College of Arts and Sciences (CAS)
http://hdl.handle.net/11073/8390
College of Arts and Sciences2022-12-07T20:29:01ZModeling of the In Vitro Release Kinetics of Sonosensitive Targeted Liposomes
http://hdl.handle.net/11073/25088
Modeling of the In Vitro Release Kinetics of Sonosensitive Targeted Liposomes
Almajed, Zeyad Mohamed; Salkho, Najla; Sulieman, Hana; Husseini, Ghaleb
Targeted liposomes triggered by ultrasound are a promising drug delivery system as they potentially improve the clinical outcomes of chemotherapy while reducing associated side effects. In this work, a comprehensive model fitting was performed for a large dataset of liposomal release profiles with seven targeting moieties (albumin, cRGD, estrone, hyaluronic acid, Herceptin, lactobionic acid, and transferrin) in addition to the control liposomes under ultrasound release protocols. Two levels of ultrasound frequencies were tested: low frequency (20 kHz) at 6.2, 9, and 10 mW/cm2 as well as high frequencies (1.07 MHz and 3 MHz) at 10.5 and 173 W/cm2. At a low frequency, Hixson–Crowell, Korsmeyer–Peppas, Gompertz, Weibull, and Lu–Hagen showed good fits to our release profiles at all three power densities. At high frequencies, the former three models reflected the best fit. These models will aid in predicting drug release profiles for future in vitro studies.
2022-12-05T00:00:00ZGraph of Linear Transformations Over R
http://hdl.handle.net/11073/25087
Graph of Linear Transformations Over R
Badawi, Ayman; El-Ashi, Yasmine Ahmed
In this paper, we study a connection between graph theory and linear transformations of finite dimensional vector spaces over R (the set of all real numbers). Let Rm, Rn be finite vector spaces over R, and let L be the set of all non-trivial linear transformations from Rm into Rn. An equivalence relation ∼ is defined on L such that two elements f, k ∈ L are equivalent, f ∼ k, if and only if ker (f ) = ker (k). Let m, n ≥ 1 be positive integers and Vm,n be the set of all equivalence classes of ∼. We define a new graph, Gm,n, to be the undirected graph with vertex set equals to Vm,n, such that two vertices, [x] , [y] ∈ Vm,n are adjacent if and only if ker (x) ∩ ker (y) 6 = 0. The relationship between the connectivity of the graph Gm,n and the values of m and n has been investigated. We determine the values of m and n so that Gm,n is a complete graph. Also, we determine the diameter and the girth of Gm,n.
2022-12-01T00:00:00ZMaximum principles and overdetermined problems for Hessian equations
http://hdl.handle.net/11073/25083
Maximum principles and overdetermined problems for Hessian equations
Enache, Cristian; Marras, Monica; Porru, Giovanni
In this article we investigate some Hessian type equations. Our main aim is to derive new maximum principles for some suitable P-functions, in the sense of L.E. Payne, that is for some appropriate functional combinations of u(x) and its derivatives, where u(x) is a solution of the given Hessian type equations. To find the most suitable P-functions, we first investigate the special case of a ball, where the solution of our Hessian equations is radial, since this case gives good hints on the best functional to be considered later, for general domains. Next, we construct some elliptic inequalities for the well-chosen P-functions and make use of the classical maximum principles to get our new maximum principles. Finally, we consider some overdetermined problems and show that they have solutions when the underlying domain has a certain shape (spherical or ellipsoidal).
2021-01-01T00:00:00ZRenormalization functions of the tricritical O(N)-symmetric Φ⁶ model beyond the next-to-leading order in 1/N
http://hdl.handle.net/11073/25082
Renormalization functions of the tricritical O(N)-symmetric Φ⁶ model beyond the next-to-leading order in 1/N
Sakhi, Said
We investigate higher-order corrections to the effective potential of the tricritical O(N)-symmetric Φ⁶ model in 3-2ε dimensions in its phase exhibiting spontaneous breaking of its scale symmetry. The renormalization group β-function and the anomalous dimension γ of this model are computed up to the next-to-next-to-leading order in the 1/N expansion technique and using a dimensional regularization in a minimal subtraction scheme.
2021-01-01T00:00:00Z