A graph is vertex-critical (edge-critical) if deleting any vertex (edge) increases its diameter. A conjecture of Simon and Murty stated thatèvery edge-critical graph of diameter two on vertices contains at most 1 4 2 edges'. This conjecture has been established for suuciently large. For vertex-critical graphs, little is known about the number of edges. Plesn ik implicitly asked whether it is al...

A multigraph M with maximum degree (M) is called critical, if the chromatic index 0 (M) > (M) and 0 (M ? e) = 0 (M) ? 1 for each edge e of M. The weak critical graph conjecture 1, 7] claims that there exists a constant c > 0 such that every critical multigraph M with at most c (M) vertices has odd order. We disprove this conjecture by constructing critical multigraphs of order 20 with maximum d...

in this paper, nonlinear vibration and instability response of an embedded pipe conveying viscose fluid is investigated. the pipe is considered as a timoshenko beam embedded on an elastic foundation which is simulated by spring constant of the winkler-model and the shear constant of the pasternak-model. the external flow force, acting on the beam in the direction of the flexural displacement is...

We prove existence of an asymptotic expansion in the inverse dimension, to all orders, for the connective constant for self-avoiding walks on Z d . For the critical point, de ned to be the reciprocal of the connective constant, the coe cients of the expansion are computed through order d 6 , with a rigorous error bound of order d 7 . Our method for computing terms in the expansion also applies ...

In this paper we study the water wave problem with capillary e ects and constant vorticity when stagnation points are not excluded. When the constant vorticity is close to certain critical values we show that there exist Wilton ripples solutions of the water wave problem with two crests and two troughs per minimal period. They form smooth secondary bifurcation curves which emerge from primary b...

We study the nonlinear O(N) sigma model on S 2 with the gravitational coupling term, by evaluating the effective potential in the large-N limit. It is shown that there is a critical curvature R c of S 2 for any positive gravitational coupling constant ξ, and the dynamical mass generation takes place only when R < R c. The critical curvature is analytically found as a function of ξ (> 0), which ...

In this work, we study the performances of ring resonators of different type by analyzing the bending loss and the condition of the critical coupling. We propose that the bending loss of microring can be reduced by wrapping a concentrically curved waveguide. The difference of propagation constant between two concentrically curved waveguides can be tuned by adjusting the bus waveguide width to o...

We use Monte Carlo simulations to obtain an improved lattice measurement of the critical coupling constant [ λ/μ ] crit for the continuum (1 + 1)-dimensional (λ/4)φ theory. We find that the critical coupling constant depends logarithmically on the lattice coupling, resulting in a continuum value of [ λ/μ ] crit = 10.8 −.05, in considerable disagreement with the previously reported [ λ/μ ] crit ...

u j : RN ×R → C, ψ j0 : RN → C for j = 1, 2, . . . , m and ajk = akj are positive real numbers. Global existence for the Cauchy problem is established for a certain range of p. A sharp form of a vector-valued Gagliardo-Nirenberg inequality is deduced, which yields the minimal embedding constant for the inequality. Using this minimal embedding constant, global existence for small initial data is...

We report a quasi-exact power law behavior for Ising critical temperatures on hypercubes. It reads J/kBTc = K0[(1 − 1/d)(q − 1)] a where K0 = 0.6260356, a = 0.8633747, d is the space dimension, q the coordination number (q = 2d), J the coupling constant, kB the Boltzman constant and Tc the critical temperature. Absolute errors from available exact estimates (d = 2 up to d = 7) are always less t...