Canonical Differential Calculi for Finitely Generated Abelian Groups and Their Fermionic Representations

Canonical differential calculi are defined for finitely generated Abelian groups with involutions existing consistently. Two such the canonical calculi are presented. Fermionic representations for canonical calculi are defined based on quantized calculi. Fermionic representations for aforementioned two canonical calculi are searched out.

Physical-Layer Secret Key Generation for Dual-Task Scenarios

Physical-layer secret key generation(PSKG)provides a lightweight way for group key(GK)sharing between wireless users in large-scale wireless networks.However,most of the existing works in this field consider only group communication.For a commonly dual-task scenario,where both GK and pairwise key(PK)are required,traditional methods are less suitable for direct extension.For the first time,we discover a security issue with traditional methods in dual-task scenarios,which has not previously been recognized.We propose an innovative segment-based key generation method to solve this security issue.We do not directly use PK exclusively to negotiate the GK as traditional methods.Instead,we generate GK and PK separately through segmentation which is the first solution to meet dual-task.We also perform security and rate analysis.It is demonstrated that our method is effective in solving this security issue from an information-theoretic perspective.The rate results of simulation are also consistent with the our rate derivation.

Growth performance and physiological parameters of the second generation selected and control groups of Pinctada martensii

In May of 2007,the second generation selected （SS） and control （SC） groups of pearl oyster Pinctada martensii were established by selecting 10% breeders with the largest and mean shell length,respectively,from the first generation selected group.Growth performance of the SS and SC groups were compared on the basis of measurement data at Days 8,18,60,95,195 and 365.On Day 365,100 individuals （60.0–75.0 mm at shell length） were sampled from each group and then subjected to the experiment where physiological parameters such as filtrate rate,oxygen consumption and ammonia excretion were measured at 15,20,25 and 30°C.The results show that the SS group had significantly larger mean shell length and shell height than the SC group at Days 8,18,60,95,195 and 365 （P 0.05）.The genetic gains at different ages varied from 6.0% to 17.0% for shell length and 5.7% to 14.6% for shell height,respectively.At 15,20,25 and 30 ° C,the SS groups had significantly larger filtrate rate than the SC group （P 0.05）.At 15 and 25 °C,the differences in oxygen consumption rate between the SS and SC groups were not significant （P 0.05）.At 20 and 30 °C,however,the oxygen consumption rate of the SS group was significantly larger than the SC group （P 0.05）.At 15,20,25 and 30 °C,there were no significant differences in ammonia excretion rate between the SS and SC groups （P 0.05）.The present results indicate that there existed considerable genetic variability in the base population and a further selection could be likely fruitful.Mass selection for faster growth might produce animals that had higher intake of metabolizable energy by virtue of faster filtrating behavior.

Five Large Generation Groups: Competing in Capital Operation

Since the reform of electric power industry in 2002, the newly established five large generation groups have been persisting in the development strategy of "taking electricity as the core and extending to up-and-downstream businesses." Stringent measures were taken in capital operation and their potential has been shown through electric power as- sets acquiring, coal and financial resources investing, capital market financing as well as power utility restructuring. The five groups are playing more and more important roles in merger and acquisition (M&A) and capital markets.

Geometric Origin of Staggered Fermion：Direct Product K—Cycle

Staggered formalism of lattice fermion can be cast into a form of direct product K-cycle in noncommutative geometry. We prove the correspondence between this staggered K-cycle and a canonically defined K-cycle for finitely generated Abelian groups where a lattice appears as a special case.

ON THE FUNDAMENTAL GROUP OF OPEN MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE

The authors establish some uniform estimates for the distance to halfway points of minimalgeodesics in terms of the distantce to end points on some types of Riemannian manifolds, andthen prove some theorems about the finite generation of fundamental group of Riemannianmanifold with nonnegative Ricci curvature, which support the famous Milnor conjecture.

The Weakly Potency of Certain HNN Extensions of Nilpotent Groups

In this paper we give a characterization for certain HNN extensions oi suogroup separable groups with normal associated subgroups to be weakly potent. We then apply our result to show that certain HNN extensions of finitely generated nilpotent groups with central associated subgroups are weakly potent.

The generation of group delay ripple of chirped fiber gratings

The analysis of the group delay ripple (GDR) generated by chirped fiber gratings is developed based on the Fabry-Perot (F-P) resonator. It shows clearly how the GDR is generated and why the periods of GDR varies along the chirped fiber gratings. It could also explain why apodization could suppress the GDR and how apodization affects the chirp of the grating. The theory could be used to devise the apodization of fiber gratings.

Survey on Lie Group Machine Learning

Lie group machine learning is recognized as the theoretical basis of brain intelligence,brain learning,higher machine learning,and higher artificial intelligence.Sample sets of Lie group matrices are widely available in practical applications.Lie group learning is a vibrant field of increasing importance and extraordinary potential and thus needs to be developed further.This study aims to provide a comprehensive survey on recent advances in Lie group machine learning.We introduce Lie group machine learning techniques in three major categories:supervised Lie group machine learning,semisupervised Lie group machine learning,and unsupervised Lie group machine learning.In addition,we introduce the special application of Lie group machine learning in image processing.This work covers the following techniques:Lie group machine learning model,Lie group subspace orbit generation learning,symplectic group learning,quantum group learning,Lie group fiber bundle learning,Lie group cover learning,Lie group deep structure learning,Lie group semisupervised learning,Lie group kernel learning,tensor learning,frame bundle connection learning,spectral estimation learning,Finsler geometric learning,homology boundary learning,category representation learning,and neuromorphic synergy learning.Overall,this survey aims to provide an insightful overview of state-of-the-art development in the field of Lie group machine learning.It will enable researchers to comprehensively understand the state of the field,identify the most appropriate tools for particular applications,and identify directions for future research.