A well-known result of Bollobás says that if { ( i , B ) } = 1 m is a set pair system such | ? and b for ? j ? 0? only then + . Füredi, Gyárfás Király recently initiated the study systems with additional property all Confirming conjecture theirs, we show this extra condition allows an improvement upper bound (at least) by constant factor.

Recently, there is rising interest in modelling the interactions of two sentences with deep neural networks. However, most of the existing methods encode two sequences with separate encoders, in which a sentence is encoded with little or no information from the other sentence. In this paper, we propose a deep architecture to model the strong interaction of sentence pair with two coupled-LSTMs. ...

This tutorial aims to be a self-contained and explicit analysis of the basic cross polarization (CP) solid-state NMR experiment (SSNMR) in the isolated spin-pair approximation using standard quantum mechanical arguments. The general result of obtaining coherence transfer between two dipolar coupled spin-active nuclei while applying radio frequency fields to both nuclei is described, with emphas...

Numerical simulations have been carried out for a pair of unidirectionally coupled identical pendula under the action of a common external ac torque. Both the master pendulum and the slave pendulum were in chaotic states. The only form of persistent locking appeared to be a computational artifact; otherwise the synchronization of slave to master was found to be intermittent. [S0031-9007(98)0663...

has been studied by many authors, see, for example, [1, 3, 5, 7, 8, 9] and the references contained therein. The above equation may be regarded as a mathematical model for a number of dynamical processes. In particular, xn may represent the size of a population in the time period n. Since it is possible that the population may be influenced by another factor of the form −ĥn f2(n,xn−τ(n)), we ar...

Propagation of weakly nonlinear long waves is studied within the framework of a system of two coupled modified Korteweg-de Vries equations. We investigate analytically and numerically the various families of soliton states for the considered model. By scaling the functions and variables we find that the resulting coupled pair of equations has only one combined parameter. This parameter depends ...

State-space formulas are derived for the minimum-entropy H∞ controller when the plant and controller are constrained to be block-lower-triangular. Such a controller exists if and only if: the corresponding unstructured problem has a solution, a certain pair of coupled algebraic Riccati equations admits a mutually stabilizing fixed point, and a pair of spectral radius conditions is met. The cont...

State-space formulas are derived for the minimumentropy H∞ controller when the plant and controller are constrained to be block-lower-triangular. Such a controller exists if and only if: the corresponding unstructured problem has a solution, a certain pair of coupled algebraic Riccati equations admits a mutually stabilizing fixed point, and a pair of spectral radius conditions is met. The contr...

The polarised singlet coupled DGLAP equations (LO) are transformed by a Taylor series expansion at low x into a pair of partial differential equations in x and t(t = lnQ2/Λ2). The pair of coupled partial differential equations is then reduced to canonical form and the resultant system solved by applying the method of characteristics under small x and t approximations. The result is compared wit...

A controlled-NOT logic gate based on conditional spectroscopy has been demonstrated recently for a pair of superconducting flux qubits [Plantenberg et al. in Nature 447:836, 2007]. Here we study the fidelity of this type of gate applied to a phase qubit coupled to a resonator (or a pair of capacitively coupled phase qubits). Our results show that an intrinsic fidelity of more than 99% is achiev...