Factorisation of Littlewood-Richardson coefficients

The hive model is used to show that the saturation of any essential Horn inequality leads to the factorisation of Littlewood-Richardson coefficients. The proof is based on the use of combinatorial objects known as puzzles. These are shown not only to account for the origin of Horn inequalities, but also to determine the constraints on hives that lead to factorisation. Defining a primitive Littlewood-Richardson coefficient to be one for which all essential Horn inequalities are strict, it is shown that every Littlewood-Richardson coefficient can be expressed as a product of primitive coefficients. Precisely the same result is shown to apply to the polynomials defined by stretched Littlewood-Richardson coefficients.     

换能器前辐射头与轴向相平行方向的弯曲振动

复合棒型换能器前面的变截面组件在工作时常伴有弯曲振动现象，这在一定程度上会影响换能器的工作性能；利用复合棒型换能器的纵向振动基频与前辐射头弯曲振动的恰当耦合，可展宽换能器的频带。本文用有限元法，研究了前辐射头在声换能器组成中的弯曲振动问题，与测试结果相吻合。     

All General Solutions of Post Equations

In a previous paper, we have described all reproductive general solutions of a Post equation, supposing that a general solution is known. In this paper we describe all general solutions of Post equation, supposing that a general solution of this equation is known （Theorem 6）. As a special case we get the previous characterization of reproductive solutions and a similar result for Boolean equations （Theorem 9）.     

On the Boolean connectivity problem for Horn relations

Gopalan et al. studied in [P. Gopalan, P.G. Kolaitis, E.N. Maneva, C.H. Papadimitriou, The connectivity of Boolean satisfiability: computational and structural dichotomies, in: Proceedings of the 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006, 2006, pp. 346-357] and [P. Gopalan, P.G. Kolaitis, E.N. Maneva, C.H. Papadimitriou, The connectivity of Boolean satisfiability: computational and structural dichotomies, SIAM J. Comput. 38 (6) (2009) 2330-2355] connectivity properties of the solution-space of Boolean formulas, and investigated complexity issues on the connectivity problems in Schaefer’s framework. A set S of logical relations is Schaefer if all relations in S are either bijunctive, Horn, dual Horn, or affine. They first conjectured that the connectivity problem for Schaefer is in P. We disprove their conjecture by showing that there exists a set S of Horn relations such that the connectivity problem for S is -complete. We also investigate a tractable aspect of Horn and dual Horn relations with respect to characteristic sets.     

Exclusive and essential sets of implicates of Boolean functions

In this paper we study relationships between CNF representations of a given Boolean function f and certain sets of implicates of f. We introduce two definitions of sets of implicates which are both based on the properties of resolution. The first type of sets, called exclusive sets of implicates, is shown to have a functional property useful for decompositions. The second type of sets, called essential sets of implicates, is proved to possess an orthogonality property, which implies that every CNF representation and every essential set must intersect. The latter property then leads to an interesting question, to which we give an affirmative answer for some special subclasses of Horn Boolean functions.     

Honking noise corrections for traffic noise prediction models in heterogeneous traffic conditions like India

In developing countries like India, the nature of the composition of traffic is heterogeneous. A heterogeneous traffic flow consists of vehicles that have different sizes, speeds, vehicle spacing and operating characteristics. As a result of the widely varying speeds, vehicular dimensions, lack of lane disciplines, honking becomes inevitable. In addition, it changes the urban soundscape of developing countries. In heterogeneous traffic conditions, horn events increase noise level (L_den) by 0.5–13 dB(A) as compared to homogenous traffic conditions. Therefore, the traffic prediction models that are used for homogenous traffic conditions are not applicable in heterogeneous traffic conditions. To increase the accuracy of noise prediction models, in depth understanding of heterogeneous traffic noise is required. Understanding the real traffic noise characteristics requires quantification of some of the basic traffic flow characteristics such as speed, flow, Level Of Service (LOS) and density. In a given roadway, the noise level changes with density and LOS on the road. In this paper, a new factor for horn correction is introduced with respect of Level Of Service (LOS). The horn correction values can be incorporated in traffic noise models such as CRTN, FHWA, and RLS 90, while evaluating heterogeneous traffic conditions.     

犀牛角及其替代品的红外光谱分析

对犀牛角及其替代品进行红外光谱分析,结果表明,犀牛角在2350cm-1有两个磷脂P-H伸缩振动的吸收峰,水牛角在此处也有两个吸收峰,强度稍高于犀牛角,而其他角样品在此处只有一个吸收峰或无吸收峰;在1733cm-1有氨基己糖和磷脂的C=O伸缩振动弱吸收峰,在881cm-1有牛磺酸的S-O伸缩振动吸收峰,其他角样品都无此吸...     

A partial Horn recursion in the cohomology of flag varieties

Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of “smaller” flag varieties. We consider the type A partial flag variety and find that its cohomology exhibits a Horn recursion on a certain deformation of the cup product defined by Belkale and Kumar (Invent. Math. 166:185–228, 2006). We also show that if a product of Schubert classes is non-vanishing on this deformation, then the associated structure constant can be written in terms of structure constants coming from induced Grassmannians.