The pricing and optimal strategies of callable warrants

In this paper, we introduce a valuation model of callable warrants under a setting of the optimal stopping problem between the holder (investor) and the issuer (firm). A warrant is the right to purchase new shares at a predetermined price. When the new stocks are issued, the value of the stock is diluted. We consider the model taking the dilution into account. After identifying optimal policies for the issuer and the investor, we explore the analytical properties of the optimal exercise and call boundaries for the holder and the issuer, respectively. Furthermore, the value of such a callable warrant and the optimal critical prices are examined numerically using the binomial method.     

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）.     

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.     

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.     

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.     

Fabrication and performance of MMW and SMMW platelet horn arrays

Future spaceborne millimeter and sub-millimeter wave sensing systems will require the sensitivity and resolution only achievable with large focal plane array receiving systems. A technique has been developed for the low cost fabrication of large arrays of millimeter and sub-millimeter wave corrugated feed horns. These arrayed horns exhibit high efficiency and symmetrical receiving patterns and are compatible with integrated receivers. W-band test results of a 3×3 array are presented.     

Fuzzy Horn logic II

The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present generalizations of results from the bivalent case. Namely, we characterize model classes of general implicational theories, finitary implicational theories, and Horn theories by means of closedness under suitable algebraic constructions.     

Fuzzy Horn logic I

The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability equals degree of truth) from which we get some particular cases by imposing restrictions on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic.