Design and analysis of a faster King-Werner-type derivative free method

We introduce a new faster King-Werner-type derivative-free method for solving nonlinear equations. The local as well as semi-local convergence analysis is presented under weak center Lipschitz and Lipschitz conditions. The convergence order as well as the convergence radii are also provided. The radii are compared to the corresponding ones from similar methods. Numerical examples further validate the theoretical results.

Weak Bi-Center and Critical Period Bifurcations of a Z2-Equivariant Quintic System

With the help of computer algebra system-Mathematica, this paper considers the weak center problem and local critical periods for bi-center of a [Formula: see text]-equivariant quintic system with eight parameters. The order of weak bi-center is identified and the exact maximum bifurcation number of critical periods generated from the bi-center is given via the combination of symbolic calculation and numerical analysis.

America’s Wars on Poverty and the Building of the Welfare State

On January 5, 2014—the fiftieth anniversary of President Lyndon Johnson’s launch of the War on Poverty—the New York Times asked a panel of opinion leaders a simple question: “Does the U.S. Need Another War on Poverty?” While the answers varied, all the invited debaters accepted the martial premise of the question—that a war on poverty had been fought and that eliminating poverty was, without a doubt, a “fight,” or a “battle.” Yet the debate over the manner—martial or not—by which the federal government and public policy has dealt with the issue of poverty in the United States is still very much an open-ended one. The evolution and development of the postwar American welfare state is a story not only of a number of “wars,” or individual political initiatives, against poverty, but also about the growth of institutions within and outside government that seek to address, alleviate, and eliminate poverty and its concomitant social ills. It is a complex and at times messy story, interwoven with the wider historical trajectory of this period: civil rights, the rise and fall of a “Cold War consensus,” the emergence of a counterculture, the Vietnam War, the credibility gap, the rise of conservatism, the end of “welfare,” and the emergence of compassionate conservatism. Mirroring the broader organization of the American political system, with a relatively weak center of power and delegated authority and decision-making in fifty states, the welfare model has developed and grown over decades. Policies viewed in one era as unmitigated failures have instead over time evolved and become part of the fabric of the welfare state.

Weak Center and Bifurcation of Critical Periods in a Cubic Z2-Equivariant Hamiltonian Vector Field

This paper focuses on the problems of weak center and local bifurcation of critical periods for a class of cubic Z2-equivariant planar Hamiltonian vector fields. By computing the period constants carefully, one can see that there are three weak centers: (±1, 0) and the origin. The corresponding weak center conditions are also derived. Meanwhile, we address the problem of the coexistence of bifurcation of critical periods that occurred from (±1, 0) and the origin.

Explaining Political Tunnel Vision: Politics and Economics in Crisis-Ridden Europe, Then and Now

The grip of austerity in European politics since 2008 presents a double puzzle: electorally weak center-left parties offering no definite alternative, and the surprisingly efficient pursuit of “fiscal consolidation”. To understand this double puzzle this article investigates the institutional bases of alternative economic thinking during the 1930s versus the post-2008 crisis years. Noting the recent prominence of a new social type, theEuropean economist-technocrat(eet), I highlight the historically specific order to which theeetis indigenous: rarefied, international professional circuits that tend to work over, not through, party politics. This contrasts sharply with the nationally-based, party-connected economists who developed new economic orthodoxies between the 1930s and 1960s, including Keynes himself. Approaching the study of economic culture in the public sphere in a Polanyian moral markets framework, I argue that the linkages between European economics and financial technocracies help to explain Europe’s double puzzle. Theoretically, I argue that a focus on expertise and parties, and not just states, is central to our understanding of economic culture in the public sphere.

MARITAL ALLIANCES AND AFFINAL RELATIVES (SHENG甥 ANDHUNGOU婚購) IN THE SOCIETY AND POLITICS OF ZHOU CHINA IN THE LIGHT OF BRONZE INSCRIPTIONS

Several hundred inscribed bronze objects dating from Western and Eastern Zhou periods were commissioned for or by married women. Several dozen inscriptions are known whose commissioners called themselvessheng生 (甥) of a number of lineages. In pre-Qin Chinese, the termsheng甥 designated several categories of affinal relatives: paternal aunts’ sons, maternal uncles’ sons, wives’ brothers, sisters’ husbands, and sons of sisters or daughters. The wide geographical and chronological spread of female- orsheng-related vessels, as well as dedications to “many affinal relatives” (hungou婚購) in bronze inscriptions point to the importance of marital ties in early Chinese society and politics.Focusing on the inscriptions commissioned bysheng, the present article suggests that even when concluded at a considerable distance, marriages produced long-term mutual obligations for male members of the participating lineages or principalities. Affinal relationships represented social and political capital that could be converted in terms of individuals’ careers and prestige or benefits for their whole lineages/states. In sum, starting from the early Western Zhou period, marital alliances represented a substantial integrative factor in early Chinese politics. On the one hand, marital alliances helped to consolidate the radial network of Zhou states centered on the Zhou king. On the other hand, they facilitated the construction of decentralized regional and interregional inter-state networks. The latter guaranteed the stability of the Zhou political system even when it had a weak center. As a result, the Zhou networks did not fall apart following crises in the Zhou royal house, but continued to expand by the inclusion of new members.

THE CENTER OF THE CATEGORY OF BIMODULES AND DESCENT DATA FOR NONCOMMUTATIVE RINGS

Let A be an algebra over a commutative ring k. We compute the center of the category of A-bimodules. There are six isomorphic descriptions: the center equals the weak center, and can be described as categories of noncommutative descent data, comodules over the Sweedler canonical A-coring, Yetter–Drinfeld type modules or modules with a flat connection from noncommutative differential geometry. All six isomorphic categories are braided monoidal categories: in particular, the category of comodules over the Sweedler canonical A-coring A ⊗ A is braided monoidal. We provide several applications: for instance, if A is finitely generated projective over k then the category of left End k(A)-modules is braided monoidal and we give an explicit description of the braiding in terms of the finite dual basis of A. As another application, new families of solutions for the quantum Yang–Baxter equation are constructed: they are canonical maps Ω associated to any right comodule over the Sweedler canonical coring A ⊗ A and satisfy the condition Ω3 = Ω. Explicit examples are provided.

On the critical periods of Liénard systems with cubic restoring forces

We study local bifurcations of critical periods in the neighborhood of a nondegenerate center of a Liénard system of the formx˙=−y+F(x),y˙=g(x), whereF(x)andg(x)are polynomials such thatdeg(g(x))≤3,g(0)=0, andg′(0)=1,F(0)=F′(0)=0and the system always has a center at(0,0). The set of coefficients ofF(x)andg(x)is split into two strata denoted bySIandSIIand(0,0)is called weak center of type I and type II, respectively. By using a similar method implemented in previous works which is based on the analysis of the coefficients of the Taylor series of the period function, we show that for a weak center of type I, at most[(1/2)deg(F(x))]−1local critical periods can bifurcate and the maximum number can be reached. For a weak center of type II, the maximum number of local critical periods that can bifurcate is at least[(1/4)deg(F(x))].