LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.

Wiener Index, Hyper-Wiener Index, Harary Index and Hamiltonicity Properties of graphs

In this paper, in terms of Wiener index, hyper-Wiener index and Harary index, we first give some sufficient conditions for a nearly balance bipartite graph with given minimum degree to be traceable. Secondly, we establish some conditions for a k-connected graph to be Hamilton-connected and traceable for every vertex, respectively.

Biodiversity of the Micro-morphologies of the Petal Epidermis of Angiosperms &Their Scientific Aesthetics, Quasi-Geometry

The micro-morphologies and biodiversities of the epidermis of flower petals of angiosperms were reported for the first time. By manual slicing anatomy and microscopic photography technique, the micro-morphologies of the upper and lower epidermis of petals of some common ornamental flowers in Kunming were studied, and the biodiversities were discovered. The results showed these much-varied pigment cells appeared not only a new compensation to anatomy, but a new criteria to taxonomy, so that a brand new research field of “Cell Taxonomy” was established instead of the current “Chromosome Taxonomy” widely used in phytosystematics research. Furthermore, the most interesting and significant phenomena was their scientific aesthetics: these pigment cells of flower petals were quite special, planary, far different from the ordinary plant cells in plant organs & tissues. By comparison to ordinary geometry, these colorful cells of the fresh flower petals could be described as “Quasi-geometry” for their special origin and micro-morphological characteristics. As for the aspect of art, it was quite similar to “Quasi-crystal” discovered by Daniel Schechtman, so that the art future was discussed, obviously another new epoch of scientific-art history began.

A Two-Unit Cold Standby Repairable System with One Replaceable Repair Facility and Delay Repair: Some Reliability Problems

This paper considers a two–unit same cold standby repairable system with a replaceable repair facility and delay repair .The failure time of unit is assumed to follow exponential distribution , and the repair time and delay time of failed unit are assumed to follow arbitrary distributions , whereas the failure and replacement time distributions of the repair facility are exponential and arbitrary . By using the Markov renewal process theory, some primary reliability quantities of the system are obtained.

Aerodynamic effects of impeller-diffuser axial misalignment in low-flow-coefficient centrifugal compressor

A numerical investigation on the aerodynamic effects of impeller-diffuser axial misalignment in the low-flow-coefficient centrifugal compressor is conducted through three-dimensional CFD analysis.The results show that the flow,especially near the diffuser inlet,is influenced by the axial misalignment obviously.When the impeller offsets to one side,the pressure at diffuser inlet close to this side will descend,and the vortex in the cavity on the other side will partially enter the diffuser and then result in the back flow.The performances of the stage and its components also change with the impeller-diffuser axial misalignment.There exists an optimum offset making the efficiency maximum at a given operating point.Furthermore,the effect of impeller-diffuser axial misalignment on the axial thrust is pronounced.The axial thrust is nearly increased linearly with the increase of axial misalignment.The aerodynamic effects of impeller-diffuser axial misalignment in the low-flow-coefficient centrifugal compressor behaves more remarkably at the large flow rate.To alleviate the aerodynamic effects of impeller-diffuser misalignment,a rounding in the meridional plane at the diffuser inlet can be applied.

The Number of Solutions of Certain Equations over Finite Fields

Let s be a positive integer,p be an odd prime,q=p^(s),and let F_(q)be a finite field of q elements.Let N_(q)be the number of solutions of the following equations:(x_(1)^(m_(1))+x_(2)^(m_(2))+…+x_(n)^(m_(n)))^(k)=x_(1)x_(2)…x_(n)x^(k_(n+1))_(n+1)…x^(k_(t))_(t)over the finite field F_(q),with n≥2,t>n,k,and k_(j)(n+1≤j≤t),m_(i)(1≤i≤n)are positive integers.In this paper,we find formulas for N_(q)when there is a positive integer l such that dD|(p^(l)+1),where D=1 cm[d_(1),…,d_(n)],d=gcd(n∑i=1M/m_(i)-kM,(q-1)/D),M=1 cm[m_(1),…,m_(n)],d_(j)=gcd(m_(j),q-1),1≤j≤n.And we determine N_(q)explicitly under certain cases.This extends Markoff-Hurwitz-type equations over finite field.

Extending Slow Manifold Near Generic Transcritical Canard Point

We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory combined with the recently developed blow-up technique, the existence of canard cycles, relaxation oscillations and solutions near the attracting branch of the critical manifold is established. The asymptotic expansion of the parameter for which canard exists is obtained by a version of the Melnikov method.