18 research outputs found

    On minima of sum of theta functions and Mueller-Ho Conjecture

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    Let z=x+iyH:={z=x+iyC:y>0}z=x+iy \in \mathbb{H}:=\{z= x+ i y\in\mathbb{C}: y>0\} and θ(s;z)=(m,n)Z2esπymz+n2 \theta (s;z)=\sum_{(m,n)\in\mathbb{Z}^2 } e^{-s \frac{\pi }{y }|mz+n|^2} be the theta function associated with the lattice Λ=ZzZ\Lambda ={\mathbb Z}\oplus z{\mathbb Z}. In this paper we consider the following pair of minimization problems minHθ(2;z+12)+ρθ(1;z),    ρ[0,), \min_{ \mathbb{H} } \theta (2;\frac{z+1}{2})+\rho\theta (1;z),\;\;\rho\in[0,\infty), minHθ(1;z+12)+ρθ(2;z),    ρ[0,), \min_{ \mathbb{H} } \theta (1; \frac{z+1}{2})+\rho\theta (2; z),\;\;\rho\in[0,\infty), where the parameter ρ[0,)\rho\in[0,\infty) represents the competition of two intertwining lattices. We find that as ρ\rho varies the optimal lattices admit a novel pattern: they move from rectangular (the ratio of long and short side changes from 3\sqrt3 to 1), square, rhombus (the angle changes from π/2\pi/2 to π/3\pi/3) to hexagonal; furthermore, there exists a closed interval of ρ\rho such that the optimal lattices is always square lattice. This is in sharp contrast to optimal lattice shapes for single theta function (ρ=\rho=\infty case), for which the hexagonal lattice prevails. As a consequence, we give a partial answer to optimal lattice arrangements of vortices in competing systems of Bose-Einstein condensates as conjectured (and numerically and experimentally verified) by Mueller-Ho \cite{Mue2002}.Comment: 42 pages; comments welcom

    3, 3′-Diindolylmethane Exhibits Antileukemic Activity In Vitro and In Vivo through a Akt-Dependent Process

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    3,3′-diindolylmethane (DIM), one of the active products derived from Brassica plants, is a promising antitumor agent. The present study indicated that DIM significantly induced apoptosis in U937 human leukemia cells in dose- and time-dependent manners. These events were also noted in other human leukemia cells (Jurkat and HL-60) and primary human leukemia cells (AML) but not in normal bone marrow mononuclear cells. We also found that DIM-induced lethality is associated with caspases activation, myeloid cell leukemia-1 (Mcl-1) down-regulation, p21cip1/waf1 up-regulation, and Akt inactivation accompanied by c-jun NH2-terminal kinase (JNK) activation. Enforced activation of Akt by a constitutively active Akt construct prevented DIM-mediated caspase activation, Mcl-1 down-regulation, JNK activation, and apoptosis. Conversely, DIM lethality was potentiated by the PI3K inhibitor LY294002. Interruption of the JNK pathway by pharmacologic or genetic approaches attenuated DIM-induced caspases activation, Mcl-1 down-regulation, and apoptosis. Lastly, DIM inhibits tumor growth of mouse U937 xenograft, which was related to induction of apoptosis and inactivation of Akt, as well as activation of JNK. Collectively, these findings suggest that DIM induces apoptosis in human leukemia cell lines and primary human leukemia cells, and exhibits antileukemic activity in vivo through Akt inactivation and JNK activation

    Iterative Learning Control with Forgetting Factor for Linear Distributed Parameter Systems with Uncertainty

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    Iterative learning control is an intelligent control algorithm which imitates human learning process. Based on this concept, this paper discussed iterative learning control problem for a class parabolic linear distributed parameter systems with uncertainty coefficients. Iterative learning control algorithm with forgetting factor is proposed and the conditions for convergence of algorithm are established. Combining the matrix theory with the basic theory of distributed parameter systems gives rigorous convergence proof of the algorithm. Finally, by using the forward difference scheme of partial differential equation to solve the problems, the simulation results are presented to illustrate the feasibility of the algorithm

    Melt extrusion deposition (MED™) 3D printing technology – A paradigm shift in design and development of modified release drug products

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    Three-dimensional printing (3DP) technology offers unique advantages for pharmaceutical applications. However, most of current 3D printing methods and instrumentations are not specifically designed and developed for pharmaceutical applications. To meet the needs in pharmaceutical applications for precision, compatibility with a wide range of pharmaceutical excipients and drug materials without additional processing, high throughput and GMP compliance, an extrusion-based 3D printer based on Melt Extrusion Deposition (MED™) 3D printing technology was developed in this study. This technology can process powder pharmaceutical excipients and drugs directly without the need of preparing filament as required by FDM 3D printing. Six different tablet designs based on compartment models were used to demonstrate the precision and reproducibility of this technology. The designed tablets were fabricated using the GMP-compliant MED™ 3D printer and were evaluated in vitro for drug release and in vivo for selected designs using male beagle dogs. Tablet designs with one or more compartments showed versatile release characteristics in modulating the release onset time, release kinetics, duration of release and mode of release. Multiple drugs or formulations were fabricated into a single tablet to achieve independent release kinetics for each drug or to fine-tune the pharmacokinetic profile of a drug. Building upon the theoretical analysis of models, precision and reproducibility of MED™ 3D printing technology, a novel product development approach, 3D printing formulation by design (3DPFbD®) was developed to provide an efficient tool for fast and efficient pharmaceutical product development. The MED™ 3D printing represents a novel and promising technology platform encompassing design and development of modified drug release products and has potential to impact the drug delivery and pharmaceutical product development