Study on General Performance of Jack-up Under Elevated Condition

Method of checking for jack-up elevated performance including leg structure strength, fixation system or jacking system beating capacity, pre-load requirements, spud can beating capacity and overturning stability is suggested in this paper. As an example, a jack-up with truss legs is analyzed by finite element analysis method. This paper may be helpful to the rig owners, operators and designers.

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

ON THE NECESSARY AND SUFFICIENT CONDITIONS TO SOLVE A HEAT EQUATION WITH GENERAL ADDITIVE GAUSSIAN NOISE

In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.

Generating Compatibility Conditions and General Relativity

The search for the generating compatibility conditions (CC) of a given operator is a very recent problem met in general relativity in order to study the Killing operator for various standard useful metrics. Accordingly, this paper can be considered as a natural continuation of a previous paper recently published in JMP under the title Minkowski, Schwarschild and Kerr metrics revisited. In particular, we prove that the intrinsic link existing between the lack of formal exactness of an operator sequence on the jet level, the lack of formal exactness of its corresponding symbol sequence and the lack of formal integrability (FI) of the initial operator is of a purely homological nature as it is based on the long exact connecting sequence provided by the so-called snake lemma in homological algebra. It is therefore quite difficult to grasp it in general and even more difficult to use it on explicit examples. It does not seem that any one of the results presented in this paper is known as most of the other authors who studied the above problem of computing the total number of generating CC are confusing this number with the degree of generality introduced by A. Einstein in his 1930 letters to E. Cartan. One of the motivating examples that we provide is so striking that it is even difficult to imagine that such an example could exist. We hope this paper could be used as a source of testing examples for future applications of computer algebra in general relativity and, more generally, in mathematical physics.

VARIATIONAL L^q-APPROXIMATION BY VARISOLVENT FAMILY UNDER THE YOUNG'S CONDITION

The new Lq approximation methods proposed by A.Pinkus and O.Shisha,which maintains the characteristic feature-alternation-of the classic Chebyshev uniform approximation, is extended to varisolvent approximation under the Young's condition.The theorems of existence, characterizations, unicity, de La Vallee Poussin and continuity of the best approximation are presented.

General Information Conditioned by a Variable Event

The aim of this paper is to present, by axiomatic way, an idea about the general conditional information of a single, fixed fuzzy set when the conditioning fuzzy event is variable. The properties of this conditional information are translated in a system of functional equations. Some classes of solutions of this functional system have been found.

On the convergence for PNQD sequences with general moment conditions

Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large positive integers k,where 1<θ≤βand f(x)>0(x≥1)is a non-decreasing function on[b;+1)for some b≥1:In this paper,we obtain the strong law of large numbers and complete convergence for the sequence fX;Xn;n≥1g,which are equivalent to the general moment conditionΣ∞n=1P(|X|>an)<1.Our results extend and improve the related known works in Baum and Katz[1],Chen at al.[3],and Sung[14].

L^P SOLUTION OF GENERAL MEAN-FIELD BSDES WITH CONTINUOUS COEFFICIENTS

In this paper we consider one dimensional mean-field backward stochastic differential equations(BSDEs)under weak assumptions on the coefficient.Unlike[3],the generator of our mean-field BSDEs depends not only on the solution(Y,Z)but also on the law PY of Y.The first part of the paper is devoted to the existence and uniqueness of solutions in Lp,1<p≤2,where the monotonicity conditions are satisfied.Next,we show that if the generator/is uniformly continuous in(μ,y,z),uniformly with respect to(t,ω) and if the terminal valueξbelongs to Lp(Ω,F,P)with 1<p≤2,the mean-field BSDE has a unique Lp solution.

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.

ON THE BASIC REPRODUCTION NUMBER OF GENERAL BRANCHING PROCESSES

Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.

Numerical simulation of groundwater under complex karst conditions and the prediction of roadway gushing in a coal mine:a case study in the Guang'an Longtan Reservoir in Sichuan Province, China

Numerical simulation of groundwater in karst areas has long been restricted by the difficulty of generalizing the hydrogeological conditions of reservoirs and of determining the relevant parameters due to the anisotropy and discontinuity of the karst water-bearing media in these areas. In this study, we used the Guang'an Longtan Coal mine in Sichuan as an example, and generalized the complex hydrogeological conditions in the reservoir area. A finite element numerical flow model was used to simulate current and future scenarios of roadway gushing at the bottom of the coal mine at pile number 1 + 700 m. The results show that the roadway section corresponding to valleys has a gushing quantity of 4323.8–4551.25 m^3/d before impoundment. Modeled water inflow after impoundment increased to 1.6 times the water inflow before impoundment, which threatens the impoundment as well as the roadway's normal operation. Therefore, roadway processing measures are needed to guarantee the safety of the impoundment and of the mining operation.

To the Complete Set of Equations for a Static Problem of General Relativity

The paper is concerned with the formulation of the static problem of general relativity. As known, this problem is reduced to ten equations for the compo-nents of the Einstein tensor and the solution of these equations is associated with two principal problems. First, since the components of the Einstein tensor identically satisfy four conservation equations, only six of these equations are mutually independent. So, the set of the Einstein equations actually contains six independent equations for ten components of the metric tensor and should be supplemented with four additional equations which are missing in the original theory. Second, for a deformable solid the Einstein tensor is associated with the energy tensor which is expressed in terms of six stresses induced by gravitation. These stresses are not known and the relativity theory does not propose any equations for them. Thus, the static problem of general relativity cannot be properly formulated because the set of governing equations is not complete. In the paper, the problem of completeness of the general relativity governing set of equations is analyzed in application to the spherically symmetric static problem and the proposed approach is further described for the general case. As an example, linearized axisymmetric problem is considered.

Riemannian Space-Time, de Donder Conditions and Gravitational Field in Flat Space-Time

Let the coordinate system xi of flat space-time to absorb a second rank tensor field Φij of the flat space-time deforming into a Riemannian space-time, namely, the tensor field Φuv is regarded as a metric tensor with respect to the coordinate system xu. After done this, xu is not the coordinate system of flat space-time anymore, but is the coordinate system of the new Riemannian space-time. The inverse operation also can be done. According to these notions, the concepts of the absorption operation and the desorption operation are proposed. These notions are actually compatible with Einstein’s equivalence principle. By using these concepts, the relationships of the Riemannian space-time, the de Donder conditions and the gravitational field in flat space-time are analyzed and elaborated. The essential significance of the de Donder conditions (the harmonic conditions or gauge) is to desorb the tensor field of gravitation from the Riemannian space-time to the Minkowski space-time with the Cartesian coordinates. Einstein equations with de Donder conditions can be solved in flat space-time. Base on Fock’s works, the equations of gravitational field in flat space-time are obtained, and the tensor expression of the energy-momentum of gravitational field is found. They all satisfy the global Lorentz covariance.

Evaporative Condensers in Comfortable Air Conditioning System

The operating theory of an evaporative condenser was expatiated.The difference between an evaporative condensing refrigeration system and a general refrigeration system was analyzed.Compared with the air-cooled and the water-cooled,the virtues of energy-conservation and water-conservation of evaporative condensers were analyzed.Some questions existing in the application of evaporative condensers were pointed out,the corresponding solving methods were analyzed accordingly,and the development trend of evaporative condensing technique in mechanical refrigeration system field and the applied foreground of evaporative condensers in comfortable air conditioning were prospected.

Supplement to the previous application of the first junction condition to a highly symmetric spacetime

Application of the first junction condition to a highly symmetric spacetime was investigated recently in Chin. Phys. Left. B 546 189 2006, where a partial differential equation arising from the connection of the Robertson-Walker and the Schwarzschild-de Sitter metrics was presented, but no solutions of the equation were provided. Here we provide a proof to the statement that there exist solutions of the equation. In addition, an example of the solution and some analyses associated with this issue are presented. We find that in connecting the two metrics, there are three conditions which should be satisfied. Of these conditions, one condition constrains the place where the two metrics can take the same value for a local system whose mass is provided which marks the boundary of the system, and the other two constrain the transformation form. In realizing the connection of the two metrics, the latter two conditions are required to be satisfied only at the boundary defined by the former condition.

Dependence of the AGCM Climatology on the Method of Prescribing Surface Boundary Conditions and Its Climatological Implication

By using IAP 9L AGCM, two sets of long-term climatological integration have been performed with the two different interpolation procedures for generating the daily surface boundary conditions. One interpolation procedure is the so-called “traditional” scheme, for which the daily surface boundary conditions are obtained by linearly interpolating between the observed monthly mean values, however the observed monthly means cannot be preserved after interpolation. The other one is the “new” scheme, for which the daily surface boundary conditions are obtained by linearly interpolating between the “artificial” monthly mean values which are based on, but are different from the observed ones, after interpolating with this new scheme, not only the observed monthly mean values are preserved, the time series of the new generated daily values is also more consistent with the observation. Comparison of the model results shows that the differences of the globally or zonally averaged fields between these two integrations are quite small, and this is due to the compensating effect between the different regions. However, the differences of the two patterns (the global or regional geographical distributions), are quite significant, for example, the magnitude of the difference in the JJA mean rainfall between these two integrations can exceed 2 mm/ day over Asian monsoon regions, and the difference in DJF mean surface air temperature can also exceed 2?C over this region. The fact that the model climatology depends quite strongly on the method of prescribing the daily surface boundary conditions suggests that in order to validate the climate model or to predict the short-term climate anomalies, either the “new? interpolation scheme or the high frequency surface boundary conditions (e.g., daily or weekly data instead of the monthly data) should be introduced. Meanwhile, as for the coupled model, the daily coupling scheme between the different component climate models ( e.g., atmospheric and oceanic general circulation models) is preferred in order to partly eliminate the “climate drift” problem which may appear during the course of direct coupling.

Convergence analysis of a nonlinear Lagrange algorithm for general nonlinear constrained optimization problems

The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.

Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity

A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity （TEGR）. A spacetime which is not asymptotically fiat is derived. The energy conditions of this spacetime are studied. It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy. The singularities of this solution are discussed.

On the Generalization of Integrator and Integral Control Action

This paper provides a solution to generalize the integrator and the integral control action. It is achieved by defining two function sets to generalize the integrator and the integral control action, respectively, resorting to a stabilizing controller and adopting Lyapunov method to analyze the stability of the closed-loop system. By originating a powerful Lyapunov function, a universal theorem to ensure regionally as well as semi-globally asymptotic stability is established by some bounded information. Consequently, the justification of two propositions on the generalization of integrator and integral control action is verified. Moreover, the conditions used to define the function sets can be viewed as a class of sufficient conditions to design the integrator and the integral control action, respectively.

Dynamic Vision-Based Machinery Fault Diagnosis With Cross-Modality Feature Alignment

Intelligent machinery fault diagnosis methods have been popularly and successfully developed in the past decades,and the vibration acceleration data collected by contact accelerometers have been widely investigated.In many industrial scenarios,contactless sensors are more preferred.The event camera is an emerging bio-inspired technology for vision sensing,which asynchronously records per-pixel brightness change polarity with high temporal resolution and low latency.It offers a promising tool for contactless machine vibration sensing and fault diagnosis.However,the dynamic vision-based methods suffer from variations of practical factors such as camera position,machine operating condition,etc.Furthermore,as a new sensing technology,the labeled dynamic vision data are limited,which generally cannot cover a wide range of machine fault modes.Aiming at these challenges,a novel dynamic vision-based machinery fault diagnosis method is proposed in this paper.It is motivated to explore the abundant vibration acceleration data for enhancing the dynamic vision-based model performance.A crossmodality feature alignment method is thus proposed with deep adversarial neural networks to achieve fault diagnosis knowledge transfer.An event erasing method is further proposed for improving model robustness against variations.The proposed method can effectively identify unseen fault mode with dynamic vision data.Experiments on two rotating machine monitoring datasets are carried out for validations,and the results suggest the proposed method is promising for generalized contactless machinery fault diagnosis.