The Pólya information divergence

Extensions of Sanov’s Theorem and the Conditional Limit Theorem (CoLT) are established for a multicolor Pólya-Eggenberger (PE) urn sampling scheme, giving the Pólya information divergence and a Pólya extension to the Maximum Relative Entropy (MaxEnt) method. Pólya MaxEnt includes the standard MaxEnt, as well as its variants used in Bose-Einstein, Fermi-Dirac and intermediate (Acharya-Swamy) statistics, as special cases. In the PE setting, standard MaxEnt is, in general, asymptotically inconsistent.     

EXTENSION OF RSA CRYPTOSYSTEMS TO MATRIX RINGS

A generalization of the RSA cryptosystem in the ring of matrices over Z/mZ is presented. It is shown that factorization of the modulus m is needed to compute the exponent of the group formed by either non-singular matrix messages or upper triangular matrices including diagonal elements thus offering the same level of security as the RSA system. The latter method employing the triangular matrices as messages seems to be more practical than the use of arbitrary non-singular matrix messages. The scheme is as suitable for privacy and authentication as its predecessor.     

Elliptic Curve Point Multiplication by Generalized Mersenne Numbers

Montgomery modular multiplication in the residue number system （RNS） can be applied for elliptic curve cryptography. In this work, unified modular multipliers over generalized Mersenne numbers are proposed for RNS Montgomery modular multiplication, which enables efficient elliptic curve point multiplication （ECPM）. Meanwhile, the elliptic curve arithmetic with ECPM is performed by mixed coordinates and adjusted for hardware implementation. In addition, the conversion between RNS and the binary number system is also discussed. Compared with the results in the literature, our hardware architecture for ECPM demonstrates high performance. A 256-bit ECPM in Xilinx XC2VP100 field programmable gate array device （FPGA） can be performed in 1.44 ms, costing 22147 slices, 45 dedicated multipliers, and 8.25K bits of random access memories （RAMs）.     

Effects of H2 or CO2 addition, equivalence ratio, and turbulent straining on turbulent burning velocities for lean premixed methane combustion

Using hydrogen or carbon dioxide as an additive, we investigate the bending effect of turbulent burning velocities (ST/SL) over a wide range of turbulent intensities (u^′/SL) up to 40 for lean premixed methane combustion at various equivalence ratios (?), where SL is the laminar burning velocity. Experiments are carried out in a cruciform burner, in which a sizable downward-propagating premixed CH₄/diluent/air flame interacts with intense isotropic turbulence in the central region without influences of ignition and unwanted turbulence from walls. Simultaneous measurements using the pressure transducer and pairs of ion-probe sensors at various positions of the burner show that effects of gas velocities and pressure rise due to turbulent combustion on ST of lean CH₄/H₂/air flames can be neglected, confirming the accuracy of the ST data. Results with increasing hydrogen additions (δ=10, 20, and 30% in volume) show that the bending of ST/SL vs u^′/SL plots is diminished when compared to data with δ=0, revealing that high reactivity and diffusivity of hydrogen additives help the reaction zone remaining thin even at high u^′/SL. In contrast, the bending effect is strongly promoted when CO₂ is added due to radiation heat losses. This leads to lower values of ST/SL at fixed u^′/SL and ?, where the slope n can change signs from positive to negative at sufficiently large u^′/SL, suggesting that the reaction zone is no longer thin. All ST data with various δ can be well approximated by a general correlation (ST−SL)/u^′=0.17Da^0.43, covering both corrugated flamelet and distributed regimes with very small data scatter, where Da is the turbulent Damköhler number. These results are useful in better understanding how turbulence and diluents can influence the canonical structures of turbulent premixed flames and thus turbulent burning rates.     

Distribution and abundance of nesting common and Caspian terns on the North American Great Lakes, 1976 to 1999

Canadian and US federal wildlife agencies completed three surveys (1976–1980, 1989–1991, and 1997–2000) to census colonial waterbirds breeding on the Great Lakes. We here summarize and comment on nest numbers and colony site distribution of common terns (Sterna hirundo) and Caspian terns (Hydroprogne caspia). Common terns are in serious trouble on the Great Lakes. Numbers declined with substantial losses in nests (− 19.1%) and colony sites (− 23.2%) between the first and third censuses. An increase in numbers at US sites (+ 26.6%) did not compensate for losses (− 33.1%) at Canadian sites. Caspian terns increased in nest numbers (+ 65.9%) and colony sites (+ 50.0%) over the same period. The increase at US sites (136.5%) was greater than at Canadian sites (11.5%). Most (70.7%, n = 186) common tern sites had nests during only one census; 17 sites (6.5%) had nests during all censuses. In contrast, 9 of 33 (27.2%) Caspian tern sites had nests during all censuses and contained a majority of nests (50–82%) in each census. Pairs of both species nested on natural substrates across the Great Lakes. Common terns nested mostly on artificial (human-constructed) substrates on the lower Great Lakes. We identify site characteristics that may have contributed to long-term (three census) occupancy by common terns (small size, artificial substrates, absence of ring-billed gulls) and Caspian terns (natural substrates on large, remote islands). We suggest an urgent need for protection and conservation of common tern colonies and identify specific priority sites for implementation of management protocols.     

Transient freezing of liquids in forced flow inside convectively cooled tubes

The aim of this investigation is to study the characteristics of solidification of a liquid flowing through a convectively cooled pipe under different flow situations. A mathematical model is developed by establishing an energy balance. The amount of heat transferred from the liquid layer to the freeze-front in a tube section is directly proportional to the convective heat transfer coefficient and the difference between the average temperature of the fluid at the section and the freezing point. The limiting conditions for the commencement of the solidification process are stated. The formulated set of conjugated heat transfer equations is analysed for both laminar and turbulent flows. The governing equations are solved numerically for a specific range of parameters and their characteristics of the process discussed.     

COMPUTATIONAL FLUID DYNAMICS （CFD） SIMULATIONS OF DRAG REDUCTION WITH PERIODIC MICRO-STRUCTURED WALL

Computational fluid dynamics（CFD） simulations are adopted to investigate rectangular microchannel flows with various periodic micro-structured wall by introducing velocity slip boundary condition at low Reynolds number. The purpose of the current study is to numerically find out the effects of periodic micro-structured wall on the flow resistance in rectangular microchannel with the different spacings between microridges ranging from 15 to 60 pm. The simulative results indicate that pressure drop with different spacing between microridges increases linearly with flow velocity and decreases monotonically with slip velocity; Pressure drop reduction also increases with the spacing between microridges at the same condition of slip velocity and flow velocity. The results of numerical simulation are compared with theoretical predictions and experimental results in the literatures. It is found that there is qualitative agreement between them.     

Compromise Fuzzy Multi-Objective Linear Programming (CFMOLP) heuristic for product-mix determination

This paper models a crisp Linear Programming (LP) as a Compromise Fuzzy Multi-Objective LP (CFMOLP). The application of CFMOLP has been focused on an industrial engineering problem that seeks profit maximisation by optimising product-mix. Imprecision of the large volume of industrial data and the conglomerated decision from all levels of management lead fuzzication of the identified constraints and the objective functions as well. The crisp model described is in the form of crisp-Multi-Objective Linear Programming (MOLP) with objective functions, functional constraints and non-negativity constraints. This model is formulated as a fuzzy-MOLP and subsequently converted into an equivalent compromise-MOLP model. The paper describes the development process for the CFMOLP model and its application along with appropriate interpretation.     

Studies on the influence of tris(pentafluorophenyl)borane on the properties of ethylene carbonate, dimethyl carbonate and poly(ethylene oxide) dimethyl ether lithium trifluoromethanesulfonate electrolytes

In this paper we present our studies on the properties of battery electrolyte based on EC/DMC (ethylene carbonate/dimethyl carbonate, w/w ratio 2:5) and PEODME (poly(ethylene oxide) dimethyl ether) (M_w = 500) doped with LiCF₃SO₃-lithium trifluoromethanesulfonate (LiTf) and modified with TPFPB (tris(pentafluorophenyl)borane) as a potential anion trapping agent. We were particularly interested how this compound behaves in different solvents, e.g. battery mixture EC/DMC and model polymeric matrix PEODME. We also verified stability of the proposed solutions by means of DSC and FTIR, determined influence on conductivity and lithium transference numbers by impedance spectroscopy, and finally attempted to define mechanism of influence of boron addition on different systems.     

关于Fibonacci三角形猜想k=13的证明

运用初等方法,引入Fibonacci数的负指标,证明了在k=13时Fibonacci三角形不存在.