One-dimensional drug release from finite Menger sponges: In silico simulation

The purpose of this work was to evaluate the consequences of the spatial distribution of components in pharmaceutical matrices type Menger sponge on the drug release kinetic from this kind of platforms by means of Monte Carlo computer simulation. First, six kinds of Menger sponges (porous fractal structures) with the same fractal dimension, d_f=2.727, but with different random walk dimension, d_w[2.149,3.183], were constructed as models of drug release device. Later, Monte Carlo simulation was used to describe drug release from these structures as a diffusion-controlled process. The obtained results show that drug release from Menger sponges is characterized by an anomalous behavior: there are important effects of the microstructure anisotropy, and porous structures with the same fractal dimension but with different topology produce different release profiles. Moreover, the drug release kinetic from heteromorphic structures depends on the axis used to transport the material to the external medium. Finally, it was shown that the number of releasing sites on the matrix surface has a significant impact on drug release behavior and it can be described quantitatively by the Weibull function.     

On a characteristic property of minimal-ruled surfaces

LetS be a surface of classC ⁴ in 3-dimensional Euclidean space. In this paper it is shown that any two of the following three conditions imply the third one: (a)S is a minimal surface, (b) Two families of Laguerre lines ofS form a conjugate net, (c)S is a non-developable ruled surface. Furthermore, it is proved that any surface (other than a sphere, a cylinder of revolution and a plane) of constant mean curvature on which the two families of Laguerre lines form a conjugate net is a minimal-helicoid.     

A fast minimal residual algorithm for shifted unitary matrices

A new iterative scheme is described for the solution of large linear systems of equations with a matrix of the form A = ρU + ζI, where ρ and ζ are constants, U is a unitary matrix and I is the identity matrix. We show that for such matrices a Krylov subspace basis can be generated by recursion formulas with few terms. This leads to a minimal residual algorithm that requires little storage and makes it possible to determine each iterate with fairly little arithmetic work. This algorithm provides a model for iterative methods for non-Hermitian linear systems of equations, in a similar way to the conjugate gradient and conjugate residual algorithms. Our iterative scheme illustrates that results by Faber and Manteuffel [3,4] on the existence of conjugate gradient algorithms with short recurrence relations, and related results by Joubert and Young [13], can be extended.     

The capillary contact angle,II: The inclined plane

In an earlier paper an hypothesis on the nature of the forces resisting motion of a liquid drop on a support surface II was introduced and tested in the (rotationally symmetric) case for which ll is a horizontal plane. In the present work II is chosen as an inclined plane, so that rotational symmetry fails. The hypothesis leads to a formal series development; in a restricted case the result is verified by a perturbation analysis, which yields the identical series. The series predictions are compared with results of computer calculations. A consequence of the analysis is an estimate for a Bohd number B₀, such that a further increase in B would result in the fluid penetrating the support surface; thus an absolute upper bound B₀, for stability of the envisaged configuration is obtained.     

Large parameter spaces of quasiconformally distinct hyperbolic structures

SupposeS is a surface of infinite type with pants decomposition ⌆. We construct a real analytic embedding of an infinite-dimensional parameter space into the Fenchel-Nielsen space ofS with respect to ⌆, whose image is made up of topologically conjugate Fuchsian groups for which no two groups in the image are quasiconformally conjugate. Moreover, all of the Fuchsian groups in this parameter space have the same Fenchel—Nielsen twist parameters. As a consequence, arbitrarily close (in the Fenchel-Nielsen topology) to a hyperbolic structure forS there is an infinite-dimensional set of disjoint Teichmüller spaces. Research supported by a University of Oklahoma Junior faculty summer fellowship and in part by NSF Grant DMS-9404174.     

Theoretical study of diffusional release of a dispersed solute from cylindrical polymeric matrix: A novel configuration for providing zero-order release profile

In the context of controlled release drug delivery approaches, the systems providing zero-order release kinetics have special advantages. Through employing these systems, drug concentration could be maintained within the therapeutic window over release time; thus maximum effectiveness alongside minimized side effects of the drug are achieved. However, obtaining zero-order drug release is extremely challenging. One of the main obstacles is the fact that implemented devices should be designed to overcome the decreasing mass transfer driving force, especially, in polymeric systems in which diffusion mechanism is dominant. In this study, we developed a new configuration of a polymeric matrix containing dispersed solute which provides sustained zero-order release. A combination of two innovative approaches including separating baffles and a two-layer coating was proposed to be incorporated into the conventional cylindrical polymeric matrix to induce zero-order release behavior. Then, an approximate mathematical model was developed to investigate the performance of the system under different conditions. The simulated results showed the potential of proposed configuration to be used as a carrier for sustained zero-order release.     

关于高维射影空间共轭网论的研究(Ⅰ)

<正> 1.引言近年来,嘉当的外形式法被应用到几何学的各分支里,起着相当大的作用.特別地要提起,苏联几何学家菲尼可夫运用这个有效的方法,在普通空间线汇论中作出了系统的研究.对高维射影空间线汇论的应用仅仅是开始的阶段.捷赫讨论了普通和高维射影空间线汇的可展变换和射影变形之后,希伟茨进一步发展后面的问题并做出总结.     

Accelerated conjugate gradient algorithm with finite difference Hessian/vector product approximation for unconstrained optimization

In this paper we propose a fundamentally different conjugate gradient method, in which the well-known parameter β_k is computed by an approximation of the Hessian/vector product through finite differences. For search direction computation, the method uses a forward difference approximation to the Hessian/vector product in combination with a careful choice of the finite difference interval. For the step length computation we suggest an acceleration scheme able to improve the efficiency of the algorithm. Under common assumptions, the method is proved to be globally convergent. It is shown that for uniformly convex functions the convergence of the accelerated algorithm is still linear, but the reduction in function values is significantly improved. Numerical comparisons with conjugate gradient algorithms including CONMIN by Shanno and Phua [D.F. Shanno, K.H. Phua, Algorithm 500, minimization of unconstrained multivariate functions, ACM Trans. Math. Softw. 2 (1976) 87–94], SCALCG by Andrei [N. Andrei, Scaled conjugate gradient algorithms for unconstrained optimization, Comput. Optim. Appl. 38 (2007) 401–416; N. Andrei, Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization, Optim. Methods Softw. 22 (2007) 561–571; N. Andrei, A scaled BFGS preconditioned conjugate gradient algorithm for unconstrained optimization, Appl. Math. Lett. 20 (2007) 645–650], and new conjugacy condition and related new conjugate gradient by Li, Tang and Wei [G. Li, C. Tang, Z. Wei, New conjugacy condition and related new conjugate gradient methods for unconstrained optimization, J. Comput. Appl. Math. 202 (2007) 523–539] or truncated Newton TN by Nash [S.G. Nash, Preconditioning of truncated-Newton methods, SIAM J. on Scientific and Statistical Computing 6 (1985) 599–616] using a set of 750 unconstrained optimization test problems show that the suggested algorithm outperforms these conjugate gradient algorithms as well as TN.     

Some remarks on profinite HNN extensions

We extend a construction of Higman, Neumann and Neumann [LS, IV.3.1] and show that every profinite groupG with only countably many open subgroups embeds in a 2-generated profinite groupE in which all torsion elements are conjugate to elements ofG; ifG is pro-p,E can be chosen pro-p. This answers a question of Wilson (oral communication) and generalises a result of Lubotzky and Wilson [LW].     

Global dynamics and cost-effectiveness analysis of HIV pre-exposure prophylaxis and structured treatment interruptions based on a multi-scale model

Structured treatment interruptions (STI) were proposed to reduce costs and side effects for HIV infected individuals, but whether the possible viral rebound within hosts after treatment interruption would lead to more new infections and additional costs among the population remains unknown. Oral pre-exposure prophylaxis (PrEP) is shown as an effective but expensive strategy to prevent the acquisition of HIV infection. To investigate the effectiveness and cost-effectiveness of STI and PrEP, we develop a multi-scale model linking within-host and between-host dynamics in the presence of drug resistance. Lyapunov functionals are constructed to analyze the global dynamics of the coupled system. We fit this model to the annual AIDS incidence and death data from 1980 to 2014 among men who have sex with men (MSM) in San Francisco and compare the impact of six various intervention scenarios (low, medium, high PrEP coverage with or without STI) on new infections and cost-effectiveness over the next 20 years. We estimate the PrEP efficacy needed to eliminate the disease for different fraction of acquired drug resistance under the above six scenarios. Numerical simulations show that expanding PrEP coverage is very cost-effective, but whether implementing STI is cost-saving depends on the efficacy of second-line drugs. That is to say, STI could always save money, but it may lead to more (less) new infections than continuous therapy and thus less (more) health benefit for high (low) efficacy of second-line drugs. These results provide insights about the long-term effect of STI and PrEP on the disease control and cost-effectiveness.     

Addendum to: A hybrid conjugate gradient method based on a quadratic relaxation of Dai–Yuan hybrid conjugate gradient parameter

Here, necessary corrections on computing the hybridization parameter of the quadratic hybrid conjugate gradient method of Babaie-Kafaki [S. Babaie-Kafaki, A hybrid conjugate gradient method based on a quadratic relaxation of Dai-Yuan hybrid conjugate gradient parameter, Optimization, DOI: 10.1080/02331934.2011.611512, 2011] are stated in brief. Throughout, we use the same notations and equation numbers as in Babaie-Kafaki (2011).     

Conjugate directions method for solving interval linear systems

We propose the interval version of the conjugate directions method, to solve the problem of linear systems, with symmetric and positive definite interval matrix A, and a right-hand side interval vector b. This revised version was published online in June 2006 with corrections to the Cover Date.     

An Extension of the Conjugate Directions Method With Orthogonalization to Large-Scale Problems With Bound Constraints

In our previous works a new method of conjugate directions for large-scale unconstrained minimization problems has been presented [1, 2]. In the paper this algorithm is extended to minimization problems with bound constraints. Because the linear minimization along the newly found conjugate vector is not needed for constructing the next conjugate vector and one arbitrarily step-size (not necessarily the optimal one) is calculated along this conjugate direction, we are able to incorporate naturally the bound constraints into the algorithm. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Error norm estimation and stopping criteria in preconditioned conjugate gradient iterations

Some techniques suitable for the control of the solution error in the preconditioned conjugate gradient method are considered and compared. The estimation can be performed both in the course of the iterations and after their termination.The importance of such techniques follows from the non‐existence of some reasonable a priori error estimate for very ill‐conditioned linear systems when sufficient information about the right‐hand side vector is lacking. Hence, some a posteriori estimates are required, which make it possible to verify the quality of the solution obtained for a prescribed right‐hand side. The performance of the considered error control procedures is demonstrated using real‐world large‐scale linear systems arising in computational mechanics. Copyright © 2001 John Wiley & Sons, Ltd.     

The conjugate heat equation and Ancient solutions of the Ricci flow

We prove Gaussian type bounds for the fundamental solution of the conjugate heat equation evolving under the Ricci flow. As a consequence, for dimension 4 and higher, we show that the backward limit of Type I κ-solutions of the Ricci flow must be a non-flat gradient shrinking Ricci soliton. This extends Perelman?s previous result on backward limits of κ-solutions in dimension 3, in which case the curvature operator is nonnegative (it follows from Hamilton–Ivey curvature pinching estimate). As an application, this also addresses an issue left in Naber (2010) [23], where Naber proves the interesting result that there exists a Type I dilation limit that converges to a gradient shrinking Ricci soliton, but that soliton might be flat. The Gaussian bounds that we obtain on the fundamental solution of the conjugate heat equation under evolving metric might be of independent interest.     

Donaldson theory on non-Kählerian surfaces and class <Emphasis Type="Italic">VII</Emphasis> surfaces with <Emphasis Type="Italic">b</Emphasis><Subscript>2</Subscript>=1

We prove that any class VII surface with b₂=1 has curves. This implies the “Global Spherical Shell conjecture” in the case b₂=1: Any minimal class VII surface withb₂=1 admits a global spherical shell, hence it is isomorphic to one of the surfaces in the known list. By the results in [LYZ], [Te1], which treat the case b₂=0 and give complete proofs of Bogomolov’s theorem, one has a complete classification of all class VII-surfaces with b₂∈{0,1}. The main idea of the proof is to show that a certain moduli space of PU(2)-instantons on a surface X with no curves (if such a surface existed) would contain a closed Riemann surface Y whose general points correspond to non-filtrable holomorphic bundles on X. Then we pass from a family of bundles on X parameterized by Y to a family of bundles on Y parameterized by X, and we use the algebraicity of Y to obtain a contradiction. The proof uses essentially techniques from Donaldson theory: compactness theorems for moduli spaces of PU(2)-instantons and the Kobayashi-Hitchin correspondence on surfaces.     

On a problem of nachbin concerning extension of operators

Problems I and II, stated below, are considered. It is shown that the answer to I may be negative even ifX andZ are finite-dimensional and that the answer to II may be negative even ifX andZ are separable andT compact. Concerning problem II some positive results are also obtained. For example, the answer to II is in the affirmative ifX is a conjugate space or anL ₁ space or ifX=c orc ₀ andZ is separable. Research supported in part by NSF Grant no. 25222.     

A scaled BFGS preconditioned conjugate gradient algorithm for unconstrained optimization

This letter presents a scaled memoryless BFGS preconditioned conjugate gradient algorithm for solving unconstrained optimization problems. The basic idea is to combine the scaled memoryless BFGS method and the preconditioning technique in the frame of the conjugate gradient method. The preconditioner, which is also a scaled memoryless BFGS matrix, is reset when the Powell restart criterion holds. The parameter scaling the gradient is selected as the spectral gradient. Computational results for a set consisting of 750 test unconstrained optimization problems show that this new scaled conjugate gradient algorithm substantially outperforms known conjugate gradient methods such as the spectral conjugate gradient SCG of Birgin and Martínez [E. Birgin, J.M. Martínez, A spectral conjugate gradient method for unconstrained optimization, Appl. Math. Optim. 43 (2001) 117–128] and the (classical) conjugate gradient of Polak and Ribière [E. Polak, G. Ribière, Note sur la convergence de méthodes de directions conjuguées, Revue Francaise Informat. Reserche Opérationnelle, 3e Année 16 (1969) 35–43], but subject to the CPU time metric it is outperformed by L-BFGS [D. Liu, J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Program. B 45 (1989) 503–528; J. Nocedal. http://www.ece.northwestern.edu/~nocedal/lbfgs.html].     

On the generalised jump of a function by its Fourier coefficients

Summary Author studies the summability (C,1+α+ρ) of the sequence nB_n(x) under weaker conditions than those ofMinakishisundaram [3] and thus generalises his theorems. on the ? Jump of a function ? and by applying a tauberian theorem obtaing a criteria for the (C, α+ρ) summability of the conjugate series.     

Automorphy for some <Emphasis Type="Italic">l</Emphasis>-adic lifts of automorphic mod <Emphasis Type="Italic">l</Emphasis> Galois representations. II

We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara’s lemma.