More Comprehensive Computational Number Theory

Computational number theory, also known as algorithmic number theory, is the study of algorithms for performing number theoretic computations. The best known problem in the field is the integer factorization, the great common divisor or the least common multiple.The largest known primes, which are usually Mersenne primes, and they were usually found by GIMPS, the Great Internet Mersenne Prime Search.

But in my opinion, the concepts of computational number theory could be more comprehensive, covering a wide range,including all the study of number theory by computers. For me, computers are so important for number theorists, just like telescopes for astronomers.

Non-parametric Treatment Comparison for Current Status Data

Current status data occur in many studies and in this case, each subject is observed only once. Furthermore, the distributions of observation times may be different for subjects in different treatment groups. This paper focuses on current status recurrent event data that concern occurrence rates of certain recurrent events such as disease infections and discuss non parametric comparison of several treatment groups. For the problem, two new tests procedures are proposed and a simulation study is conducted and shows that they are more efficient than the existing ones. An illustrative example on lung tumors is provided.

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Lie-admissible co-algebras

After introducing the concept of Lie-admissible co-algebras, we study a remarkable class corresponding to co-algebras whose co-associator satisfies invariance conditions with respect to the symmetric group 3. We then study the convolution and tensor products. An interesting class of Lie-admissible co-algebras is obtained by dualizing the Gi-associative algebras. These Lie-admissible algebras has been introduced and developed. Let us point out these initially notations.

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Non-metallic Particles Manipulation in Liquid Metals During Electromagnetic Processing

Research in manipulation of non-metallic particles in a liquid metal by using an electromagnetic (EM) field is promoted by both the requirement of more efficient materials design and the development of cost-effective electromagnetic apparatus. The particles of sub/micrometer size scan be agglomerated, segregated, aligned and/ or removed by applying a suitable EM field during liquid metal processing. The efficiency and applicability depends highly on the nature of the particles and the difference from the liquid metal matrix. In the present paper, the fundaments/physics of non-metallic particles manipulation by EM processing are discussed and some potential application possibilities in industry are proposed.

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Bias Analysis for the Principal Stratum Direct Effect in The Presence of Confounded Intermediate Variables

In epidemiological and clinical research, investigators often want to estimate the direct effect of a treatment on an outcome, which is not relayed by intermediate variables. Even if the total effect is UN confounded, the direct effect is not identified when unmeasured variables affect the intermediate and outcome variables.

This article focuses on the principal stratum direct effect (PSDE) of a randomized treatment, which is the difference between expectations of potential outcomes within latent subgroups of subjects for whom the intermediate variable would be constant, regardless of the randomized treatment assignment. Unfortunately, the PSDE will not generally be estimated in an unbiased manner without untestable conditions, even if monotonicity is assumed. Thus, we propose bounds and a simple method of sensitivity analysis for the PSDE under a monotonicity assumption.