covered with a colostomy bag. Between the 5th and 7th postoperative day, the colon was easily dropped into the peritoneal cavity. The defect in the abdominal wall was closed with interrupted nonabsorbable suture. The skin was left open for secondary closure. RESULTS: The mean hospital stay (± SD) was 11.5 ± 2.6 d (8-20 d). The exteriorized colon was successfully dropped back into the peritoneal cavity in all patients except two. One developed a leak from oesophago- jejunostomy and from the exteriorized colon. She subsequently died of sepsis and multiple organ failure (MOF). In a second patient the colon proximal to the exteriorized anastomosis prolapsed and developed severe serositis, an elective ileo-colic anastomosis (to the left colon) was successfully performed. CONCLUSION: Exteriorized colon anastomosis is simple, avoids the inconvenience of colostomy and can be an alternative to routine colostomy. It is suitable where colostomy is socially unacceptable or the facilities and care is not available.

THE SINGULAR LIMIT OF SECOND-GRADE FLUID EQUATIONS IN A 2D EXTERIOR DOMAIN

In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a wellknown non-Newtonian fluid model, with two parameters: α, which represents the length-scale,while ν > 0 corresponds to the viscosity. We prove that, as ν, α tend to zero, the solution of the second-grade fluid equations with suitable initial data converges to the one of Euler equations, provided that ν = o(α^(4/3)). Moreover, the convergent rate is obtained.

LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.