Two centuries ago, in his celebrated work Disquisitiones Arithmeticae of 1801, Gauss laid down the beautiful law of composition of integral binary quadratic forms which would play such a critical role in number theory in the decades to follow. Even today, two centuries later, this law of composition still remains one of the primary tools for understanding and computing with the class groups of quadratic orders. It is hence only natural to ask whether higher analogues of this composition law exist that could shed light on the structure of other algebraic number rings and ﬁelds. ...
Efﬁciency is a prime concern in syntactic MT decoding, yet signiﬁcant developments in statistical parsing with respect to asymptotic efﬁciency haven’t yet been explored in MT. Recently, McDonald et al. (2005b) formalized dependency parsing as a maximum spanning tree (MST) problem, which can be solved in quadratic time relative to the length of the sentence. They show that MST parsing is almost as accurate as cubic-time dependency parsing in the case of English, and that it is more accurate with free word order languages. ...
Special and general relativity are the theories describing the physics of space
and time. Space and time are explored with clocks and electromagnetic signals.
Therefore, special and general relativity are related to precise clocks and the
thorough understanding of signal propagation. The ever-increasing accuracy
of clocks together with novel methods for precision time transfer and clock
synchronization are pivotal for the new generation of experiments probing the
validity of Einstein’s theories from subatomic distances to cosmic scales....
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Convergence Results on a Second-Order Rational Difference Equation with Quadratic Terms
Abstract In this paper we demonstrate how Lyapunov-Krasovskii functionals can be used to obtain exponential bounds for the solutions of time-invariant linear delay systems. Keywords: time delay system, exponential estimate, Lyapunov-Krasovskii functional.
The objective of this note is to describe a systematic procedure of constructing quadratic Lyapunov functionals for (exponentially) stable linear delay systems in order to obtain exponential estimates for their solutions.
We prove that a nonrenormalizable smooth unimodal interval map with critical order between 1 and 2 displays decay of geometry, by an elementary and purely “real” argument. This completes a “real” approach to Milnor’s attractor problem for smooth unimodal maps with critical order not greater than 2. 1. Introduction The dynamical properties of unimodal interval maps have been extensively studied recently. A major breakthrough is a complete solution of Milnor’s attractor problem for smooth unimodal maps with quadratic critical points. ...
We study unitary random matrix ensembles of the form
−1 Zn,N | det M |2α e−N Tr V (M ) dM,
where α −1/2 and V is such that the limiting mean eigenvalue density for n, N → ∞ and n/N → 1 vanishes quadratically at the origin. In order to compute the double scaling limits of the eigenvalue correlation kernel near the origin, we use the Deift/Zhou steepest descent method applied to the Riemann-Hilbert problem for orthogonal polynomials on the real line with respect to the weight |x|2α e−N V (x) . ...
Annals of Mathematics
In our ﬁrst article  we developed a new view of Gauss composition of binary quadratic forms which led to several new laws of composition on various other spaces of forms. Moreover, we showed that the groups arising from these composition laws were closely related to the class groups of orders in quadratic number ﬁelds, while the spaces underlying those composition laws were closely related to certain exceptional Lie groups.
In the ﬁrst two articles of this series, we investigated various higher analogues of Gauss composition, and showed how several algebraic objects involving orders in quadratic and cubic ﬁelds could be explicitly parametrized. In particular, a central role in the theory was played by the parametrizations of the quadratic and cubic rings themselves. These parametrizations are beautiful and easy to state.
Hindawi Publishing Corporation Advances in Diﬀerence Equations Volume 2010, Article ID 127093, 11 pages doi:10.1155/2010/127093
Research Article On the Existence of Locally Attractive Solutions of a Nonlinear Quadratic Volterra Integral Equation of Fractional Order
Mohamed I. Abbas
Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt Correspondence should be addressed to Mohamed I. Abbas, m i firstname.lastname@example.org Received 19 May 2010; Accepted 25 November 2010 Academic Editor: Mouﬀak Benchohra Copyright q 2010 Mohamed I. Abbas.
We present a novel transition system for dependency parsing, which constructs arcs only between adjacent words but can parse arbitrary non-projective trees by swapping the order of words in the input. Adding the swapping operation changes the time complexity for deterministic parsing from linear to quadratic in the worst case, but empirical estimates based on treebank data show that the expected running time is in fact linear for the range of data attested in the corpora.
(BQ) Ebook Problems in mathematical analysis of problems and exercises in mathematical anal ysis covers the maximum requirements of general courses in higher mathematics for higher technical schools. it contains over 3,000 problems sequentially arranged in chapters i to x covering all branches of higher mathematics (with the exception of ana lytical geometry) given in college courses.
In this topic, we will look at: Justification for analysis, quadratic and polynomial growth, counting machine instructions, Landau symbols, Big-Q as an equivalence relation, little-o as a weak ordering.