TCHEBYSHEFF INEQUALITY THEOREM

2001 ◽  
pp. 70-77
Keyword(s):  
Inequality Theorem

The generalized Laguerre inequalities and functions in the Laguerre-Pólya class

2013 ◽  
Vol 11 (9) ◽  
Author(s):  
George Csordas ◽  
Anna Vishnyakova
Keyword(s):  
Entire Function ◽  
Open Problem ◽  
A Priori ◽  
Sufficient Conditions ◽  
Class Definition ◽  
Lindelöf Theorem ◽  
Order And Type ◽  
Geometric Result ◽  
Real Entire Function ◽  
Inequality Theorem

AbstractThe principal goal of this paper is to show that the various sufficient conditions for a real entire function, φ(x), to belong to the Laguerre-Pólya class (Definition 1.1), expressed in terms of Laguerre-type inequalities, do not require the a priori assumptions about the order and type of φ(x). The proof of the main theorem (Theorem 2.3) involving the generalized real Laguerre inequalities, is based on a beautiful geometric result, the Borel-Carathédodory Inequality (Theorem 2.1), and on a deep theorem of Lindelöf (Theorem 2.2). In case of the complex Laguerre inequalities (Theorem 3.2), the proof is sketched for it requires a slightly more delicate analysis. Section 3 concludes with some other cognate results, an open problem and a conjecture which is based on Cardon’s recent, ingenious extension of the Laguerre-type inequalities.

scholarly journals Change in Semigraph Energy Due to Edge Deletion and its Relation with Distance Energy

2019 ◽  
Vol 8 (2S10) ◽  
pp. 873-875
Keyword(s):  
Adjacency Matrix ◽  
Singular Values ◽  
Edge Deletion ◽  
Graph Energy ◽  
Inequality Theorem

If there is an adjacency matrix A, the sum total of the singular values of A is known as the graph energy. We can find the change in energy of a graph by removing the edges using the inequality theorem on singular values. In this paper we discuss about the change in semigraph energy due to deletion of edges and its relation with distance energy

scholarly journals Extensions of the Heisenberg-Weyl inequality

1986 ◽  
Vol 9 (1) ◽  
pp. 185-192 ◽  
Author(s):  
H. P. Heinig ◽  
M. Smith
Keyword(s):  
Entropy Inequality ◽  
Optimal Form ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Weyl Inequality ◽  
Uncertainty Inequality ◽  
Weighted Entropy ◽  
Inequality Theorem

In this paper a number of generalizations of the classical Heisenberg-Weyl uncertainty inequality are given. We prove then-dimensional Hirschman entropy inequality (Theorem 2.1) from the optimal form of the Hausdorff-Young theorem and deduce a higher dimensional uncertainty inequality (Theorem 2.2). From a general weighted form of the Hausdorff-Young theorem, a one-dimensional weighted entropy inequality is proved and some weighted forms of the Heisenberg-Weyl inequalities are given.

On Wald's equations in continuous time

1970 ◽  
Vol 7 (1) ◽  
pp. 59-68 ◽  
Author(s):  
W. J. Hall
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Stopping Time ◽  
Wiener Processes ◽  
Independent Increments ◽  
Randomly Stopped Sums ◽  
Continuous Time Processes ◽  
Wald's Identity ◽  
Stopped Sums ◽  
Inequality Theorem

Various formulas of Wald relating to randomly stopped sums have well known continuous-time analogs, holding in particular for Wiener processes. However, sufficiently general forms of most of these do not appear explicitly in the literature. Recent papers by Robbins and Samuel (1966) and by Brown (1969) provide general results on Wald's equations in discrete time and these are here extended (Theorems 2 and 3) to Wiener processes and other homogeneous additive processes, that is, continuous-time processes with stationary independent increments. We also give an inequality (Theorem 1) related to Wald's identity in continuous time, and we derive, as corollaries of Wald's equations, bounds on the variance of an arbitrary stopping time. The Wiener process versions of these results find application in a variety of stopping problems. Specifically, all are used in Hall ((1968), (1969)); see also Bechhofer, Kiefer, and Sobel (1968), Root (1969), and Shepp (1967).

scholarly journals The Inequality Theorem

1910 ◽  
Vol 4 ◽  
pp. 33-34
Author(s):  
C. Tweedie
Keyword(s):  
Geometrical Method ◽  
Average Ability ◽  
Inequality Theorem

(xm - 1)/ m >(xn - 1)/n, m > n.— I have sometimes found the following geometrical method of attack useful in explaining this theorem to students of only average ability. The Lemmas introduced are almost self-evident, and admit of simple analytical demonstration.

scholarly journals Chen Inequalities for Warped Product Pointwise Bi-Slant Submanifolds of Complex Space Forms and Its Applications

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 200
Author(s):  
Akram Ali ◽  
Ali Alkhaldi
Keyword(s):  
Mean Curvature ◽  
Warped Product ◽  
Complex Space ◽  
Holomorphic Sectional Curvature ◽  
Warping Function ◽  
Space Forms ◽  
Slant Submanifolds ◽  
The Mean ◽  
Complex Space Forms ◽  
Inequality Theorem

In this paper, by using new-concept pointwise bi-slant immersions, we derive a fundamental inequality theorem for the squared norm of the mean curvature via isometric warped-product pointwise bi-slant immersions into complex space forms, involving the constant holomorphic sectional curvature c, the Laplacian of the well-defined warping function, the squared norm of the warping function, and pointwise slant functions. Some applications are also given.

scholarly journals Analysis of the Gyroscopic Stability of the Wheelset

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hao Dong ◽  
Jing Zeng ◽  
Liang Wu ◽  
Huanyun Dai
Keyword(s):  
Asymptotic Stability ◽  
High Speed ◽  
Critical Value ◽  
Rolling Stock ◽  
Instability Criterion ◽  
Necessary Condition ◽  
Railway Vehicle ◽  
Gyroscopic Effect ◽  
Key Factor ◽  
Inequality Theorem

The wheelset of the railway vehicle is a rotor which itself has gyroscopic effect. Nowadays, the rolling stock has entered the era of high speed, and the wheel rotates faster than in the past. The influence of gyroscopic effect on stability is little understood. Metelitsyn’s inequality theorem for asymptotic stability has some advantages to analyze this problem although this method is sufficient but not necessary condition. Based on its deduction, the extremal eigenvalues criterion and compared with Routh-Hurwitz criterion, both are applied to solve the critical value of speed. Further, according to the instability criterion, gyroscopic contributory ratio is derived to study how the role the gyroscopic effect plays in stability. Moreover, the effect of gyroscopic matrix or gyroscopic terms pitch rotor inertia Iy on stability coefficient is investigated. The results show that Iy is a key factor to wheelset gyroscopic stability. The gyroscopic effect becomes significant, and the stability increases with increasing Iy. The results also indicate that the critical value of speed solved by Metelitsyn theorem is more conservative than the one it solved by Hurwitz criterion, which proves that Metelitsyn inequality theorem for asymptotic stability is a sufficient but not necessary condition in the way of attaining the numerical simulation result. Finally, the test for the influence of gyroscopic effect on stability needs to be further studied.

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