Some Theorems on Leibniz n-Algebras from the Category Un(Lb)

We study the Leibniz n-algebra Un(∑),whose multiplication is defined viathe bracket of a Leibniz algebra ∑ as[x1,...,xn]=[x1,[...,[xn-2,[xn-1,xn]]...]].Weshow that Un(∑) is simple if and only if ∑ is a simple Lie algebra.An analog of Levi'stheorem for Leibniz algebras in Un(Lb) is established and it is proven that the Leibnizn-kernel of Un(Σ) for any semisimple Leibniz algebra Σ is the n-algebra Un(Σ).     

Pure tetrahedral quadruple systems with index two

An oriented tetrahedron defined on four vertices is a set of four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order $n$ with index $\lambda$, denoted by ${\text{TQS}}_{\lambda }\left(n\right)$, is a pair $\left(X,\mathrm{?}\right)$, where $X$ is an $n$‐set and $\mathrm{?}$ is a set of oriented tetrahedra (blocks) such that every cyclic triple on $X$ is contained in exactly $\lambda$ members of $\mathrm{?}$. A ${\text{TQS}}_{\lambda }\left(n\right)$ is pure if there do not exist two blocks with the same vertex set. When $\lambda =1$, the spectrum of a pure TQS $\left(n\right)$ has been completely determined by Ji. In this paper, we show that there exists a pure ${\text{TQS}}_2\left(n\right)$ if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$. A corollary is that a simple ${\text{QS}}_4\left(n\right)$ also exists if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$.     

就单摆问题引入大学物理教学新模式

单摆教学的过程中引入MATLAB数值计算的教学新模式,可以有效地改善大学物理教学的枯燥方式,有助于提高学生对大学物理课中抽象的、复杂的物理现象和规律的理解,也有助于促进对所学数学知识的实际应用.这种新教学模式是深化高等工程教育改革、加快新工科建设、促进创新型工科人才培养的有效手段.     

Something out of nothing: a Bayesian learning computational model for the social construction of value

ABSTRACT

This article develops a formalism for the social construction of value. Using a model based on Bayesian agents, it demonstrates how “something” arises out of “nothing” via the emergence of durable value conventions and shows how the developed framework can be used to investigate socially constructed valuations under a variety of circumstances. The resulting analysis clarifies why assumptions that collectives will converge upon the “intrinsic” (i.e., non-socially originating) value of an object (e.g., market efficiency) may not hold for mixed social and non-social valuation regimes, explains the dependency of socially constructed valuations on early accidents, demonstrates the effects of confident actors on constructed values, and identifies the production of time-dependent ratcheting effects from the interaction of bubbles with value conventions.     

Decomposable super‐simple NRBIBDs with block size 4 and index 6

Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable ‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable ‐BIBDs are (mod ) and . In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable ‐RBIBD, namely (mod ) and , are sufficient. A few new pairwise balanced designs are also given.     

Complete hom-Lie superalgebras

Abstract

In this article, we investigate some basic results on complete hom-Lie superalgebras. In particular, we present some sufficient conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra. Making use of these conditions, we build a family of complete hom-Lie superalgebras.