Non-blocking message total ordering protocol

Message total ordering is a critical part in active replication in order to maintain consistency among members in a fault tolerant group. The paper proposes a non-blocking message total ordering protocol （NBTOP） for distributed systems. Non-blocking property refers to that the members in a fault tolerant group keep on running independently without waiting for installing the same group view when a fault tolerant group evolves even when decision messages collide. NBTOP takes advantage of token ring as its logical control way. Members adopt re-requesting mechanism （RR） to obtain their lost decisions. Forward acknowledgement mechanism （FA） is put forth to solve decision collisions. The paper further proves that NBTOP satisfies the properties of total order, agreement, and termination. NBTOP is implemented, and its performance test is done. Comparing with the performance of Totem, the results show that NBTOP has a better total ordering delay. It manifests that non-blocking property helps to improve protocol efficiency.

Ranking grey numbers based on dominance grey degrees

With respect to the decision making problems where a lot of fuzzy and grey information always exists in the real-life decision making information system methods as fuzzy mathematics, it is difficult for such uncertainty probability, and interval numbers to deal with. To this end, based on the thought and method of grey numbers, grey degrees and interval numbers, the concept of dominance grey degree is defined. And then a method of ranking interval grey numbers based on the dominance grey degree is proposed. After discussing the relevant properties, the paper finally uses an example to demonstrate the effectiveness and applicability of the model. The result shows that the proposed model can more accurately describe uncertainty decision making problems, and realize the total ordering process for multiple-attribute decision-making problems.

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅱ)——Also on the unity of the Continuous Induction,the Mathem atical Induction and the Transfinite Induction

In this paper,a common characteristic of real number system and well ordered set is revealed and proved to be an equivalent form of the Dedekind Axiom or the Continuous Induction in R. Basing on it,we get the unified form of the mathematical induction,the transfinite induction and the continuous induction and generalize induction to totally ordered set that has the same characteristic.

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and theTransfiniteInduction

In this paper,a common characteristic of real number system and well ordered set is revealed and proved to be an equivalent form of the Dedekind Axiom or the Continuous Induction in R. Basing on it,we get the unified form of the mathematical induction,the transfinite induction and the continuous induction and generalize induction to totally ordered set that has the same characteristic.

SOME COMPARISONS BETWEEN GENERALIZED ORDER STATISTICS

Some stochastic comparisons of generalized order statistics under the right spread order, the location independent riskier order and the total time transform order are investigated in this paper. The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.

OPTIMAL POLICY WITH A TOTAL ORDER QUANTITY COMMITMENT CONTRACT IN THE PRESENCE OF A SPOT MARKET

In this paper, the optimal policy is considered when the buyer faces two supply sources： one is the contract supplier from which the buyer orders over a specific contract period （say, a year） at a pre-agreed price, and the other is the spot market. However, when ordering from the contract supplier, the buyer must fulfill a pre-determined total order quantity, or the so-called definite total order quantity commitment, over the whole contract period. In other words, the commitment secures the buyer a fixed price but obliges him/her a total order quantity over the contract period. Although the spot market gives the buyer more flexibility in terms of order quantities, its prices are volatile. Such a combination of contract and spot procurements is often observed in practice. Within the contract period, there are multiple sub-periods, during each of which the buyer reviews the inventory, issues an individual order, and uses the on-hand inventory to meet the random demand. Thus, in each （ordering） period, the buyer will weigh between the current known spot price （by procuring from the spot market） and a lower future price （by waiting while consuming the remaining commitment）. An optimal dual ordering policy is characterized for each period, depending on the on-hand inventory level, the spot price, and the remaining commitment quantity. The optimal policy in each period is also shown to be independent of the contract price. Through a numerical study, the inventory cost is demonstrated to be （1） insensitive to the contract price when the total commitment quantity is lower than the total expected demand over the contract period and （2） non-increasing in the variability of spot prices.

Trace Semantics and Algebraic Laws for Total Store Order Memory Model

Modern multiprocessors deploy a variety of weak memory models(WMMs).Total Store Order(TSO)is a widely-used weak memory model in SPARC implementations and x86 architecture.It omits the store-load constraint by allowing each core to employ a write buffer.In this paper,we apply Unifying Theories of Programming(abbreviated as UTP)in investigating the trace semantics for TSO,acting in the denotational semantics style.A trace is expressed as a sequence of snapshots,which records the changes in registers,write buffers and the shared memory.All the valid execution results containing reorderings can be described after kicking out those that do not satisfy program order and modification order.This paper also presents a set of algebraic laws for TSO.We study the concept of head normal form,and every program can be expressed in the head normal form of the guarded choice which is able to model the execution of a program with reorderings.Then the linearizability of the TSO model is supported.Furthermore,we consider the linking between trace semantics and algebraic semantics.The linking is achieved through deriving trace semantics from algebraic semantics,and the derivation strategy under the TSO model is provided.

The centralizer of an element in a Lie algebra of type L

In this paper, we investigate the Lie algebra L(A,α,δ) of type L and obtain the respective sufficient conditions for L(A,α,δ δ to be semisimple, and for Z(ω) = Fω as well, where 0 ≠ ω ? L(A, α, δ, δ) and Z(ω) is the centralizer of ω.

Valuations on arithmetic surfaces

In this paper, we give the definition of the height of a valuation and the definition of the big field ? p,G , where p is a prime and G ? ? is an additive subgroup containing 1. We conclude that ? p,G is a field and ? p,G is algebraically closed. Based on this the author obtains the complete classification of valuations on arithmetic surfaces. Furthermore, for any m ? p,G n ∈ ?, let V m,n be an ∝-vector space of dimension n - m + 1, whose coordinates are indexed from m to n. We generalize the definition of ? p,G , where p is a prime and G ? V m,n is an additive subgroup containing 1. We also conclude that ? p,G is a field if m ? 0 ? n.

Blowing-ups and Valuations on Surfaces

In this paper, we show that all the nontrivial valuations on surfaces can be given by the infinite sequences of blowing-ups, and give the process of blowing-ups.

Verma modules for rank two Heisenberg-Virasoro algebra

Let■be a compatible total order on the additive group Z^2,and L be the rank two HeisenbergVirasoro algebra.For any c=(c1,c2,c3,c4)∈C^4,we define a Z^2-graded Verma module M(c,■)for L.A necessary and sufficient condition for M(c,■)to be irreducible is provided.Moreover,the maximal Z^2-graded submodules of M(c,■)are characterized when M(c,■)is reducible.

Improving energetics in an ideal baroclinic instability case with a Physical Conserving Fidelity model

To improve the energetics in the life cycle of an ideal baroclinic instability case, we develop a Physical Conserving Fidelity model （F-model）, and we compare the simulations from the F-model to those of the traditional global spectral semi-implicit model （control model）. The results for spectral kinetic energy and its budget indicate different performances at smaller scales in the two models. A two-way energy flow emerges in the generation and rapid growth stage of the baroclinic disturbance in the F-model. However, only a downscale mechanism dominates in the control model. In the F-model, the meso- and smaller scales are energized initially, and then an active upscale nonlinear cascade occurs. Thus, disturbances at prior scales are forced by both downscale and upscale energy cascades and by conversion from potential energy. An analysis of the eddy kinetic energy budget also shows remarkable enhancement of the energy conversion rate in the F-model. As a result, characteristics of the ideal baroclinic wave are greatly improved in the F-model, in terms of both intensity and time of formation.

ESTIMATION AND UNCERTAINTY QUANTIFICATION FOR PIECEWISE SMOOTH SIGNAL RECOVERY

This paper presents an application of the sparse Bayesian learning(SBL)algorithm to linear inverse problems with a high order total variation(HOTV)sparsity prior.For the problem of sparse signal recovery,SBL often produces more accurate estimates than maximum a posteriori estimates,including those that useℓ1 regularization.Moreover,rather than a single signal estimate,SBL yields a full posterior density estimate which can be used for uncertainty quantification.However,SBL is only immediately applicable to problems having a direct sparsity prior,or to those that can be formed via synthesis.This paper demonstrates how a problem with an HOTV sparsity prior can be formulated via synthesis,and then utilizes SBL.This expands the class of problems available to Bayesian learning to include,e.g.,inverse problems dealing with the recovery of piecewise smooth functions or signals from data.Numerical examples are provided to demonstrate how this new technique is effectively employed.