内射子、双内射子及平坦子、上平坦子

本文引进了双内射子的概念,给出了内射子、平坦子、完全内射子、上平坦子的一些新刻划．对环R上的有限生成投身模的自同态环,以及其与环R之间的关系进行了广泛的讨论．     

Factorizations,denseness, separation,and relatively compact objects

Some of the relationships among the topological notions: ‘Hausdorff’, ‘compact’, ‘perfect’, and ‘closed’ are abstracted to a more general categorical setting, where they are shown to remain intact. An investigation is made of factorization structures (especially for single morphisms) and their relationships to strong limit operators and to the Pumplu¨n-Ro¨hrl Galois correspondence between classes of objects and classes of morphisms in any category. Many examples as well as internal characterizations of Galois-closed classes are provided.     

MV-代数、BL-代数、R0-代数与多值逻辑

证明三种不同形式的MV－代数刻画的等价性，分析MV－代数、BL－代数与R0代数的逻辑背景，提出若干可进一步研究的课题。     

Classical solvability for one-dimensional, free boundary, Florin, Muskat-Verigin, and Stefan problems

Three one-dimensional problems with free boundary for second order parabolic equations are considered, namely, the Florin, Muskat-Verigin, and Stefan problems. Existence and uniqueness theorems in the weighted Hölder spaces are established for these problems. Coercive estimates for solutions are found. Bibliography:44 titles.     

Обобщение регулярны х в круге функций, близких к выпуклым, на случай многих комплексных перемен ных

Extremal problems are treated for the classR _d, the latter being a two-dimensional generalization of the class of complex variable functions which are regular in a disc and close-to-convex.     

B0,I0,B1,I1,C0-半群

利用半群的理想和双理想呈现的包含关系定义了新的半群类B0,I0,B1,I1,C0-半群,讨论其性质,证明了正则半群S是C0-半群的充要条件是S是矩形带;B0,I0,B1,I1,C0-半群各自的直积半群和关于同余的商半群保持B0,I0,B1,I1,C0性.     

Myth,language, and complex ideologies

Ideologies use for their conservation and propagation persuasive methods of communication: rhetoric. Rhetoric is analyzed from the semiotic and logical‐mathematical points of view. The following hypotheses are established: (1) language L is a self‐explanatory system, mediated by a successive series of systems of cultural conventions, (2) connotative significances of an ideological advertising rhetoric must be known, and (3) the notion of ideological information is a neutral notion that does not imply the valuation of ideology or its conditions of veracity or falsification. Rhetorical figures like metonymy, metaphor, parable analogy, and allegory are defined as relations. Metaphor and parable are order relations. Operations of metonymic and metaphoric substitution are defined and several theorems derived from these operations have been deduced. © 2014 Wiley Periodicals, Inc. Complexity 20: 63–81, 2014     

Concerning the Collins, Reed, Roscoe, Rudin Metrisation Theorem

New criteria, in terms of the Collins-Roscoe structuring mechanism,are given for a space to be semi-stratifiable. Known characterisationsof metrisable, developable and stratifiable spaces are deduced.     

Discontinuous dynamics of a non-linear, self-excited, friction-induced, periodically forced oscillator

The discontinuous dynamics of a non-linear, friction-induced, periodically forced oscillator is studied. The analytical conditions for motion switchability at the velocity boundary in such a nonlinear oscillator are developed to understand the motion switching mechanism. Using such analytical conditions of motion switching, numerical predictions of the switching scenarios varying with excitation frequency and amplitude are carried out, and the parameter maps for specific periodic motions are presented. Chaotic and periodic motions are illustrated through phase planes and switching sections for a better understanding of motion mechanism of the nonlinear friction oscillator. The periodic motions with switching in such a nonlinear, frictional oscillator cannot be obtained from the traditional analysis (e.g., perturbation and harmonic balance method).     

Infinite median graphs, (0, 2)-graphs,and hypercubes

Hypercubes are characterized among connected bipartite graphs by interval conditions in several ways. These results are based on the following two facts: (i) connected bipartite graphs are median provided that all their intervals induce median graphs, and (ii) median (0, 2)-graphs are hypercubes. No cardinality restrictions are made.     

Quasi-symmetric 2, 3, 4-designs

Quasi-symmetric designs are block designs with two block intersection numbersx andy It is shown that with the exception of (x, y)=(0, 1), for a fixed value of the block sizek, there are finitely many such designs. Some finiteness results on block graphs are derived. For a quasi-symmetric 3-design with positivex andy, the intersection numbers are shown to be roots of a quadratic whose coefficients are polynomial functions ofv, k and λ. Using this quadratic, various characterizations of the Witt—Lüneburg design on 23 points are obtained. It is shown that ifx=1, then a fixed value of λ determines at most finitely many such designs.     

Partial cubes: structures, characterizations, and constructions

Partial cubes are isometric subgraphs of hypercubes. Structures on a graph defined by means of semicubes, and Djokovi?’s and Winkler’s relations play an important role in the theory of partial cubes. These structures are employed in the paper to characterize bipartite graphs and partial cubes of arbitrary dimension. New characterizations are established and new proofs of some known results are given.The operations of Cartesian product and pasting, and expansion and contraction processes are utilized in the paper to construct new partial cubes from old ones. In particular, the isometric and lattice dimensions of finite partial cubes obtained by means of these operations are calculated.     

Puzzles,tableaux, and mosaics

We define mosaics, which are naturally in bijection with Knutson-Tao puzzles. We define an operation on mosaics, which shows they are also in bijection with Littlewood-Richardson skew-tableaux. Another consequence of this construction is that we obtain bijective proofs of commutativity and associativity for the ring structures defined either of these objects. In particular, we obtain a new, easy proof of the Littlewood-Richardson rule. Finally we discuss how our operation is related to other known constructions, particularly jeu de taquin.     

Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.     

Scarcity,competition, and value

We suggest a value for finite coalitional games with transferable utility that are enriched by non-negative weights for the players. In contrast to other weighted values, players stand for types of agents and weights are intended to represent the population sizes of these types. Therefore, weights do not only affect individual payoffs but also the joint payoff. Two principles guide the behavior of this value. Scarcity: the generation of worth is restricted by the scarcest type. Competition: only scarce types are rewarded. We find that the types’ payoffs for this value coincide with the payoffs assigned by the Mertens value to their type populations in an associated infinite game.     

Ортопоперечники классов многомерных периодических функций, мажоранта смещанных модулей непрерывности которых содержит как степенные, так и логарифмические множители

Ortho-widths are studied for classes of multivariate periodic functions in the spaces L ^p , 1 ≤ p ≤ ∞, whose mixed moduli of continuity are bounded by a certain product of power-and logarithmic type functions.     

Terminality,normality, and transversality conditions

The maximum principle distinguishes between two phases of the optimal control problem. Some of the stated conditions are to be satisfied at points other than endpoints and some conditions are to be satisfied specifically at the endpoints. This paper utilizes the first set of conditions from the maximum principle to reexamine the second set. In the process, a new necessary condition to be satisfied at the endpoints is obtained. This condition is for certain cases easier to apply than the transversality conditions, yields additional information which may be of computational advantage, and lends itself quite naturally to an exposition of abnormal solutions. The relationship of the new condition to the transversality conditions and a discussion on normality are included. Several examples are given to illustrate the results.This research was supported in part by NASA under Grant NGR-03-002-224 and NSF Science Faculty Fellowship. The authors are indebted to Professors G. Leitmann, G. Basile, and E. Cliff for their helpful comments and suggestions.     

Fermat Dynamics, Matrix Arithmetics, Finite Circles, and Finite Lobachevsky Planes

Congruences generalizing Fermat's little theorem are proved for the traces of powers of integer matrices. Their relations to Lobachevsky geometries over finite fields and combinatorics of the matrix squaring operation as well as to the corresponding Riemann surfaces with their Kepler cubes are discussed.     

Copulae,Self-Affine Functions,and Fractal Dimensions

We use the fact that the functions defined on the unit interval whose graphs support a copula are those that are Lebesgue-measure-preserving in order to characterize self-affine functions whose graphs are the support of a copula. This result allows computation of the Hausdorff, packing, and box-counting dimensions. The discussion is applied to classic examples such as the Peano and Hilbert curves, and the results are extended to discontinuous self-affine functions.     

Achievable sets, brambles, and sparse treewidth obstructions

One consequence of the graph minor theorem is that for every k there exists a finite obstruction set Obs(TW?k). However, relatively little is known about these sets, and very few general obstructions are known. The ones that are known are the cliques, and graphs which are formed by removing a few edges from a clique. This paper gives several general constructions of minimal forbidden minors which are sparse in the sense that the ratio of the treewidth to the number of vertices n does not approach 1 as n approaches infinity. We accomplish this by a novel combination of using brambles to provide lower bounds and achievable sets to demonstrate upper bounds. Additionally, we determine the exact treewidth of other basic graph constructions which are not minimal forbidden minors.