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71.
72.
We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature orientable surfaces immersed in a Riemannian Killing submersion. As a consequence, the strong stability of such surfaces is studied. We also characterize constant mean curvature Hopf tori as the only ones attaining the bound in certain cases. 相似文献
73.
Horváth and Kiss (Proc. Amer. Math. Soc., 2005) proved the upper bound estimate for Dirichlet eigenvalue ratios of the Schrödinger problem ?y′′ + q(x)y = λy with nonnegative and single‐well potential q. In this paper, we prove that if q(x) is a nonpositive, continuous, and single‐barrier potential, then for λn > λm≥ ? 2q?, where . In particular, if q(x) satisfies the additional condition , then λ1 > 0 and for n > m ≥ 1. For this result, we develop a new approach to study the monotonicity of the modified Prüfer angle function. 相似文献
74.
Let m ≤ n ≤ k. An m × n × k 0‐1 array is a Latin box if it contains exactly m n ones, and has at most one 1 in each line. As a special case, Latin boxes in which m = n = k are equivalent to Latin squares. Let be the distribution on m × n × k 0‐1 arrays where each entry is 1 with probability p, independently of the other entries. The threshold question for Latin squares asks when contains a Latin square with high probability. More generally, when does support a Latin box with high probability? Let ε > 0. We give an asymptotically tight answer to this question in the special cases where n = k and , and where n = m and . In both cases, the threshold probability is . This implies threshold results for Latin rectangles and proper edge‐colorings of Kn,n. 相似文献
75.
Sarika Goyal 《Mathematische Nachrichten》2019,292(10):2189-2202
In this article, we study the eigenvalues of p‐fractional Hardy operator where , , , and Ω is an unbounded domain in with Lipschitz boundary containing 0. The weight function V may change sign and may have singular points. We also show that the least positive eigenvalue is simple and it is uniquely associated to a nonnegative eigenfunction. Moreover, we proved that there exists a sequence of eigenvalues as . 相似文献
76.
We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same problem was treated and an essential ingredient was to establish the concept of the multiplicity of a focal point. But there was still a rather restrictive condition needed, which is eliminated here by using the concept of finite eigenvalues (or zeros) from the theory of matrix pencils. 相似文献
77.
《Discrete Mathematics》2022,345(12):113173
For a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius in a graph with positive weights on edges, which is used to present an upper bound on the (where ) smallest normalized Laplacian eigenvalue of irregular graphs under minor assumptions. Moreover, when , the result may be regarded as an Alon–Boppana type bound for a class of irregular graphs. 相似文献
78.
Alireza Bananej Amir Hassanpour Hossein Razzaghi Mehdí Vaez zade Ali Mohammadi 《Optics & Laser Technology》2010,42(8):1187-1192
Monolayer ZrO2 and TiO2 films were prepared on BK7 glass by physical vapor deposition (PVD) and were subsequently annealed for 1 h at 300 °C. By using the transmission spectra of two samples and the envelope method, the refractive index dispersion and extinction coefficients have been calculated. Laser induced damage threshold (LIDT) measurement shows that despite slight differences between the extinction coefficients of the two samples, the LIDT parameter of the ZrO2 film is greater than that of the TiO2 film. This fact leads us to consider thermal conductivity as an important parameter for interpreting the LIDT difference. According to our theoretical analysis, as a consequence of increase in the number of thermal barriers along poorer film, its thermal conductivity, and hence LIDT, decreased, which is in agreement with our experimental results. The measured porosity of the two samples shows higher porosity for TiO2 single layer, which is in agreement with atomic force (AFM) images. The gradual and smooth damage morphology of ZrO2 observed in optical images implies higher thermal conductivity than TiO2. 相似文献
79.
80.
A mathematical model based on a straightforward geometrical background is developed which enables predictions of a transition of one dispersed phase to a cocontinuous one (i.e., the percolation threshold) on addition of another dispersed phase during melt mixing in ternary polymer blends. The present work concerns only ternary blends with two separate dispersions of the inner phases in which no encapsulation takes place. In addition, in order to simplify the model, one of the inner phases was represented by hard, nondeformable microspheres The expression developed describes well an experimental relationship between the percolation threshold, the concentration above which the former dispersed phase transforms to a continuous one, and concentrations of both inner phases. The results agree well with the experimental data obtained in a previous work. 相似文献