Keywords--Concavity, Finite differences, Green's function. In [1], Gatica, Oliker and Waltman employed concavity to show that if y " ( t ) _< 0, 0 < t < 1, then

Manipulating the degrees of concavity or Miller indices of high-index facets is significant for metal nanocrystals to further tailor their properties; however, generating a concave surface with negative curvature is still in the early development stage and tuning the degree of concavity remains a challenge. Herein, we have developed a simple and effective site-selective etching strategy to mani...

We introduce the antipodal pairs property for probability measures on finite Boolean algebras and prove that conditional versions imply strong forms of log-concavity. We give several applications of this fact, including improvements of some results of Wagner [15]; a new proof of a theorem of Liggett [9] stating that ultra-log-concavity of sequences is preserved by convolutions; and some progres...

5 A Brief Review of Optimization 27 5.1 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.2 Lagrange . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.3 Constrained Optimization . . . . . . . . . . . . . . . . . 29 5.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.5 Understanding Lagrangians . . . . . . . . . . . . . . . . 31 5.6 Concavity and Quas...

functional mitral regurgitation (mr) results from left ventricular remodeling, leaflet tethering or tenting. coronary artery disease is one of the important causes of functional mr due to tethering. detection of functional mr and its severity are important factors in patient prognosis. there are different methods for detection of functional mr and its severity, including anterior mitral leaflet...

In this paper, we study the conjecture of Gardner and Zvavitch from [22], which suggests that standard Gaussian measure γ enjoys 1n-concavity with respect to Minkowski addition symmetric convex sets. We prove fact up a factor 2: is, show for K L, λ∈[0,1],γ(λK+(1−λ)L)12n≥λγ(K)12n+(1−λ)γ(L)12n. More generally, inequality holds sets containing origin. Further, under suitable dimension-free uniform...

many genetic disorders or possible abnormalities that may occur in the future generations can be predicted through analyzing the features of the chromosomes. for this purpose, karyotype is often used which to make it, there is necessary to identify each one of the 24 chromosomes from the microscopic images. the first step of this process is to define the morphological and band pattern based fea...

OF THE DISSERTATION Negative correlation and log-concavity by Michael Neiman Dissertation Director: Jeff Kahn This thesis is concerned with negative correlation and log-concavity properties and relations between them, with much of our motivation provided by [40], [46], and [12]. Our main results include a proof that “almost exchangeable” measures satisfy the “FederMihail” property; counterexamp...

Abstract In this paper, we study the initial boundary value problem of pseudo-parabolic p ( x )-Laplacian equation with logarithmic nonlinearity. The existence global solution is obtained by using potential well method and inequality. addition, sufficient conditions blow-up are concavity method.